Related papers: Electrodynamic spherical harmonic
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
We study the spectra and response of two electrons moving on a surface of a sphere and interacting via harmonic potential, to external static and laser fields. The spectrum of such system law is analysed in the light of varying coupling…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
We propose a theory in electromagnetic dynamics, in which time and space are equivalent with each other and have totally twelve dimensions. Then, we solve that with realistic assumptions and find a steady state as a solution. The solution…
The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast…
A global weak solution of the biharmonic wave map equation in the energy space for spherical targets is constructed. The equation is reformulated as a conservation law and solved by a suitable Ginzburg-Landau type approximation.
We address the question of existence of regular spherically symmetric electrically charged solutions in Nonlinear Electrodynamics coupled to General Relativity. Stress-energy tensor of the electromagnetic field has the algebraic structure…
Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability…
We determine sufficient and necessary conditions for a spherically symmetric initial data set to satisfy the dynamical horizon conditions in the spacetime development. The constraint equations reduce to a single second order linear master…
In MHD symmetric systems the equilibrium physical quantities are dependent on two variables only. In this cases it is possible to find a magnetic surface function that has the same symmetry. Under the assumption that the metric determinant…
A discrete harmonic surface is a trivalent graph which satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimizing under local deformations. Given a topological trivalent graph, a holomorphic…
In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We…
The quasiradial wave functions and energy spectra of the alternative model of spherical oscillator on the $D$-dimensional sphere and two-sheeted hyperboloid are found.
Symmetry problems in harmonic analysis are formulated and solved. One of these problems is equivalent to the refined Schiffer's conjecture which was recently proved by the author. Let $k=const>0$ be fixed, $S^2$ be the unit sphere in…
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test…
An Electrodynamics solver for moving sources is introduced. The main challenges and formulation are highlighted. The solver enables the simulation of fields for sources undergoing arbitrary motion. Two examples of uniformly moving current…
Boundary integral equation is derived for the problem of scattering of electromagnetic waves by 3D homogeneous body of arbitrary shape.
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…