Related papers: Electromagnetic fields from contact forms
We prove that there is a knot $K$ transverse to $\xi_{std}$, the tight contact structure of $S^3$, such that every contact 3-manifold $(M, \xi)$ can be obtained as a contact covering branched along $K$. By contact covering we mean a map…
We show that the appropriate notion of magnetic field on three-dimensional contact sub-Riemannian manifolds is given by a closed Rumin differential two-form. We introduce horizontal magnetic flows starting from magnetic potential one-forms,…
We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate…
The time dependent Dirac-Maxwell's Equations in presence of electric and magnetic sources are written in chiral media and the solutions for the classical problem are obtained in unique simple and consistent manner. The quaternion…
We show that solutions of Thurston equation on triangulated 3-manifolds in a commutative ring carry topological information. We also introduce a homogeneous Thurston equation and a commutative ring associated to triangulated 3-manifolds.
In this paper after reviewing the Schouten and de Rham definition of impair and pair differential form fields (not to be confused with differential form fields of even and odd grades) we prove that in a relativistic spacetime it is possible…
In a gravitational field, we analyze the Maxwell equations, the correponding electromagnetic wave and continuity equations. A particular solution for parellel electric and magnetic fields in a gravitational background is presented. These…
We employ a recently developed method for constructing rational electromagnetic field configurations in Minkowski space to investigate several properties of these source-free finite-action Maxwell ("knot") solutions. The construction takes…
We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(\boldsymbol{g},\boldsymbol{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of…
We study a rotating black hole with anisotropic matter and electromagnetic fields. We show that the electromagnetic field has the same form as the corresponding one in the Kerr-Newman geometry. The reason is thanks to the specific form of…
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
We consider the magnetoelectric effect produced by a capacitor formed by two semispherical perfectly conducting plates subjected to a potential difference and surrounded by a spherical shell of a topologically insulating material. The…
Electromagnetism is the energy originating from an electric charge. Our purpose is to enlarge Maxwell. Include the charge transfer phenomenology. A four bosons electromagnetism is derived. An EM completeness is achieved. The charge's set…
Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter…
We study the regularity of weak solutions to the 3D valued stationary Hall magnetohydrodynamic equations on $ \Bbb R^2$. We prove that every weak solution is smooth. Furthermore, we prove a Liouville type theorem for the Hall equations.
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation…
In this article we have illustrated how is possible to formulate Maxwell's equations in vacuum in an independent form of the usual systems of units. Maxwell's equations, are then specialized to the most commonly used systems of units:…
The systolic ratio of a contact form on a closed three-manifold is the quotient of the square of the shortest period of closed Reeb orbits by the contact volume. We show that every co-orientable contact structure on any closed…
A modified Faraday's law of electromagnetic induction in media is put forward.
This paper examines the theory of electron magnetic dipole moment interactions with magnetic fields or other electrons in classical and quantum electrodynamics. We show that these interactions may be described by a version of the Poynting…