相关论文: Collapsing Solutions of the Maxwell Equations
We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic…
Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of…
The vacuum entanglement entropy of Maxwell theory, when evaluated by standard methods, contains an unexpected term with no known statistical interpretation. We resolve this two-decades old puzzle by showing that this term is the…
We obtain a two-parameter set of solutions, which represents a spherically symmetric space-time with a superposition of a neutral fluid and an electric field. The electromagnetic four-potential of this Einstein-Maxwell space-time is taken…
This article presents a mathematical framework for solving Maxwell's equations in cylindrical and spherical geometries with continuous angular indices. We extend beyond standard discrete harmonic decomposition to a continuous spectral…
A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic…
This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first…
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…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of…
In previous work we found that many of the spectral properties of low mass x-ray binaries, including galactic black hole candidates could be explained by a magnetic propeller model that requires an intrinsically magnetized central object.…
A new solution to the Einstein-Maxwell field equations is presented describing a cylindrically symmetric homogeneous cosmology. The solution is conformally flat, it possesses seven Killing vectors of which the timelike one is rotating and…
Strict mathematics reveals that the strict solution of a Vlasov-Maxwell equation set cannot be of a zero-temperature mathematical form. This universal property of Vlasov-Maxwell system can lead to a closed equation set of three macroscopic…
The main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation,…
We study the dynamics of the critical collapse of a spherically symmetric scalar field. Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained. In the central region, owing to the…
We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…