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search.filters.applied.f.access: openAccess × Author: Peschka, Dirk × End date: 2019 × End date: 2018 × Start date: 2018 × DDC: 510 ×

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Now showing 1 - 6 of 6
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    Variational approach to contact line dynamics for thin films
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Peschka, Dirk
    This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed and discussed. Feasibility of this modeling approach is shown by constructing a numerical scheme in 1D and by computing numerical solutions for the problem of gravity driven droplets. Some implications of the contact line model are highlighted in this setting.
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    Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Farrell, Patricio; Peschka, Dirk
    We analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices. Three common challenges, that can corrupt the precision of numerical solutions, will be discussed: boundary layers at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.
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    Doping optimization for optoelectronic devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Peschka, Dirk; Rotundo, Nella; Thomas, Marita
    We present a mathematical and numerical framework for the optimal design of doping profiles for optoelectronic devices using methods from mathematical optimization. With the goal to maximize light emission and reduce the thresholds of an edge-emitting laser, we consider a driftdiffusion model for charge transport and include modal gain and total current into a cost functional, which we optimize in cross sections of the emitter. We present 1D and 2D results for exemplary setups that point out possible routes for device improvement.
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    Gradient structures for flows of concentrated suspensions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Peschka, Dirk; Thomas, Marita; Ahnert, Tobias; Münch, Andreas; Wagner, Barbara
    In this work we investigate a two-phase model for concentrated suspensions. We construct a PDE formulation using a gradient flow structure featuring dissipative coupling between fluid and solid phase as well as different driving forces. Our construction is based on the concept of flow maps that also allows it to account for flows in moving domains with free boundaries. The major difference compared to similar existing approaches is the incorporation of a non-smooth twohomogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flows.
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    Optimization of a multiphysics problem in semiconductor laser design
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Adam, Lukáš; Hintermüller, Michael; Peschka, Dirk; Surowiec, Thomas M.
    A @multimaterial topology optimization framework is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed. Rigorous proofs are provided for the sensitivity of the fundamental mode of the device with respect to the changes in the underlying topology. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a Ge-on-Si microbridge are given. The highly favorable electronic properties of this design are demonstrated by steady-state simulations of the corresponding van Roosbroeck (drift-diffusion) system.
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    Signatures of slip in dewetting polymer films
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Peschka, Dirk; Haefner, Sabrina; Jacobs, Karin; Münch, Andreas; Wagner, Barbara
    Thin liquid polymer films on hydrophobic substrates are susceptable to rupture and formation of holes, which in turn initiate a complex dewetting process that eventually evolves into characteristic stationary droplet patterns. Experimental and theoretical studies suggest that the specific type of droplet pattern largely depends on the nature of the polymer-substrate boundary condition. To follow the morphological evolution numerically over long time scales and for the multiple length scales involved has so far been a major challenge. In this study a highly adaptive finite-element based numerical scheme is presented that allows for large-scale simulations to follow the evolution of the dewetting process deep into the nonlinear regime of the model equations, capturing the complex dynamics including shedding of droplets. In addition, the numerical results predict the previouly unknown shedding of satellite droplets during the destabilisation of liquid ridges, that form during the late stages of the dewetting process. While the formation of satellite droplets is well-known in the context of elongating fluid filaments and jets, we show here that for dewetting liquid ridges this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip.