-
C23
Mass conservative coupling of fluid flow and species transport in electrochemical flow cells
Project heads:
-
Project members:
-
Duration: 04/07-12/08
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/projects/Matheon_c23/index.html
-
C22
Adaptive solution of parametric eigenvalue problems for partial differential equations
Project heads:
-
Project members:
-
Duration: 08/07 - 05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www3.math.tu-berlin.de/Matheon/projects/C22/
-
A13
Meshless Discrete Galerkin Methods for Polymer Chemistry and Systems Biology
Project heads:
-
Project members:
-
Duration: 04/07 - 05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.zib.de/Numerik/projects/Matheon-A13/project.frameset.en.html
-
D19
Local existence, uniqueness, and smooth dependence for quasilinear parabolic problems with non-smooth data
Project heads:
-
Project members:
-
Duration: 07/07-12/08
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.wias-berlin.de/project-areas/micro-el/Matheon-D19
-
D20
Pulse shaping in photonic crystal-fibers
Project heads:
-
Project members:
-
Duration: 05/07 - 12/08
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.wias-berlin.de/research-groups/laser/projects/FZ86_D20/
-
A14
Optimal Models for the Structure and Dynamics of Macromolecular Complexes using Actin as an Example
Project heads:
-
Project members:
-
Duration: 10/07 - 05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://compmolbio.biocomputing-berlin.de/index.php
-
B18
Applications of Network Flows in Evacuation Planning
Project heads:
-
Project members:
-
Duration: 10/07 - 05/14
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.math.tu-berlin.de/coga/projects/Matheon/B18/
-
F8
Discrete differential geometry and kinematics in architectural design
Project heads:
-
Project members:
-
Duration: 01/09 - 12/09
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www3.math.tu-berlin.de/Matheon/projects/f8/
-
E8
"Multidimensional Portfolio Optimization"
Project heads:
-
Project members:
-
Duration: 07/08 - 05/14
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://www.math.hu-berlin.de/~becherer
-
C24
"Modelling and Optimization of Biogas Reactors"
Project heads:
-
Project members:
-
Duration: 11/08-10/09
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
-
C25
"State trajectory compression in optimal control"
Project heads:
-
Project members:
-
Duration: 10/08-07/09
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://geom.mi.fu-berlin.de/projects/Matheon/f9/index.html
-
B19
Nonconvex Mixed-Integer Nonlinear Programming
Project heads:
-
Project members:
-
Duration: 10/08 - 04/09
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.math.hu-berlin.de/~stefan/B19
-
C26
"Storage of hydrogen in hydrides"
Project heads:
-
Project members:
-
Duration: 05/08 - 05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/projects/Matheon-c26/C26/MatheonC26b.html
-
E9
"Beyond replication: Hedging in markets with frictions"
Project heads:
-
Project members:
-
Duration: 08/08 - 05/14
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://wws.mathematik.hu-berlin.de/~penner/E9.html
-
D21
Synchronization phenomena in coupled dynamical systems
Project heads:
-
Project members:
-
Duration: 06/08-05/14
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.hu-berlin.de/~yanchuk/RG/
-
C27
Simulation of magnetic rotary shaft seals
Project heads:
-
Project members:
-
Duration: 01/09-04/09
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.hu-berlin.de/~muellerr/C27
-
C28
Optimal control of phase separation phenomena
Project heads:
-
Project members:
-
Duration: 07/09-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.hu-berlin.de/~hp_hint/C28
-
A15
Viscosity properties of biomembrane surfaces
Project heads:
-
Project members:
-
Duration: 02/09 - 05/14
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.math.fu-berlin.de/en/groups/cellmechanics/
-
A16
Numerical treatment of the chemical master equation using sums of separable functions
Project heads:
-
Project members:
-
Duration: 03/09-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.math.tu-berlin.de/~garcke/Files/Matheon_project.html
-
B20
Optimization of gas transport
Project heads:
-
Project members:
-
Duration: 05/09 - 05/14
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/en/optimization/mip/projects-long/Matheon-b20-optimization-of-gas-transport.html
-
B21
Optical Access Networks
Project heads:
-
Project members:
-
Duration: 06/09-05/14
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www3.math.tu-berlin.de/coga/projects/Matheon/B21/
-
C29
Numerical methods for large-scale parameter-dependent systems
Project heads:
-
Project members:
-
Duration: 06/09-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www3.math.tu-berlin.de/Matheon/projects/C29
-
F9
Trajectory compression
Project heads:
-
Project members:
-
Duration: 08/09 - 05/14
