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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…
This paper is concerned with the asymptotic behavior of small data solutions to the three-dimensional Vlasov-Maxwell system in the exterior of a light cone. The plasma does not have to be neutral and no compact support assumptions are…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original…
In classical treatment of Maxwell equations, the initial and boundary conditions are introduced by mathematical consideration rather than strictly using the Maxwell equations. As a result, the initial and boundary conditions are not logic…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…
We study a fractional analogue of a plasma problem arising from physics. Specifically, for a fixed bounded domain $\Omega$ we study solutions to the eigenfunction equation \[ (- \Delta)^s u = \lambda(u- \gamma)_+ \] with $u \equiv 0$ on…
We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…
Surface modes are coupled electromagnetic/electrostatic excitations of free electrons near the vacuum-plasma interface and can be excited on a sufficiently dense plasma half-space. They propagate along the surface plane and decay in either…
An ideal conductor electrode in contact with a semi-infinite two-dimensional two-component plasma in an external potential is considered. The model is mapped onto an integrable sine-Gordon theory with Dirichlet boundary conditions. The…
Using the Observable form of Maxwell's equations, we reveal that effective parameters at materials boundaries emerge naturally as anisotropic transfer functions. The complexity of the boundary dictates the order of these functions.…
We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Amp{\`e}re model proposed in [3]. The main…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
The hybrid Vlasov-Maxwell system of equations is suitable to describe a magnetized plasma at scales of the order of or larger than proton kinetic scales. An exact stationary solution is presented by revisiting previous results with a…
In this paper we propose new boundary conditions at the hot walls with thermionic electron emission for two-temperature thermal arc models. In the derived boundary conditions the walls are assumed to be made from refractory metals and that…
The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
We consider relativistic plasma particles subjected to an external gravitation force in a $3$D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the…
Exact equations describing flexoelectric deformation in solids, derived previously within the framework of a continuum media theory, are partial differential equations of the fourth order. They are too complex to be used in the cases…
The influence of electromagnetic skin effect on anomalous charged particle transport in dense, non-relativistic, collisionless plasma with a small-scale turbulent magnetic field was investigated using quasi-linear kinetic equations, through…
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…