Related papers: Fractional Electromagnetic Field Theory and Its Ap…
Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
The expression for the intensity of the electromagnetic field radiation is derived in the approximation next to the dipole one. The presented approach is based on fundamental equations from the introductory course on classical…
The propagation of a 3D crack in an heterogeneous material is studied using a phase field model. It is shown that in the case of randomly distributed inclusions of soft material in a matrix, the nature of the distribution has little effect…
When propagating through periodically structured media, i. e. photonic crystals, optical waves will be modulated with the periodicity. As a result, the dispersion of waves will no longer behave as in a free space, and so called frequency…
In this paper we consider the electric multipole moments of fractal distribution of charges. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on…
We study one of the interesting properties of the electromagnetic wave propagation in the curved Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum…
This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe…
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic…
Exactly soluble models in the theory of electromagnetic propagation and scattering are essentially restricted to horizontally stratified or spherically symmetric geometries, with results also available for certain waveguide geometries.…
Within the framework of generally covariant (pre-metric) electrodynamics, we specify a local vacuum spacetime relation between the excitation $H=({\cal D},{\cal H})$ and the field strength $F=(E,B)$. We study the propagation of…
We consider the low-energy effective field theory describing the infrared dynamics of non-dissipative fluids. We extend previous work to accommodate conserved charges, and we clarify the matching between field theory variables and…
The problem of calculation of electromagnetic field energy outside the transparency domain is discussed. It is shown that charged particle contribution to the energy of electromagnetic perturbations in the general case can be described in…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
We analyze electromagnetic field propagation through a random medium which consists of hyperbolic metamaterial domains separated by regions of normal "elliptic" space. This situation may occur in a problem as common as 9 micrometer light…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
Optical space in metamaterials may be engineered to emulate four dimensional Kaluza-Klein theory. Nonlinear optics of such metamaterials mimics interaction of quantized electric charges. An electromagnetic wormhole is designed, which…
Using the FDTD method, we investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel air cylinders in a dielectric medium. The corresponding frequency band structure is computed using the standard…
Quasistatics is introduced so that it fits smoothly into the standard textbook presentation of electrodynamics. The usual path from statics to general electrodynamics is rather short and surprisingly simple. A closer look reveals however…