Prof. Dr. Alexander Mielke

Guest member of the Executive Committee

Weierstraß-Institut für Angewandte Analysis und Stochastik
Mohrenstraße 39
10117 Berlin
+49 (0) 30 20372563
alexander.mielke@wias-berlin.de
Website

PI in the projects OT1 and SE2

Institut für Mathematik, HU Berlin
RUdower Chaussee 25
12489 Berlin
+49 (0) 30 2093 5431


Research focus

applied analysis
nonlinear partial differential equations
continuum mechanics and semiconductor modeling
variational methods for evolution

Projects as a project leader

  • D-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: Lukas Adam / Dr. Dirk Peschka
    Duration: 01.06.2014 - 31.05.2017
    Status: running
    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/
  • D-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/
  • D-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: 01.06.2014 - 31.05.2017
    Status: running
    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
  • C-AP2

    Pattern formation in systems with multiple scales

    Prof. Dr. Alexander Mielke

    Project heads: Prof. Dr. Alexander Mielke
    Project members: -
    Duration: 01.01.2011 - 31.12.2018
    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/
  • C-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/