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In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response…
We consider the scattering of time periodic electro-magnetic fields by metallic obstacles, the eddy current problem. In this interface problem different sets of Maxwell equations must be solved in the obstacle and outside, while the…
A global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as $Re_{\delta}\rightarrow \infty$, the dynamically defined boundary…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
The light scattering problem for a confocal multilayered spheroid has been solved by the extended boundary condition method (EBCM) with a corresponding spheroidal basis. The solution preserves the advantages of the approach applied…
This work was motivated by a lacking general consensus in the exact form of the boundary conditions (BCs) required on the solid surfaces for the continuum modeling of RF plasmas. Various kinds of number and energy density BCs on solid…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
An exact analytic solution is obtained for a uniformly expanding, neutral, highly conducting plasma sphere in an ambient dipole magnetic field with an arbitrary orientation of the dipole moment in the space. Based on this solution the…
A high-accuracy solution of the diffraction problem has become necessary for the treatment of certain special questions of statistical physics. This article reports the creation of a computer program that serves as an instrumental method of…
We consider the equations of electromagnetism set on a domain made of a dielectric and a conductor subdomain in a regime where the conductivity is large. Assuming smoothness for the dielectric--conductor interface, relying on recent works…
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…
A new method to find the propagation equation system governing the scattering of an electromagnetic wave by a nonlinear medium is proposed. The aim is to let the effects appear spontaneously, deleting as far as possible the phenomenological…
We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…
A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the "one-fluid"…
In this paper, we present a model based on a local thermodynamic equilibrium, weakly ionized plasma-mixture model used for medical and technical applications in etching processes. We consider a simplified model based on the Maxwell-Stefan…
The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…