Related papers: On polarization interface conditions for time-harm…
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…
We investigate the dynamics of a nonequilibrium interface between coexisting phases in a system described by a Cahn-Hilliard equation with an additional driving term. By means of a matched asymptotic expansion we derive equations for the…
The paper is concerned with well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles with local perturbations. The classical Rayleigh…
The spectrum of magnetic edge states and their transport properties in the presence of a perpendicular non-homogeneous magnetic field in a quantum wire formed by a parabolic confining potential are obtained. Systems are studied where the…
We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period $\eta > 0$; we study the behaviour of solutions $(E^{\eta}, H^{\eta})$…
Surface plasmon polaritons propagating along curved metal-dielectric interfaces experience geometry-induced modifications absent on flat surfaces. In this work, we derive a covariant, effective two-dimensional wave equation for the…
A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson…
In this paper, we consider a semiconducting device with an active zone made of a single-layer material. The associated Poisson equation for the electrostatic potential (to be solved in order to perform self-consistent computations) is…
We consider the electric and magnetic field fluctuations in the vacuum state in the region external to a half-space filled with a homogeneous non-dissipative dielectric. We discuss an appropriate limit to an ideal metal and concentrate our…
In the classical statement of the plasma-vacuum interface problem in ideal magnetohydrodynamics (MHD) one neglects the displacement current in the vacuum region that gives the div-curl system of pre-Maxwell dynamics for the vacuum magnetic…
At a boundary between two transparent, linear, isotropic, homogeneous materials, derivations of the electromagnetic boundary conditions and the Fresnel relations typically proceed from the Minkowski {E,B,D,H} representation of the…
In this paper we investigate the effect of a Signorini-type interface condition on the asymptotic behaviour, as $\varepsilon$ tends to zero, of problems posed in $\varepsilon$-periodic domains with inclusions. The Signorini-type condition…
The nature of magnetic order and transport properties near surfaces is a topic of great current interest. Here we model metal-insulator interfaces with a multi-layer system governed by a tight-binding Hamiltonian in which the interaction is…
We consider for the full time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements…
We obtain nontrivial solutions of some elliptic interface problems with nonhomogeneous jump conditions that arise in localized chemical reactions and nonlinear neutral inclusions. Our proofs in bounded domains use Morse theoretical…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded domain. One phase is assumed to be magnetic, the other phase…
We study the time evolution of interfaces of the ferromagnetic XXZ chain in a magnetic field. A scaling limit is introduced where the strength of the magnetic field tends to zero and the microscopic time to infinity while keeping their…
Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The…
There is not a unique solution to the electro- or magnetostatic problem where the "boundary condition" is merely a specification of the fields along a line. As a practical example, we consider the case where it is desired to have a magnetic…