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Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in…
This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…
Plasma-boundaries floating in an ionized gas are usually negatively charged. They accumulate electrons more efficiently than ions which leads to the formation of a quasi-stationary electron film at the boundaries. We propose, in a…
We generalize the closest point method (CPM) to solve surface partial differential equations with general boundary conditions. The proposed extrapolation method provides a unified framework for treating a broad class of inhomogeneous…
We study the potential and the charge distribution across the interface of a plasma and a dielectric wall. For this purpose, the charge bound to the wall is modelled as a quasi-stationary electron surface layer which satisfies Poisson's…
We study the equilibrating effects of the boundary and intermolecular collision in the kinetic theory for rarefied gases. We consider the Maxwell-type boundary condition, which has weaker equilibrating effect than the commonly studied…
Maxwell's boundary conditions (MBCs) were long known insufficient to determine the optical responses of spatially dispersive medium. Supplementing MBCs with additional boundary conditions (ABCs) has become a normal yet controversial…
We derive a model to describe the interaction of an rf-SQUID (radio frequency superconducting quantum interference device) based metasurface with free space electromagnetic waves. The electromagnetic fields are described on the base of…
We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. We discuss the analytic properties of the discretisation, outline the implementation, and showcase numerical examples.
Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…
A systematic search for the Lie point symmetries admitted by the steady hydromagnetic two-dimensional incompressible viscous flow boundary layer equation and associated boundary conditions is performed. Unlike previous works, the specific…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
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…
Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance…
Vacuum-energy calculations with ideal reflecting boundaries are plagued by boundary divergences, which presumably correspond to real (but finite) physical effects occurring near the boundary. Our working hypothesis is that the stress tensor…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
We study a 1D geometry of a plasma confined between two conducting floating walls with applications to laboratory plasmas. These plasmas are characterized by a quasi-neutral bulk that is joined to the wall by a thin boundary layer called…
Multifluid simulations of plasma sheaths are increasingly used to model a wide variety of problems in plasma physics ranging from global magnetospheric flows around celestial bodies to plasma-wall interactions in thrusters and fusion…
We prove global existence of strong solutions for the Vlasov-Poisson system in a convex bounded domain in the plasma physics case assuming homogeneous Dirichlet boundary conditions for the electric potential and the specular reflection…
For the first time it is shown that for thin metallic films thickness of which does not exceed thickness of skin - layer, the problem of description of surface plasma oscillations allows analytical solution under arbitrary ratio of length…