Related papers: Fractional Electromagnetic Field Theory and Its Ap…
A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that…
We compute electromagnetic fields created by a relativistic charged spin-half particle in empty space at distances comparable to the particle Compton wavelength. The particle is described as a wave packet evolving according to the Dirac…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
We use the theory of the fluctuating electromagnetic field to calculate the frictional drag between nearby two-and three dimensional electron systems. The frictional drag results from coupling via a fluctuating electromagnetic field, and…
Fresnel's equations describe reflection and transmission of electromagnetic waves at an interface between two media. It turns out that these equations can be used in quasistatics and even statics, for example to straightforwardly calculate…
We derive basic equations of electromagnetic fields in fractal media which are specified by three indepedent fractal dimensions {\alpha}_{i} in the respective directions x_{i} (i=1,2,3) of the Cartesian space in which the fractal is…
The dynamical responses of ferromagnet to the propagating electromagnetic field wave passing through it are modelled and studied here by Monte Carlo simulation in two dimensional Ising ferromagnet. Here, the electromagnetic wave is linearly…
We present a description of the electromagnetic field for propagation invariant beams using scalar potentials. Fundamental dynamical quantities are obtained: the energy density, the Poynting vector and the Maxwell stress tensor. As an…
We developed an analytical approach, for a wave propagation in metal-dielectric nanostructures in the quasi-static limit. This consideration establishes a link between fractional geometry of the nanostructure and fractional…
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite point-vector fields with discrete and localized point interactions. These fields are taken as a…
We consider a simple model of one-dimensional magnetic crystal and examine the propagation of an electromagnetic wave through such a medium. Calculating the dispersion relation ${\bf k}(\omega)$ allows us to illustrate how the spread of the…
We formulate a theory on the dynamics of conduction electrons in the presence of moving magnetic textures in ferromagnetic materials. We show that the variation of local magnetization in both space and time gives rise to topological fields,…
Textbooks play a fundamental role in teaching and learning in school science classrooms. In this paper we investigate the presentation of the nature of the electromagnetic field in a dozen of the world's most popular introductory university…
The propagation of free electromagnetic radiation in the field of a plane gravitational wave is investigated. A solution is found one order of approximation beyond the limit of geometrical optics in both transverse--traceless (TT) gauge and…
The dispersion relation of vertically oscillating fluid surfaces has been a subject extensively studied in the past, as well as surface instabilities produced by electrohydrodynamic (EHD) waves in similar configurations. In the present work…
We study the self-similar structure of electromagnetic showers and introduce the notion of the fractal dimension of a shower. Studies underway of showers in various materials and at various energies are presented, and the range over which…
We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. These variables enable us to not…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…