Prof. Dr. Alexander Mielke

Projects as a project leader

• SE2

  Electrothermal modeling of large-area OLEDs

  PD Dr. Annegret Glitzky / Prof. Dr. Alexander Mielke

  Project heads: PD Dr. Annegret Glitzky / Prof. Dr. Alexander Mielke
  Project members: Dr. Matthias Liero
  Duration: -
  Status: completed
  Located at: Weierstraß-Institut
  

  Description

  The aim of the project D-SE2 is to find adequate spatially resolved PDE models for the electrothermal description of organic semiconductor devices describing self-heating and thermal switching phenomena. Moreover, the project intends to investigate their analytical properties, derive suitable numerical approximation schemes, and provide simulation results which can help to optimize large-area organic light emitting diodes.
  Click here for more information
  
  http://www.wias-berlin.de/projects/ECMath-SE2/index.html

• SE-AP2

  Pattern formation in systems with multiple scales

  Prof. Dr. Alexander Mielke

  Project heads: Prof. Dr. Alexander Mielke
  Project members: -
  Duration: 01.01.2011 - 31.12.2022
  Status: running
  Located at: Technische Universität Berlin
  

  Description

  Pattern formation in nonlinear partial differential equations depends on nontrivial interactions between different internal length scales and nonlinearities of the system as well as on the size and geometry of the underlying domain. The challenge is to understand how effects on the small scales generate effective pattern formation on the larger scales. Using well-chosen model problems reflecting the focus applications of the CRC, we will investigate the mathematical foundations of the derivation of effective models for pattern formation in multiscale problems. Controls for the effective models will be used to construct controls for the original system.
  
  http://www.itp.tu-berlin.de/collaborative_research_center_910/sonderforschungsbereich_910/project_groups/a_theoretical_methods/tp_a5/

• SE-AP10

  Analysis of multiscale systems driven by functionals

  Prof. Dr. Alexander Mielke

  Project heads: Prof. Dr. Alexander Mielke
  Project members: -
  Duration: 01.03.2011 - 31.03.2016
  Status: completed
  Located at: Weierstraß-Institut
  

  Description

  Many complex phenomena in the sciences are described by nonlinear partial differential equations, the solutions of which exhibit oscillations and concentration effects on multiple temporal or spatial scales. To understand the interplay of effects on different scales, it is central to determine those quantities on the microscale that are needed for the correct description of the macroscopic evolution. Our aim is to develop a mathematical framework for modeling and analyzing systems with multiple scales. In particular, we want to derive new effective equations on the macroscale that fully take into account the effects on the microscale. This will include Hamiltonian dynamics as well as different types of dissipation like gradient flows or rate-independent dynamics. The choice of models will be guided by specific applications in
  

  • material modeling (e.g., thermoplasticity, pattern formation, porous media) and
  • optoelectronics (drift-diffusion equations, pulse interaction, Maxwell-Bloch systems).

  
  The research will address mathematically fundamental issues like existence and stability of solutions but will be mainly devoted to the modeling of multiscale phenomena in evolution systems. We will focus on systems with geometric structures, where the dynamics is driven by functionals. Thus, we can go much beyond the classical theory of homogenization and singular perturbations. The novel features of our approach to multiscale problems are

  • the combination of different dynamical effects in one framework,
  • the use of geometric and metric structures for partial differential equations,
  • the exploitation of Gamma-convergence for evolution systems driven by functionals.

  
  
  http://www.wias-berlin.de/projects/erc-adg/

• OT1

  Mathematical modeling, analysis, and optimization of strained Germanium-microbridges

  Prof. Dr. Michael Hintermüller / Prof. Dr. Alexander Mielke / Prof. Dr. Thomas Surowiec / Dr. Marita Thomas

  Project heads: Prof. Dr. Michael Hintermüller / Prof. Dr. Alexander Mielke / Prof. Dr. Thomas Surowiec / Dr. Marita Thomas
  Project members: Dr. Lukas Adam / Dr. Dirk Peschka
  Duration: -
  Status: completed
  Located at: Humboldt Universität Berlin / Weierstraß-Institut
  

  Description

  The goal of the project Mathematical Modeling, Analysis, and Optimization of Strained Germanium-Microbridges is to optimize the design of a strained Germanium microbridge with respect to the light emission. It is a joint project with the Humboldt-University Berlin (M. Hintermüller, T. Surowiec) and the Weierstrass Institute (A. Mielke, M. Thomas), that also involves the close collaboration with the Department for Materials Research at IHP (Leibniz-Institute for Innovative High Performance Microelectronics, Frankfurt Oder).
  
  http://www.wias-berlin.de/projects/ECMath-OT1/

• OT-AP1

  Multi-Dimensional Modeling and Simulation of Electrically Pumped Semiconductor-Based Emitters

  PD Dr. Uwe Bandelow / Dr. Thomas Koprucki / Prof. Dr. Alexander Mielke / Prof. Dr. Frank Schmidt

  Project heads: PD Dr. Uwe Bandelow / Dr. Thomas Koprucki / Prof. Dr. Alexander Mielke / Prof. Dr. Frank Schmidt
  Project members: -
  Duration: 01.01.2008 - 31.12.2019
  Status: running
  Located at: Weierstraß-Institut / Konrad-Zuse-Zentrum für Informationstechnik Berlin
  

  Description

  The aim of this joint project of WIAS and ZIB is the comprehensive and self-consistent optoelectronic modeling and simulation of electrically pumped semiconductor-based light emitters with spatially complex 3D device structure and quantum dot active regions. The required models and methods for an accurate representation of devices, such as VCSELs and single photon emitters, featuring open cavities, strong interactions between optical fields and carriers, quantum effects, as well as heating will be developed and implemented, resulting in a set of tools, that will be provided for our partners in the CRC 787.
  
  http://www.zib.de/projects/multi-dimensional-modeling-and-simulation-vertical-cavity-surface-emitting-lasers-vcsels http://wias-berlin.de/projects/sfb787-b4/