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www.zib.de/de/numerik/projekte/projektdetails/article/Matheon-f9-1.html
-
E11
Beyond Value at Risk: Dynamic Risk Measures and Applications
Project heads:
-
Project members:
-
Duration: 09/09-06/13
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://www.mathematik.hu-berlin.de/~kupper
-
E10
Large deviation-, heat kernel- and PDE methods in the study of volatility of financial markets
Project heads:
-
Project members:
-
Duration: 11/09-05/14
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://www.math.tu-berlin.de/~friz/
-
A17
Computational surgery planning
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.zib.de/de/numerik/projekte/projektdetails/article/Matheon-a17.html
-
A18
Mathematical system biology
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.math.fu-berlin.de/en/groups/mathlife/projects/A18/index.html
-
A19
Modeling and optimization of functional molecules
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.biocomputing-berlin.de/biocomputing/en/projects/Matheon_project_a19_modelling_and_optimization_of_functional_molecules/
-
A20
Numerical methods in quantum chemistry
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://page.math.tu-berlin.de/~gauckler/a20/
-
B22
Rolling stock roster planning for railways
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/en/projects/current-projects/project-details/article/Matheon-b22-rolling-stock-roster-planning.html
-
B23
Robust optimization for network applications
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.coga.tu-berlin.de/v-menue/projekte/Matheon_b23/parameter/en/
-
B24
Scheduling material flows in logistic networks
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.coga.tu-berlin.de/v-menue/projekte/Matheon_b24/parameter/en/
-
C30
Automatic reconfiguration of robotic welding cells
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.coga.tu-berlin.de/v-menue/projekte/Matheon_c30/parameter/en/
-
C31
Numerical minimization of nonsmooth energy functionals in multiphase materials
Project heads:
-
Project members:
-
Duration: 06/10-07/12
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.hu-berlin.de/~hp_hint/C31
-
C32
Modeling of phase separation and damage processes in alloys
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/people/griepent/C32.html
-
D22
Modeling of electronic properties of interfaces in solar cells
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.wias-berlin.de/people/liero/glitzky_projects_7.jsp
-
D23
Design of nanophotonic devices and materials
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.zib.de/en/numerik/computational-nano-optics/projects/details/article/Matheon-d23.html
-
ZE1
Teachers at university
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
http://didaktik1.mathematik.hu-berlin.de/index.php?article_id=49
-
ZE2
Mathematics teacher training initiative
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
http://didaktik.mathematik.hu-berlin.de/index.php?article_id=387&clang=0
-
ZE3
Industry-driven applications of mathematics in the classroom
Project heads:
-
Project members:
-
Duration: 10/10-05/14
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
-
ZE5
Enhancing engineering students perception of mathematical concepts (UNITUS)
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
-
F10
Image and signal processing in the biomedical
sciences: diffusion weighted imaging - modeling and beyond
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www.wias-berlin.de/projects/Matheon_a3
-
C33
Modeling and Simulation of Composite Materials
Project heads:
-
Project members:
-
Duration: 06/10-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www2.mathematik.hu-berlin.de/~numa/C33/
-
B25
Scheduling Techniques in Constraint Integer Programming
Project heads:
-
Project members:
-
Duration: 07/10-12/10
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www3.math.tu-berlin.de/Matheon/projects/B25
-
C34
Open Pit Mine planning via a Continuous Optimization Approach
Project heads:
-
Project members:
-
Duration: 07/10-12/10
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
-
C35
Global higher integrability of minimizers of variational problems with mixed boundary conditions
Project heads:
-
Project members:
-
Duration: 07/10-12/10
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
-
D24
Network-Based Remodeling of Mechanical and Mechatronic Devices
Project heads:
-
Project members:
-
Duration: 07/10-12/10
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www3.math.tu-berlin.de/Matheon/projects/D24/
-
D25
Computation of shape derivatives for conical diffraction by polygonal gratings
Project heads:
-
Project members:
-
Duration: 07/10-12/10
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.wias-berlin.de/projects/Matheon-d25/
-
F11
Accelerating Curvature Flows on the GPU
Project heads:
-
Project members:
-
Duration: 07/10-12/10
