Related papers: Multidomain spectral approach with Sommerfeld cond…
The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged…
We explore the existence of quasisymmetric magnetic fields in asymmetric toroidal domains. These vector fields can be identified with a class of magnetohydrodynamic equilibria in the presence of pressure anisotropy. First, using Clebsch…
The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the…
We propose a method for numerical relativity in which the spatial grid is finite and no outer boundary condition is needed. As a "proof of concept" we implement this method for the case of a self-gravitating, spherically symmetric scalar…
Many physically interesting quantities of the electromagnetic field can be computed using the electromagnetic scalar product. However, none of the existing expressions for such scalar product are directly applicable when the fields are only…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
We consider the time-harmonic Maxwell's equations with a polarization interface condition. The interface condition demands that one component of the electric field vanishes at the interface and that the corresponding component of the…
Sufficient conditions for a discrete spectrum of the biharmonic equation in a two-dimensional peak-shaped domain are established. Different boundary conditions from Kirchhoff's plate theory are imposed on the boundary and the results depend…
The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations…
We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius' method and Moebius transformations in the vicinity of each of…
In this paper we look for solutions of a semilinear Maxwell type equation, in even dimension, greater than four. These solutions are critical points of a functional which is strongly degenerate because of the presence of the exterior…
Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary conditions and invocation of the Dirichlet-to-Neumann map, we introduce a new, nonlocal…
A companion paper has argued that the best way to associate single-particle quantum states of a scalar field to the modes of a narrowly collimated beam of classical radiation modeled in the paraxial approximation uses the ``henochromatic''…
A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and…
The three-dimensional quasi-geostrophic equation is considered over a cylindrical domain with a multiply connected horizontal cross-section. Homogeneous Neumann boundary conditions, tantamount to homogeneous density fields, are imposed on…
This paper is on magnetic Schrodinger operators in two dimensional domains with corners. Semiclassical formulas are obtained for the sum and number of eigenvalues. The obtained results extend former formulas for smooth domains in \cite{Fr,…
Boundary conditions and the corresponding states of a quantum field theory depend on how the horizons are taken into account. There is ambiguity as to which method is appropriate because different ways of incorporating the horizons lead to…
In this paper we describe the spectrum of the quantum periodic Benjamin-Ono equation in terms of the multi-phase solutions of the underlying classical system (the periodic multi-solitons). To do so, we show that the semi-classical…
A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different…
A robust and efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector Helmholtz…