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There is considerable interest in the application of quantum information science to advance computations in plasma physics. Many of the topics in fusion plasma physics are classical in nature. In order to implement them on quantum computers…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
A boundary integral formulation of electromagnetics that involves only the components of $\boldsymbol{E}$ and $\boldsymbol{H}$ is derived without the use of surface currents that appear in the classical PMCHWT formulation. The kernels of…
We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex…
An original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight…
In this paper, an efficient and accurate unified approach is proposed to solve transverse magnetic scattering problems by multilayer embedded objects. In the proposed approach, an equivalent current density is derived when the equivalent…
We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials ${\bf A},\phi$…
Last year physicists in Europe have measured the velocity of the neutrinos particles. They found the neutrinos moving faster than the speed of light in vacuum. This result means that Einstein's relativity principle and its consequences in…
The discussion of our recent work concerning the vector solution of boundary-value problems in electromagnetism is extended to the case of no azimuthal symmetry by means of the spin-weighted spherical harmonics.
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
Maxwell's equations are cast in the form of the Schr\"{o}dinger equation. The Lanczos propagation method is used in combination with the fast Fourier pseudospectral method to solve the initial value problem. As a result, a time-domain,…
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the…
Certain classes of electromagnetic boundaries satisfying linear and local boundary conditions can be defined in terms of the dispersion equation of waves matched to the boundary. A single plane wave is matched to the boundary when it…
Traditional boundary integral methods suffer from the singularity of Green's kernels. The paper develops, for a model problem of 2D scattering as an illustrative example, singularity-free boundary difference equations. Instead of converting…
This paper considers the probability density and current distributions generated by a point-like, isotropic source of monoenergetic charges embedded into a uniform magnetic field environment. Electron sources of this kind have been realized…
A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…
The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…