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End date: 2013 × Start date: 2012 × DDC: 510 × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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Now showing 1 - 10 of 233
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    Modeling and simulations of beam stabilization in edge-emitting broad area semiconductor devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Radziunas, Mindaugas; Cˇ iegis, Raimondas
    A 2+1 dimensional PDE traveling wave model describing spatial-lateral dynamics of edge-emitting broad area semiconductor devices is considered. A numerical scheme based on a split-step Fourier method is presented and implemented on a parallel compute cluster. Simulations of the model equations are used for optimizing of existing devices with respect to the emitted beam quality, as well as for creating and testing of novel device design concepts
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    Moment asymptotics for branching random walks in random environment
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Gün, Onur; König, Wolfgang; Sekulov´c, Ozren
    We consider the long-time behaviour of a branching random walk in random environment on the lattice Zd. The migration of particles proceeds according to simple random walk in continuous time, while the medium is given as a random potential of spatially dependent killing/branching rates. The main objects of our interest are the annealed moments m_np , i.e., the p-th moments over the medium of the n-th moment over the migration and killing/branching, of the local and global population sizes. For n = 1, this is well-understood citeGM98, as m_1 is closely connected with the parabolic Anderson model. For some special distributions, citeA00 extended this to ngeq2, but only as to the first term of the asymptotics, using (a recursive version of) a Feynman-Kac formula for m_n. In this work we derive also the second term of the asymptotics, for a much larger class of distributions. In particular, we show that m_n^p m_1^np are asymptotically equal, up to an error e^o(t). The cornerstone of our method is a direct Feynman-Kac-type formula for mn, which we establish using the spine techniques developed in citeHR1.1
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    Optimal control of elastic vector-valued AllenCahn variational inequalities
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Farshbaf-Shaker, Mohammad Hassan; Hecht, Claudia
    In this paper we consider a elastic vector-valued AllenCahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.
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    Equilibrium shapes of poly-crystalline silicon nanodots
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Korzec, Maciek D.; Roczen, Maurizio; Schade, Martin; Wagner, Barbara; Rech, Bernd
    This study is concerned with the topography of nanostructures consisting of arrays of poly-crystalline nanodots. Guided by transmission electron microscopy (TEM) measurements of crystalline Si (c-Si) nanodots that evolved from a dewetting process of an amorphous Si (a-Si) layer from a SiO2 coated substrate, we investigate appropriate formulations for the surface energy density and transitions of energy density states at grain boundaries. We introduce a new numerical minimization formulation that allows to account for adhesion energy from an underlying substrate. We demonstrate our approach first for the free standing case, where the solutions can be compared to well-known Wulff constructions, before we treat the general case for interfacial energy settings that support partial wetting. We then use our method to predict the morphologies of poly-crystalline silicon nanodots.
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    Overcoming the shortcomings of the Nernst-Planck model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Dreyer, Wolfgang; Guhlke, Clemens; Müller, Rüdiger
    This is a study on electrolytes that takes a thermodynamically consistent coupling between mechanics and diffusion into account. It removes some inherent deficiencies of the popular Nernst-Planck model. A boundary problem for equilibrium processes is used to illustrate the new features of our model.
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    A criterion for a two-dimensional domain to be Lipschitzian
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Rehberg, Joachim
    We prove that a two-dimensional domain is already Lipschitzian if only its boundary admits locally a one-dimensional, bi-Lipschitzian parametrization.
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    Convergence analysis of the FEM coupled with Fourier-mode expansion for the electromagnetic scattering by biperiodic structures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, Andreas
    Scattering of time-harmonic electromagnetic plane waves by a doubly periodic surface structure in R3 can be simulated by a boundary value problem of the time-harmonic curl-curl equation. For a truncated FEM domain, non-local boundary value conditions are required in order to satisfy the radiation conditions for the upper and lower half spaces. Alternatively to boundary integral formulations, to approximate radiation conditions and absorbing boundary methods, Huber et al. [11] have proposed a coupling method based on an idea of Nitsche. In the case of profile gratings with perfectly conducting substrate, the authors have shown previously that a slightly modified variational equation can be proven to be equivalent to the boundary value problem and to be uniquely solvable. Now it is shown that this result can be used to prove convergence for the FEM coupled by truncated wave mode expansion. This result covers transmission gratings and gratings bounded by additional multi-layer systems.
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    An adaptive SUPG method for evolutionary convection-diffusion equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) de Frutos, Javier; García-Archilla, Bosco; John, Volker; Novo, Julia
    An adaptive algorithm for the numerical simulation of time-dependent convectiondiffusion-reaction equations will be proposed and studied. The algorithm allows the use of the natural extension of any error estimator for the steady-state problem for controlling local refinement and coarsening. The main idea consists in considering the SUPG solution of the evolutionary problem as the SUPG solution of a particular steady-state convectiondiffusion problem with data depending on the computed solution. The application of the error estimator is based on a heuristic argument by considering a certain term to be of higher order. This argument is supported in the one-dimensional case by numerical analysis. In the numerical studies, particularly the residual-based error estimator from [18] will be applied, which has proved to be robust in the SUPG norm. The effectivity of this error estimator will be studied and the numerical results (accuracy of the solution, fineness of the meshes) will be compared with results obtained by utilizing the adaptive algorithm proposed in [6]
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    Adaptive smoothing as inference strategy: More specificity for unequally sized or neighboring regions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Welvaert, Marijke; Tabelow, Karsten; Seurinck, Ruth; Rosseel, Yves
    Although spatial smoothing of fMRI data can serve multiple purposes, increasing the sensitivity of activation detection is probably its greatest benefit. However, this increased detection power comes with a loss of specificity when non-adaptive smoothing (i.e. the standard in most software packages) is used. Simulation studies and analysis of experimental data was performed using the R packages neu-Rosim and fmri. In these studies, we systematically investigated the effect of spatial smoothing on the power and number of false positives in two particular cases that are often encountered in fMRI research: (1) Single condition activation detection for regions that differ in size, and (2) multiple condition activation detection for neighbouring regions. Our results demonstrate that adaptive smoothing is superior in both cases because less false positives are introduced by the spatial smoothing process compared to standard Gaussian smoothing or FDR inference of unsmoothed data.
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    Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
    Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation. We address the main issue of proving the existence of such limits for infinite-dimensional systems and of characterizing them by a couple of variational properties that combine a local stability condition and a balanced energy-dissipation identity. A careful description of the jump behavior of the solutions, of their differentiability properties, and of their equivalent representation by time rescaling is also presented. Our techniques rely on a suitable chain-rule inequality for functions of bounded variation in Banach spaces, on refined lower semicontinuity-compactness arguments, and on new BV-estimates that are of independent interest.