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Running projects

Financed by ECMath

  • OT6

    Optimization and Control of Electrowetting on Dielectric for Digital Microfluidics in Emerging Technologies

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: Dr. Soheil Hajian
    Duration: -
    Status: running
    Located at: Humboldt Universität Berlin


    A number of emerging key technologies in microbiology, medical diagnostic devices, personal genomics, as well as next-generation low-energy OLED displays and liquid lenses make use of a phenomenon known as electrowetting on dielectric (EWOD). Electrowetting involves the manipulation of small (microscopic) droplets on a dielectric surface by the actuation of the underlying current. In fact, droplets in a typical EWOD device are situated between two separated hydrophobic surfaces, one of which contains an array of controllable electrodes. The air-liquid-solid contact angle can then by changed by varying the voltages on separate electrodes, which causes the droplets to move. Thus, the voltages are a natural choice for influencing (controlling) the motion of a droplet. The project pursues both sharp interface and phase field models, respectively, for the movement of droplets in an EWOD device. Both models make use of a macroscopic description for contact line pinning, which is due to contact angle hysteresis as well as molecular adhesion at the solid-liquid-air interface, for a faithful representation of the droplets velocity and cover different aspects properly. Due to the non-trivial dependencies on the moving interface in the sharp interface context, the proof of existence of an optimal control remains impossible without further restrictive assumptions or constraints, e.g., on the geometry, and the complexity of the phase field model poses severe challenges for a fast (real-time) numerical solution as needed for EWOD devices. For these reasons, instead of computing time-discrete or optimal controls the project work pursues an idea from model predictive control (MPC).
  • OT7

    Model-based geometry reconstruction of quantum dots from TEM

    Dr. Thomas Koprucki / Dr. Karsten Tabelow

    Project heads: Dr. Thomas Koprucki / Dr. Karsten Tabelow
    Project members: Anieza Maltsi
    Duration: -
    Status: running
    Located at: Weierstraß-Institut


    Semiconductor quantum dots are nanostructures that form a technological path to innovative optoelectronic and photonic devices. Among them single quantum dots are promising candidates for single and entangled photon sources which are of importance for future quantum technologies such as quantum information processing, quantum cryptography, and quantum metrology. The growth of QDs with desired electronic properties would highly benefit from the assessment of QD geometry, distribution, and strain profile in a feedback loop between growth and analysis of their properties. In this project, we will therefore develop a novel 3D model-based geometry reconstruction (MBGR) of QDs. This will include an appropriate model for the QD configuration in real space, a characterization of corresponding simulated TEM images as well as a statistical procedure for the estimation of QD properties and classification of QD types based on acquired TEM image data. The MBGR approach will enable a high-throughput characterization of QD samples by TEM via QD geometry, distribution and strain field. Furthermore, it will provide a guiding example for mathematically enhanced microscopy for the reconstruction of other nanoscale objects in different applications.
  • OT8

    Modeling, analysis, and optimization of optoelectronic semiconductor devices driven by experimental data

    Dr. Marita Thomas

    Project heads: Dr. Marita Thomas
    Project members: Dr. Dirk Peschka
    Duration: -
    Status: running
    Located at: Weierstraß-Institut


    The goal of the Matheon project D-OT8: Modeling, analysis, and optimization of optoelectronic semiconductor devices driven by experimental data is to optimize the design of a strained germanium microbridge with respect to the light emission. In the funding period June 2016-December 2018 we will develop tools for the parameter identification and optimal design of experiment for optoelectronic applications. The project also involves the close collaboration with the Department for Materials Research at IHP (Leibniz-Institute for Innovative High Performance Microelectronics, Frankfurt Oder).
  • OT9

    From single photon sources to tailored multi-photon states

    Dr. Sven Burger / Prof. Dr. Frank Schmidt

    Project heads: Dr. Sven Burger / Prof. Dr. Frank Schmidt
    Project members: Felix Binkowski
    Duration: -
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin


    This project investigates methods to model and simulate nanoscale light emitters in complex environments. Semiconductor quantum dots can be used as light sources in quantum information processing. Typical applications like secure communication or quantum-computing require integration of quantum dots into optical nanostructures. For the analysis and design of such structures and their interaction with radiation emitted by the quantum dots, numerical modeling and simulations are essential. In this project we concentrate on the specific problems arising when pointlike sources like quantum dots are interacting with nanostructures which support optical resonances. We plan to develop, extend and analyze methods for efficiently simulating coupling to optical resonators with material dispersion and for methods for handling coupled resonators.
  • OT10

    Model Reduction for Nonlinear Parameter-Dependent Eigenvalue Problems in Photonic Crystals

    Dr. Robert Altmann / Prof. Dr. Volker Mehrmann

    Project heads: Dr. Robert Altmann / Prof. Dr. Volker Mehrmann
    Project members: Marine Froidevaux
    Duration: -
    Status: running
    Located at: Technische Universität Berlin


    Photonic crystals are special materials having a periodic structure that can be used for trapping, filtering and guiding light. The key property of such materials is their ability to prevent light waves with specific frequencies from propagating in any direction. Because it is very challenging to build photonic crystals featuring a spectrum that can comply with the specific requirements of applications, a mathematical description and analysis of the electromagnetic properties of photonic crystals is needed, in order to support engineers in finding suitable components as well as optimal crystal geometries for new promising applications. The goal of the project is to develop an efficient solver for parameter-dependent non-linear eigenvalue problems arising in the search of photonic band-gaps. This solver should combine, in a computing-time optimal way, adaptive finite element methods (AFEM) for PDE eigenvalue problems, numerical methods for nonlinear eigenvalue problems, and low-dimensional approximations for a parameter space. The free parameters needed for the design of photonic crystals describe, e. g., the geometry of the crystal or the electromagnetic properties of the material. In order to optimize the properties of the photonic crystals over a given parameter set, we need to apply techniques from model order reduction. We plan to use approximations of the eigenfunctions, obtained by AFEM for several parameters in order to construct a reduced basis. These computations may be performed in parallel and, ideally, result in a set of eigenfunctions that contains good approximations of the eigenfunctions for all parameter values. We want to approximate the set of locally-expressed eigenfunctions with a low-dimensional non-local basis. Moreover, having efficient computations in mind, we need rigorous error bounds in order to equilibrate the different kinds of errors introduced at every level of approximation. Indeed, the total numerical error includes the discretization error arising from the AFEM, the algebraic error arising from the (iterative) solution of the nonlinear eigenvalue problems, and the model reduction error arising from the discretization of the parameter set. Since all these errors are normally measured in different norms, a unifying setting has to be developed in order to be able to compare all types of errors.

Financed by others

  • 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


    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. /
  • OT-AP10

    Analysis of discretization methods for nonlinear evolution equations

    Prof. Dr. Etienne Emmrich

    Project heads: Prof. Dr. Etienne Emmrich
    Project members: -
    Duration: 01.09.2012 - 31.12.2018
    Status: running
    Located at: Technische Universität Berlin


    Nonlinear evolution equations are the mathematical models for time-dependent processes in science and engineering. Relying upon the theory of monotone operators and compactness arguments, we study existence of solutions, convergence of discretization methods, and feedback control for equations of dissipative type. We focus on nonlocality in time (distributed delay, memory effects) and interpret time-delayed feedback control as a nonlocal-in-time coupling. Applications arise in soft matter and dynamics of complex fluids such as liquid crystals.