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://geom.mi.fu-berlin.de/projects/Matheon/f11/index.html
-
ZE6
Learner as Creator - The Portal PlayMolecule
Project heads:
-
Project members:
-
Duration: 07/10-03/11
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
http://www.playmolecule.de
-
F12
Fast algorithms for fluids
Project heads:
-
Project members:
-
Duration: 07/10-05/12
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www3.math.tu-berlin.de/geometrie/f12/
-
ZO7
Mathematische Installationen/ Mathematical Installations
Project heads:
-
Project members:
-
Duration: 10/10-05/14
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
http://www3.math.tu-berlin.de/geometrie/zo7/
-
A1
Modelling, simulation, and optimal control of thermoregulation in the human vascular system
Project heads:
-
Project members:
-
Duration: 06/02-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.zib.de/weiser/projekte/Matheon-A1/projectlong.en.html
-
A2
Modelling and simulation of human motion for osteotomic surgery
Project heads:
-
Project members:
-
Duration: 06/02-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.mi.fu-berlin.de/Matheon-A2
-
A3
Image and signal processing in medicine and biosciences
Project heads:
-
Project members:
-
Duration: 06/02-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.wias-berlin.de/projects/Matheon_a3/
-
A4
Towards a mathematics of biomolecular flexibility: Derivation and fast simulation of reduced models for conformation dynamics
Project heads:
-
Project members:
-
Duration: 06/02-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.math.fu-berlin.de/groups/biocomputing/projects/projekt_A4/index.html
-
A5
Analysis and modelling of complex networks
Project heads:
-
Project members:
-
Duration: 06/02-09/08
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www2.informatik.hu-berlin.de/alkox/forschung/Matheon_a5/
-
A6
Stochastic Modelling in Pharmacokinetics
Project heads:
-
Project members:
-
Duration: 10/02-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://compphysiol.mi.fu-berlin.de/cms/mathematical_physiology/rubrik/3/3017.mathematical_physiology.htm
-
A7
Numerical Discretization Methods in Quantum Chemistry
Project heads:
-
Project members:
-
Duration: 07/04-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.math.tu-berlin.de/~gagelman/A7.html
-
B1
Strategic planning in public transport
Project heads:
-
Project members:
-
Duration: 12/02-05/06
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/Optimization/Projects/TrafficLogistic/Matheon-B1/
-
B2
Dynamics of nonlinear networks
Project heads:
-
Project members:
-
Duration: 03/03-04/04
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://dynamics.mi.fu-berlin.de/projects/networks.php
-
B3
Integrated Planning of Multi-layer Telecommunication Networks
Project heads:
-
Project members:
-
Duration: 07/02 - 05/14
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/en/optimization/telecommunications/projects/projectdetails/article/Matheon-b3.html
-
B4
Optimization in telecommunication: Planning the UMTS radio interface
Project heads:
-
Project members:
-
Duration: 08/02-05/10
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/Optimization/Projects/Telecom/Matheon-B4/
-
B5
Line planning and periodic timetabling in railway traffic
Project heads:
-
Project members:
-
Duration: 03/03-05/06
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www3.math.tu-berlin.de/Matheon/projects//B5/
-
B6
Origin destination control in airline revenue management by dynamic stochastic programming
Project heads:
-
Project members:
-
Duration: 07/02-05/06
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.math.hu-berlin.de/~romisch/projects/FZB6/revenue.html
-
B7
Computation of performance measures of communication networks
Project heads:
-
Project members:
-
Duration: 10/02-05/10
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.math.tu-berlin.de/~aurzada/project-b7/
-
B8
Time-dependent multi-commodity flows: Theory and applications
Project heads:
-
Project members:
-
Duration: 10/02-12/08
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www3.math.tu-berlin.de/Matheon/projects/B8/
-
B9
Dual methods for special coloring problems
Project heads:
-
Project members:
-
Duration: 09/02-05/06
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.math.tu-berlin.de/~fpfender/B9.html
-
B10
Describing polyhedra by polynomial inequalities
Project heads:
-
Project members:
-
Duration: 07/03-08/04
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.math.tu-berlin.de/~bosse/project_B10.html
-
B11
Randomized methods in network optimization
Project heads:
-
Project members:
-
Duration: 05/03-05/06
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/Optimization/Projects/DiscStruct/Matheon-B11/index.en.html
-
C1
Coupled systems of reaction-diffusion equations and application to the numerical solution of direct methanol fuel cell (DMFC) problems
