736 Works

Optimization of a multiphysics problem in semiconductor laser design

Lukáš Adam, Michael Hintermüller, Dirk Peschka & Thomas M. Surowiec
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,...

A subdifferential criterion for calmness of multifunctions

René Henrion & Jiří Outrata
A criterion for the calmness of a class of multifunctions between finite-dimensional spaces is derived in terms of subdifferential concepts developed by Mordukhovich. The considered class comprises general constraint set mappings as they occur in optimization or mappings associated with a certain type of variational systems. The criterion for calmness is obtained as an appropriate reduction of Mordukhovich's well-known characterization of the stronger Aubin property (roughly spoken, one may pass to the boundaries of normal...

Multiscale modeling of vascularized tissues via non-matching immersed methods

Luca Heltai & Alfonso Caiazzo
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two manifold) at a given pressure. We derive different variational formulations of the coupled problem, in which the effect of the vasculature can be surrogated in the elasticity equations via singular or hyper-singular forcing terms. These terms only depends on information...

Percolation for D2D networks on street systems

Elie Cali, Taoufik En-Najjari, Nila Novita Gafur, Christian Christian Hirsch, Benedikt Jahnel & Robert I. A. Patterson
We study fundamental characteristics for the connectivity of multi-hop D2D networks. Devices are randomly distributed on street systems and are able to communicate with each other whenever their separation is smaller than some connectivity threshold. We model the street systems as Poisson-Voronoi or Poisson-Delaunay tessellations with varying street lengths. We interpret the existence of adequate D2D connectivity as percolation of the underlying random graph. We derive and compare approximations for the critical device-intensity for percolation,...

Patch-wise adaptive weights smoothing

Jórg Polzehl, Kostas Papafitsoros & Karsten Tabelow
Image reconstruction from noisy data has a long history of methodological development and is based on a variety of ideas. In this paper we introduce a new method called patch-wise adaptive smoothing, that extends the Propagation-Separation approach by using comparisons of local patches of image intensities to define local adaptive weighting schemes for an improved balance of reduced variability and bias in the reconstruction result. We present the implementation of the new method in an...

Acoustic scattering from corners, edges and circular cones

Johannes Elschner & Guanghui Hu
Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions and a planar corner point in two dimensions. The opening angles of cones and edges are allowed to be non-convex. We prove that such an obstacle scatters any incoming wave non-trivially (i.e., the far field patterns cannot vanish identically),...

Stochastic, analytic and numerical aspects of coagulation processes

Wolfgang Wagner
In this paper we review recent results concerning stochastic models for coagulation processes and their relationship to deterministic equations. Open problems related to the gelation effect are discussed. Finally we present some new conjectures based on numerical experiments performed with stochastic algorithms.

Prescribed conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients

Fabio Punzo & Enrico Valdinoci
We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed pointwise conditions at infinity (in space), which can be time-dependent. Moreover, we study the asymptotic behaviour of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.

Reduced-order unscented Kalman filter in the frequency domain: Application to computational hemodynamics

Lucas O. Müller, Alfonso Caiazzo & Pablo J. Blanco
Objective: The aim of this work is to assess the potential of the reduced order unscented Kalman filter (ROUKF) in the context of computational hemodynamics, in order to estimate cardiovascular model parameters when employing real patient-specific data. Methods: The approach combines an efficient blood flow solver for one-dimensional networks (for the forward problem) with the parameter estimation problem cast in the frequency space. Namely, the ROUKF is used to correct model parameter after each cardiac...

On the characterization of self-regularization properties of a fully discrete projection method for Symm's integral equation

Sergei V. Pereverzev & Siegfried Prößdorf
The influence of small perturbations in the kernel and the right-hand side of Symm's boundary integral equation, considered in an ill-posed setting, is analyzed. We propose a modification of a fully discrete projection method which is more economical in the sense of complexity and allows to obtain the optimal order of accuracy in the power scale with respect to the level of the noise in the kernel or in the parametric representation of the boundary.

Brownian motion in attenuated or renormalized inverse-square Poisson potential

Peter Nelson & Renato Soares Dos Santos
We consider the parabolic Anderson problem with random potentials having inverse-square singularities around the points of a standard Poisson point process in ℝ d, d ≥3. The potentials we consider are obtained via superposition of translations over the points of the Poisson point process of a kernel 픎 behaving as 픎 (x)≈ Θ|x|-2 near the origin, where &Theta ∈(0,(d-2)2/16]. In order to make sense of the corresponding path integrals, we require the potential to be...

Maximum likelihood estimate for nonparametric signal in white noise by optimal control

Grigori N. Milstein & Michael Nussbaum
The paper is devoted to questions of constructing the maximum likelihood estimate for a nonparametric signal in white noise by considering corresponding problems of optimal control. For signals with bounded derivatives, sensitivity theorems are proved. The theorems state a stability of the maximum likelihood estimate with respect to changing output data. They make possible to reduce the original problem to a standard problem of optimal control which is solved by iterative procedure. For signals of...

