Related papers: Electromagnetic space-time crystals. II. Fractal c…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
Canonical quantization of electromagnetic field inside the time--spatially dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic and matter excitation fields create the closed system, Hamiltonian of which may be…
Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and…
Recent years have witnessed a great research boom in soft matter physics. by now, most advances, however, are of either empirical results or purely mathematical extensions. The major obstacle is lacking of insights into fundamental…
Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integro-differentiation. The…
A method is described for calculating the approximate fractal dimension from a set of N values y sampled from a waveform between time zero and t. The waveform was subjected to a double linear transformation that maps it into a unit square.
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
The dimensionality of an electronic quantum system is decisive for its properties. In 1D electrons form a Luttinger liquid and in 2D they exhibit the quantum Hall effect. However, very little is known about the behavior of electrons in…
A method is presented to investigate diffraction of an electromagnetic plane wave by an infinitely thin infinitely conducting circular cylinder with longitudinal slots. It is based on the use of the combined boundary conditions method that…
It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable…
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…
This paper presents an analysis of the band structure of a spacetime potential lattice created by a standing electromagnetic wave. We show that there are energy band gaps. We estimate the effect, and propose a measurement that could confirm…
This paper investigates the possibility of generating Floquet-time crystals in higher dimensions ($d\geq 2$) through the time-periodic driving of integrable free-fermionic models. The realization leads to rigid time-crystal phases that are…
We study several numerical discretization techniques for the one-space plus one-time dimensional Dirac equation, including finite difference and space-time finite element methods. Two finite difference schemes and several space-time finite…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
Rapid modulation of the electromagnetic response in both time and space creates temporal boundaries in the medium and leads to time-reflection and time-refraction of light and to the eventual formation of the photonic time crystal within…
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…
Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper (Chumak \& Rastorguev, 2015) involving a generalization of the nearest neighbour and random force distributions to fractal…