Project heads:
-
Project members:
-
Duration: 01/03-05/06
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/research-groups/nummath/fuelcell/C1/
-
C2
Efficient simulation of flows in semiconductor melts
Project heads:
-
Project members:
-
Duration: 08/03-05/06
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/research-groups/nummath/drittm/c2/index.html
-
C3
Modelling, analysis, and simulation of modular real-time systems
Project heads:
-
Project members:
-
Duration: 11/02-12/04
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.zib.de/Optimization/Projects/Online/Matheon-C3/
-
C4
Numerical solution of large nonlinear eigenvalue problems
Project heads:
-
Project members:
-
Duration: 08/02-05/09
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www3.math.tu-berlin.de/Matheon/projects/C4/
-
C5
Stochastic and nonlinear methods for solving resource constrained scheduling problems
Project heads:
-
Project members:
-
Duration: 10/02-05/06
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www3.math.tu-berlin.de/Matheon/projects/C5/
-
C6
Stability, sensitivity, and robustness in combinatorial online-optimization
Project heads:
-
Project members:
-
Duration: 01/03-05/06
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.zib.de/Optimization/Projects/Online/Matheon-C6/
-
C7
Stochastic Optimization Models for Electricity Production in Liberalized Markets
Project heads:
-
Project members:
-
Duration: 09/02-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.hu-berlin.de/~romisch/projects/FZC7/electricity.html
-
C8
Shape optimization and control of curved mechanical structures
Project heads:
-
Project members:
-
Duration: 02/03-01/05
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/project-areas/phase-tran/curved-fzt86/
-
C9
Simulation and Optimization of Semiconductor Crystal Growth from the Melt Controlled by Traveling Magnetic Fields
Project heads:
-
Project members:
-
Duration: 08/02-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/projects/Matheon-c9
-
C10
Modelling, Asymptotic Analysis and Numerical Simulation of Interface Dynamics on the Nanoscale
Project heads:
-
Project members:
-
Duration: 12/02-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/people/peschka/c10/
-
C11
Modeling and optimization of phase transitions in steel
Project heads:
-
Project members:
-
Duration: 04/03-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/projects/Matheon-c11/
-
C12
General purpose, Linearly Invariant Algorithm for Large-Scale Nonlinear Programming
Project heads:
-
Project members:
-
Duration: 01/04-05/10
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.hu-berlin.de/~griewank/C12/
-
C13
Adaptive simulation of phase-transitions
Project heads:
-
Project members:
-
Duration: 11/03-05/10
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.hu-berlin.de/~cc/english/research/dfg_project_c13.html
-
C14
Macroscopic models for precipitation in crystalline solids
Project heads:
-
Project members:
-
Duration: 10/04-05/10
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.hu-berlin.de/~wwwaa/MatheonC14
-
C15
Pattern formation in magnetic thin films
Project heads:
-
Project members:
-
Duration: 06/05-09/08
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.mathematik.hu-berlin.de/~wwwaa/web/forschung/fzt86/fzt86-melcher.html
-
D1
Simulation and control of switched systems of differential-algebraic equations
Project heads:
-
Project members:
-
Duration: 10/02-05/10
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www3.math.tu-berlin.de/Matheon/projects/D1/index.html
-
D2
Passivation of linear time invariant systems arising in circuit simulation and electric field computation*
[*old title: Numerical solution of large unstructured linear systems in circuit simulation]
Project heads:
-
Project members:
-
Duration: 10/02-05/14
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www3.math.tu-berlin.de/Matheon/projects/D2/
-
D3
Global singular perturbations
Project heads:
-
Project members:
-
Duration: 03/03-12/04
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://dynamics.mi.fu-berlin.de/projects/laser1.php
-
D4
Quantum mechanical and macroscopic models for optoelectronic devices
Project heads:
-
Project members:
-
Duration: 09/04-05/10
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.wias-berlin.de/projects/Matheon-d4/index.jsp
-
D5
Structure analysis for simulation and control problems of differential algebraic equations
Project heads:
-
Project members:
-
Duration: 06/02-05/06
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.mathematik.hu-berlin.de/~lamour/Matheon/
-
D6
Numerical methods for stochastic differential-algebraic equations applied to transient noise analysis in circuit simulation
Project heads:
-
Project members:
-
Duration: 10/03-05/06
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.hu-berlin.de/~romisch/projects/FZD6/noise.html
-
D7