Homogenization of Scalar Wave Equations with Hysteresis

Jan Franců & Pavel Krejčí
The paper deals with a scalar wave equation of the form ρutt = (퓕[ux])x + ƒ, where 퓕 is a Prandtl-Ishlinskii operator and ρ, ƒ are given functions. This equation describes longitudinal vibrations of an elastoplastic rod. The mass density ρ and the Prandtl-Ishlinskii distribution function η are allowed to depend on the space variable x. We prove existence, uniqueness and regularity of solution to a corresponding initial-boundary value problem. The system is then homogenized...

On the existence of classical solutions for a two phase flow through saturated porous media

Sabine Hengst
In this paper an elliptic-parabolic coupled system arising from a two-phase flow through a saturated porous medium is considered. The uniqueness and the existence of classical solutions are proved. The asymptotic behavior of solutions for large time is shown, too.

Memory equations as reduced Markov processes

Holger Stephan & Artur Stephan
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory equation, we give an explicit construction of the corresponding Markov process. From a physical point of view the Markov process can be understood as the change of the type of some quasiparticles along one-way...

Modeling diffusional coarsening in microelectronic solders

Wolfgang Dreyer & Wolfgang H. Müller
This paper presents a detailed numerical simulation of the coarsening phenomenon observed in microelectronic solder materials that are subjected to high homologeous temperatures in combination with thermo-mechanical stresses. The simulations are based on a phase field model which, for simplicity, is explicitly formulated for a binary alloy. To this end, the thermomechanical stresses originating within a Representative Volume Element (RVE) of the solder material are calculated first. This is achieved by means of a closed-form...

The moment Lyapunov exponent for conservative systems with small periodic and random perturbations

Peter Imkeller & Grigori N. Milstein
Much effort has been devoted to the stability analysis of stationary points for linear autonomous systems of stochastic differential equations. Here we introduce the notions of Lyapunov exponent, moment Lyapunov exponent, and stability index for linear nonautonomous systems with periodic coefficients. Most extensively we study these problems for second order conservative systems with small random and periodic excitations. With respect to relations between the intrinsic period of the system and the period of perturbations we...

On the Dynamics of Single Mode Lasers with Passive Dispersive Reflector

Fritz Henneberger, Klaus R. Schneider, Jan Sieber, Vasile Z. Tronciu & Hans-Jürgen Wünsche
For passive dispersive reflector (PDR) lasers we investigate a single mode model containing two functions characterizing the influence of the PDR. We study numerically the effect of the shape of these functions on the existence and robustness of self-pulsations. The possibility of tuning the frequency and modulation depth of the self-pulsations has been demonstrated.

A discrete collocation method for Symm's integral equation on curves with corners

Johannes Elschner & Ernst P. Stephan
This paper is devoted to the approximate solution of the classical first-kind boundary integral equation with logarithmic kernel (Symm's equation) on a closed polygonal boundary in ℝ2. We propose a fully discrete method with a trial space of trigonometric polynomials, combined with a trapezoidal rule approximation of the integrals. Before discretization the equation is transformed using a nonlinear (mesh grading) parametrization of the boundary curve which has the effect of smoothing out the singularities at...

Tricomi's composition formula and the analysis of multiwavelet approximation methods for boundary integral equations

Siegfried Prößdorf
The present paper is mainly concerned with the convergence analysis of Galerkin-Petrov methods for the numerical solution of periodic pseudodifferential equations using wavelets and multiwavelets as trial functions and test functionals. Section 2 gives an overview on the symbol calculus of multidimensional singular integrals using Tricomi's composition formula. In Section 3 we formulate necessary and sufficient stability conditions in terms of the so-called numerical symbols and demonstrate applications to the Dirchlet problem for the Laplace...

Hybrid method and vibrational stability for nonlinear singularly perturbed systems under parametric excitations

Vadim V. Strygin
The well-known classic feedback and feedforward techniques are the main tools for investigations of the control problems. Unlike these strategies, the vibrational control technique, introduced by S.M. Meerkov [1], has proven to be a viable alternative to conventional feedback and feedforward strategies in stabilization problems when the outputs, states and disturbances are difficult to access. Mathematical modelling of such systems is closely connected with nonlinear singularly perturbed systems under parametric excitations. In this paper a...

Correct voltage distribution for axisymmetric sinusoidal modeling of induction heating with prescribed current, voltage, or power

Olaf Klein & Peter Philip
We consider the problem of determining the voltage in coil rings, which arise as an axisymmetric approximation of a single connected induction coil during modeling of induction heating. Assuming axisymmetric electromagnetic fields with sinusoidal time dependence, the voltages are computed from the condition that the total current must be equal in each ring. Depending on which of the quantities total current, total voltage, or total power is to be prescribed, the ring voltages are given...

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