Related papers: On polarization interface conditions for time-harm…
We consider the plasma-vacuum interface problem in a classical statement when in the plasma region the flow is governed by the equations of ideal compressible magnetohydrodynamics, while in the vacuum region the magnetic field obeys the…
When the surface of a first material is brought into contact with the surface of a second material the contact region is called an interface. Since the time of James Clerk Maxwell it has been customary to treat a material electrically as…
Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…
We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we…
The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma…
We consider for the 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 measurements of the…
The standard Maxwell formulation of the problem of polarized dielectrics suffers from a number of difficulties, both conceptual and practical. These difficulties are particularly significant in the case of liquid interfaces, where the…
We study the local-in-time well-posedness for an interface that separates an anisotropic plasma from a vacuum. The plasma flow is governed by the ideal Chew-Goldberger-Low (CGL) equations, which are the simplest collisionless fluid model…
We consider the time-harmonic Maxwell equations set on a domain made up of two subdomains that represent a magnetic conductor and a non-magnetic material, and we assume that the relative magnetic permeability $\mu_{r}$ between the two…
In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations.The implementation of high order…
We consider the free boundary problem for relativistic plasma--vacuum interfaces in two and three spatial dimensions. The plasma flow is governed by the equations of ideal relativistic magnetohydrodynamics, while the vacuum magnetic and…
In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in R^3. This representation leads to a…
The envelope-function method with generalized boundary conditions is applied to the description of localized and resonant interface states. A complete set of phenomenological conditions which restrict the form of connection rules for…
We investigate the behaviour of solutions of a fractional semilinear partial differential equation that models the evolution of an interface in a random medium. We show a pinning result and apply it to the related homogenizing process.
We study the initial-boundary value problem resulting from the linearization of the plasma-vacuum interface problem in ideal compressible magnetohydrodynamics (MHD). We suppose that the plasma and the vacuum regions are unbounded domains…
Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at…
After formulating the frequency-domain Maxwell equations for a homogeneous, linear, bianisotropic material occupying a bounded region, we found that the axionic piece vanishes from both the differential equations valid in the region and the…
The properties of the modified Maxwell electrodynamics (ModMax) are investigated in presence of external and uniform electric and magnetic fields. We expand the non-linear theory around an electromagnetic background up to second order in…
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary…
The standard equilibrium equation for magnetized plasma is extended to account for the magnetic polarization force. A factor of the pressure gradient arising from the magnetic decomposition of the Hall term survives the limit of vanishing…