Numerical simulation of integrated circuits for future chip generations
Project heads:
-
Project members:
-
Duration: 09/02-05/08
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.hu-berlin.de/~monica/projectD7.html
-
D8
Nonlinear dynamical effects in integrated optoelectronic structures
Project heads:
-
Project members:
-
Duration: 06/02-05/14
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.wias-berlin.de/projects/Matheon-d8/project_d8.jsp
-
D9
Design of nano-photonic devices
Project heads:
-
Project members:
-
Duration: 01/03-05/10
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.zib.de/en/numerik/computational-nano-optics/projects/archive-projects-short-details/article/Matheon-d9-photonic-devices.html
-
D10
Entropy decay and shape design for nonlinear drift diffusion systems
Project heads:
-
Project members:
-
Duration: 05/03-01/05
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.tu-berlin.de/~plato/dfg.html
-
D11
Numerical Treatment of PDEs on unbounded Domains
Project heads:
-
Project members:
-
Duration: 11/02-05/06
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.tu-berlin.de/~ehrhardt/Projects/dfg.html
-
D12
General linear methods for integrated circuit design
Project heads:
-
Project members:
-
Duration: 12/02-05/06
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.hu-berlin.de/~steffen/d12_project.htm
-
D13
Control and numerical methods for coupled systems
Project heads:
-
Project members:
-
Duration: 09/03-05/10
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.tu-berlin.de/~stykel/Research/ProjectD13/
-
E1
Microscopic modelling of complex financial assets
Project heads:
-
Project members:
-
Duration: 06/02-05/10
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://www.wias-berlin.de/projects/Matheon-e1/
-
E2
Securitization: assessment of external risk factors
Project heads:
-
Project members:
-
Duration: 06/02-05/14
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
-
E3
Probabilistic interaction models for the microstructure of asset price fluctuation
Project heads:
-
Project members:
-
Duration: 06/02-05/06
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://wws.mathematik.hu-berlin.de/~foellmer
-
E4
Beyond value at risk: Quantifying and hedging the downside risk
Project heads:
-
Project members:
-
Duration: 06/02-04/08
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://page.math.tu-berlin.de/~bank
-
E5
Statistical and numerical methods in modelling of financial derivatives and valuation of risk
Project heads:
-
Project members:
-
Duration: 06/02-05/14
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://www.wias-berlin.de/research/ats/calibration/E5poster-2010.pdf
-
E6
Adaptive FE Algorithm for Option Evaluation
Project heads:
-
Project members:
-
Duration: 02/04-05/05
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://www.math.hu-berlin.de/~cc/english/research/dfg_project_e6.html
-
E7
Adaptive monotone multigrid methods for option pricing
Project heads:
-
Project members:
-
Duration: 01/05-05/06
Status:
completed
Description
Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.
Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.
At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.
Topics:
- measurement and hedging of risks
- interaction models for asset price fluctuation
http://numerik.mi.fu-berlin.de/Matheon-E7/index.php
-
F1
Discrete surface parametrization
Project heads:
-
Project members:
-
Duration: 06/02-05/14
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www3.math.tu-berlin.de/geometrie/ddg/
-
F2
Atlas-based 3d image segmentation
Project heads:
-
Project members:
-
Duration: 06/02-05/14
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www.zib.de/en/numerik/projects/details/article/Matheon-f2-1.html
-
F3
Visualization of Algorithms
Project heads:
-
Project members:
-
Duration: 06/02-12/03
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www3.math.tu-berlin.de/Matheon/projects/F3/tiki-index.php?page=Matheon+F3
-
F4
Geometric shape optimization
Project heads:
-
Project members:
-
Duration: 06/02-05/14
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://geom.mi.fu-berlin.de/projects/Matheon/f4/index.html
-
F5
Mathematics in Virtual Reality
Project heads:
-
Project members:
-
Duration: 01/05-05/10
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www3.math.tu-berlin.de/Matheon/projects/f5/
-
G1
Combinatorial optimization at work
Project heads:
-
Project members:
-
Duration: 09/04-05/06
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Projects
http://www.zib.de/Optimization/Projects/education/Matheon-G1/
-
Z1.1
Current mathematics at schools
Project heads:
-
Project members:
-
Duration: 11/02-05/10
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
http://www.mathematik.hu-berlin.de/~kramer/dfgfz/g2.html
-
Z1.2
Teachers at universities
Project heads:
-
Project members:
-
Duration: 09/02-05/10
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
