Related papers: Time-Dependent Wave-Structure Interaction Revisite…
We consider a model of an elastic body immersed between two layers of incompressible viscous fluid. The elastic displacement $w$ is governed by the damped wave equation $w_{tt} + \alpha w_t + \Delta w =0$ without any stabilization terms,…
The linear Schr\"odinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with…
Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner/Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting…
We present a general formalism for computing self-consistent, numerical solutions to the time-dependent radiative transfer equation in low velocity, multi-level ions undergoing radiative interactions. Recent studies of time-dependent…
We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…
We present here nonoverlapping optimized Schwarz methods applied to heat transfer problems with heterogeneous diffusion coefficients. After a Laplace transform in time, we derive the error equation and obtain the convergence factor. The…
The dispersion relation is derived for the coherent waves in fluid or elastic media supporting viscous and thermal effects and containing randomly distributed spherical scatterers. The formula obtained is the generalization of Lloyd and…
A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…
In this paper, we consider a contact problem with adhesion between a viscoelastic body and a rigid support, taking thermal effects into account. The PDE system we deal with is derived within the modelling approach proposed by M. Fremond…
We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…
When describing elastic deformations of a body sometimes it is worth to take in account elastic spatial dispersion. If spatial dispersion is weak, as usually happens, then it can be reduced to dependence of thermodynamic potential on strain…
This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive…
We give a principled approach for the selection of a boundary integral, retarded potential representation for the solution of scattering problems for the wave equation in an exterior domain.
Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent…
We use the internal-variable, effective-temperature thermodynamics developed in two preceding papers to reformulate the shear-transformation-zone (STZ) theory of amorphous plasticity. As required by the preceding analysis, we make explicit…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
In this paper, we consider an inverse electromagnetic medium scattering problem of reconstructing unknown objects from time-dependent boundary measurements. A novel time-domain direct sampling method is developed for determining the…
We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…