Related papers: On polarization interface conditions for time-harm…
Quite a many electron transport problems in condensed matter physics are analyzed with a quasiparticle Boltzmann equation. For sufficiently slowly varying weak external potentials it can be derived from the basic equations of quantum…
This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier-Stokes…
We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous,…
We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical…
The analytical method of solving the boundary problems for a system of equations describing the behaviour of electrons and an electric field in the Maxwell plasma half-space is developed. Here the diffusion reflection of electrons from the…
We extend the coupled-wire construction of quantum Hall phases, and search for fractional topological insulating states in models of weakly coupled wires at zero external magnetic field. Focussing on systems beyond double copies of…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
We prove that the time-harmonic solutions to Maxwell's equations in a 3D exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted Sobolev spaces and construct new compactly supported…
We review Maxwell's equations and constitutive relations for 3D bianisotropic media in a generalized form: we consider all four variables and allow for nonzero polarization or magnetization, and also nonzero nonzero magnetic charge or…
Magnetic field plays a crucial role in various novel phenomena in heavy-ion collisions. We solve the Maxwell equations numerically in a medium with time-dependent electric conductivity by using the Finite-Difference Time-Domain (FDTD)…
We compare two singularly perturbed elliptic systems modeling partially phase segregation. Although the formulations are fundamentally different, we prove that their limiting configurations have identical free boundaries. The result shows…
This paper considers the time-harmonic Maxwell equations with impedance boundary condition.We present $H^2$-norm bound and other high-order norm bounds for strong solutions. The $H^2$-estimate have been derived in [M. Dauge, M. Costabel and…
This paper develops a general approach to the derivation of the boundary conditions for hydrodynamic equations for charged and neutral plasma components. It includes both a well-known classical case for pure diffusion, and considers the…
We consider the time evolution of the electric and magnetic field operators for a two-level atom, interacting with the electromagnetic field, placed near an infinite perfectly conducting wall. We solve iteratively the Heisenberg equations…
We consider a general compressible MHD system, where the magnetic field propagates in a heterogeneous medium. Using suitable penalization in terms of the transport coefficients we perform several singular limits. As a result we obtain: 1. A…
We investigate a large class of linear boundary value problems for the general first-order one-dimensional hyperbolic systems in the strip $[0,1]\times\R$. We state rather broad natural conditions on the data under which the operators of…
Most of our current understanding of phase separation is based on ideas that disregard correlaions. Here we illuminate unexpected effects of correlations on the structure and thermodynamics of interfaces and in turn phase separation, which…
A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma,…
The dynamics of an interface between the normal and superconducting phases under nonstationary external conditions is studied within the framework of the time-dependent Ginzburg-Landau equations of superconductivity, modified to include…