http://didaktik.mathematik.hu-berlin.de/index.php?article_id=49&clang=0
-
G4
Virtual math-science lab
Project heads:
-
Project members:
-
Duration: 06/02-05/06
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Projects
http://www.math.tu-berlin.de/~thor/videoeasel/
-
G5
(*) Discrete Mathematics for Highschool Education
Project heads:
-
Project members:
-
Duration: 04/04-04/06
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Projects
http://www.math.tu-berlin.de/~westphal/projekt/
-
Z1.3
Visualization of Algorithms
Project heads:
-
Project members:
-
Duration: 06/04-05/08
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
http://cermat.org/visage/
-
C16
Simulation of phase field models and geometric evolution problems
Project heads:
-
Project members:
-
Duration: 08/05-12/08
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://bartels.ins.uni-bonn.de/research/projects/c16/index.html?noframe
-
D14
Nonlocal and nonlinear effects in fiber optics
Project heads:
-
Project members:
-
Duration: 05/05-05/14
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.wias-berlin.de/projects/Matheon-d14/project_d14.jsp
-
G8
Computer Oriented Mathematics
Project heads:
-
Project members:
-
Duration: 10/04-12/05
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Projects
http://numerik.mi.fu-berlin.de/Matheon-G8/index.php
-
A10
Automatic model reduction for complex dynamical systems
Project heads:
-
Project members:
-
Duration: 06/05-12/07
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.math.fu-berlin.de/groups/biocomputing/projects/projekt_A10/index.html
-
A9
Simulation and control of positive descriptor systems
Project heads:
-
Project members:
-
Duration: 03/05-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www3.math.tu-berlin.de//Matheon/projects/A9
-
C17
Adaptive multigrid methods for local and nonlocal phase-field models of solder alloys
Project heads:
-
Project members:
-
Duration: 12/05-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://numerik.mi.fu-berlin.de/Matheon-C17/
-
A8
Constraint-based modeling in systems biology
Project heads:
-
Project members:
-
Duration: 04/05-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://www.math.fu-berlin.de/en/groups/mathlife/projects/A8.html
-
D16
Adapted linear algebra for TR1 updates
Project heads:
-
Project members:
-
Duration: 06/05-05/06
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.tu-berlin.de/~stange/d16.html
-
Z1.4
Innovations in Mathematics Education for the Engineering science
Project heads:
-
Project members:
-
Duration: 06/06-05/10
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Topics:
- modern mathematics at school
- school teachers at universities
- network of math-science oriented schools
- public awareness of mathematics
- media presence
http://www.math.tu-berlin.de/MatheonZ1.4/
-
F6
Multilevel Methods on Manifold Meshes
Project heads:
-
Project members:
-
Duration: 05/05-05/14
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://geom.mi.fu-berlin.de/projects/Matheon/f6/index.html
-
C18
Analysis and numerics of multidimensional models for elastic phase transformations in shape-memory alloys
Project heads:
-
Project members:
-
Duration: 06/06-05/14
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/projects/Matheon-c18/index.jsp
-
B13
Optimization under uncertainty in logistics and scheduling
Project heads:
-
Project members:
-
Duration: 06/06 - 05/10
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www3.math.tu-berlin.de/Matheon/projects/B13/
-
B12
Symmetries in integer programming
Project heads:
-
Project members:
-
Duration: 06/06-04/09
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/Optimization/Projects/MIP/Matheon-B12/index.en.html
-
D17
Chip design verification with constraint integer programming
Project heads:
-
Project members:
-
Duration: 06/06-04/09
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.zib.de/Optimization/Projects/Verification/Matheon-D17/index.en.html
-
B15
Service design in public transport
Project heads:
-
Project members:
-
Duration: 06/06-05/14
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/en/optimization/traffic/projects-long/Matheon-b15-service-design-in-public-transport.html
-
B14
Combinatorial aspects of logistics
Project heads:
-
Project members:
-
Duration: 06/06-05/10
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.zib.de/Optimization/Projects/TrafficLogistic/Matheon-B14/index.en.html
-
D15
Functional nano-structures
Project heads:
-
Project members:
-
Duration: 04/05-05/10
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.zib.de/en/numerik/computational-nano-optics/projects/archive-projects-short-details/article/Matheon-d15-functional-nano-structures.html
-
G7
(*) Vivid Mathematics
Project heads:
-
Project members:
-
Duration: 10/04-05/06
Status:
completed
Description
The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.
