Technology Transfer – Our Expertise

Whatever your mathematical problem may be – we are sure to be able to help you thanks to the unique combination of expertise offered by five leading mathematical and computer science research institutes in Berlin in conjunction with our close research contacts with experts worldwide.

Matheon stands for:
Modelling, simulation and optimization of real-world processes

Modelling. This is always the first essential step in problem solving. A good mathematical model represents the essential aspects of the system or process under consideration. Many scientists at Matheon are devoted to putting the available process knowledge into such usable formalized forms.

Simulation. The resulting models can be quite complex, such that a reliable numerical simulation on the basis of these models can be a real challenge, and many scientists in Matheon are focusing their research on this.

Optimization. The final step is the mathematical optimization of a process, which goes far beyond improving a process on the basis of clever trial and evaluation. The mathematical theory provides powerful methods designed to find the best possible solution within a well-defined setting.

Real-world processes. Very diverse processes – from science, engineering, social sciences or economics – can be treated by mathematical methods. Often, these processes show one or several of the following characteristics and require the corresponding mathematical approaches. And for all of them we have specific experts at Matheon.

Discrete math:
Logistic choices and decisions, transport networks for goods and information, ...

• Do you intend to produce several different products on the same conveyor line and wish to choose the sequence of production optimally with respect to incoming orders and available resources?
• Are you planning a telecommunications network yielding an optimal compromise between functionality and costs?
• Do you aim to find optimal timetables, duty schedules, workflow plans etc.?

What all these problems have in common is that they can be treated with methods from discrete mathematics, i.e. a mathematical area where integrality issues (integral variables or yes/no decisions) dominate the mathematical structure.

Applied analysis and scientific computing:
Complex deterministic processes from natural sciences, medicine and engineering, ...

• Do you aim to simulate the human body on the molecular, cellular or global level?
• Do you wish to optimize the laser treatment of steel?
• Are you interested in simulating a new generation of electric circuit but cannot neglect the interaction of conductors any more?
• How strong are the vibrations of a high speed train?

What all these problems have in common is that they can be described by means of a certain class of system models, so called differential equations. The modeling, investigation of inherent system properties, as well as numerical simulation and optimization of these systems are some of the main issues in applied analysis and scientific computing.

Statistics and stochastics:
Large and incomplete data, systems with randomness and uncertainty, ...

• Do you wish to plan an electricity network with fluctuating energy sources like wind and solar energy?
• How large are the financial risks in view of future climate changes?
• Can I deduce the probability of a fatigue of material from random inspections? And how many random inspections are necessary to obtain a reliable indication?

In such kind of problems, my information is often given in the form of large databases with collected information. The task is then to analyze, interpret and explain the given data and reveal the underlying interdependencies, which in the best case enables reliant prognoses for the future. Corresponding models have to take into account that essential information may be missing and that interdependencies may be unknown and may even fail to be deterministic: this is the mathematical field of statistics and stochastics.

Geometry and visualization:
Design, construction and visualization of 3D objects with complex forms, ...

• You intend to construct the glass front of a building with complex curved geometry: what is the best way to locate the steel beams?
• You aim to design complex surfaces like a car model by means of your computer: How can you ensure that the surface has certain desired properties?
• You have several gigabytes of data from a fluid flow simulation. How can you graphically extract the essential features like vortex motions?

What all these problems have in common is that they deal with real or abstract geometrical objects. The formal description, analysis of inherent properties and clever transformation and visualization of these objects are some of the main issues in the mathematical fields of geometry and visualization.

Our strength:
Working together across interdisciplinary borders, ...

The complex processes arising in today's key technologies often show several of the above characteristics at the same time. It is the strength of Matheon that we can assemble the appropriate team with scientists from these different mathematical fields in order to meet the requirements of your specific problem.