There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.
To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.
The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.
Projects
-
A11
Non-adiabatic effects in molecular
dynamics
Project heads:
-
Project members:
-
Duration: 09/05-05/10
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
http://page.mi.fu-berlin.de/lasser/A11.html
-
B16
Mechanisms for Network Design Problems
Project heads:
-
Project members:
-
Duration: 09/05-05/10
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www3.math.tu-berlin.de/Matheon/projects/B16/
-
B17
Improvement of the linear algebra kernel of
Simplex-based LP- and MIP-solvers
Project heads:
-
Project members:
-
Duration: 08/06-01/07
Status:
completed
Description
Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.
In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.
Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.
This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.
Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.
Topics:
- planning of optical, multilayer, and UMTS telecommunication networks
- line planning, periodic timetabling, and revenue management in public transport networks
- optimization in logistics, scheduling and material flows
- optimization under uncertainty
- symmetries in integer programming
- game theoretic methods in network design
http://www.math.tu-berlin.de/~luce/B17
-
C19
(*) Analysis and numerics of the peridynamic equation
Project heads:
-
Project members:
-
Duration: 06/06-02/07
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.tu-berlin.de/~emmrich/project.htm
-
C20
Car frame structure optimization - Design to Cost
Project heads:
-
Project members:
-
Duration: 06/06-09/06
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.math.hu-berlin.de/~griewank/#VW
-
A12
Biomolecular Transition as Shortest Paths in Incompletely Explored Transition Networks
Project heads:
-
Project members:
-
Duration: 09/06-12/08
Status:
completed
Description
"Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.
In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.
In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes:
As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).
Topics:
- computer-assisted surgery
- patient-specific therapy planning
- protein data base analysis
- protein conformation dynamics
- systems biology
- pharmacokinetics
-
F7
Visualization of Quantum molecular Systems
Project heads:
-
Project members:
-
Duration: 09/06-09/08
Status:
completed
Description
Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.
In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.
Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.
Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.
Topics:
- discrete differential geometry
- geometry processing
- image processing
- virtual reality PORTAL
http://www.zib.de/visual/projects/molqm/
-
D18
Sparse representation
of solutions of differential equations
Project heads:
-
Project members:
-
Duration: 11/06-04/08
Status:
completed
Description
The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.
Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.
Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.
In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.
Topics:
- shape memory alloys in airfoils
- production of semiconductor crystals
- methanole fuel cell optimization
- online production planning metamaterials
http://www.math.tu-berlin.de/~jokar/D18
-
C21
Reduced-order modelling and optimal control of robot guided laser material treatments
Project heads:
-
Project members:
-
Duration: 10/06 - 09/08
Status:
completed
Description
Production is one of the most important parts of the economy and at the
very heart of the creation of value. Due to the central importance of
production, big efforts have been made to improve production processes
ever since the beginning of the industrial revolution. Nowadays, many
production processes are highly automated. Computer programs based on
numerical algorithms monitor the processes, improve efficiency and
robustness, and guarantee high quality products. Consequently,
mathematics is playing a steadily increasing role in this field. The
possibilities of applying mathematical methods in production are
wide-ranging. The Application Area cannot cover their full scale. For
that reason, the projects concentrate on the development of new
mathematical methods for special topics in manufacturing and production
planning, two central aspects of production, in which the participating
groups have longstanding expertise in mathematical modeling, simulation
and optimization.
In the field of manufacturing, we focus on innovative technologies
having a big impact on technological progress: growth and processing of
semiconductor bulk single crystals, phase transitions in modern steels
and solder alloys, modeling of active and passive behavior of functional
materials like shape-memory materials, growth of thin films. In the
projects devoted to production planning, the main aim is the effective
control of the whole production flow. Among the subjects to be studied,
there is also electricity portfolio management.
Topics:
- phase transitions in steels and solder alloys
- production of semiconductor crystals
- modeling of active and passive behavior of functional materials
- online production planning
- growth of thin films
http://www.wias-berlin.de/people/anst/Forschung/Optcontr/intro.shtml
