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The work is dedicated to the theoretic analysis of wire media, i.e. lattices of perfectly conducting wires comprised of two or three doubly periodic arrays of parallel wires which are orthogonal to one another. An analytical method based on…
We consider nonlinear dispersive equations of Schr\"odinger-type involving fractional powers $0<s\le 1$ of the Laplacian and a defocusing power-law nonlinearity. We conduct numerical simulations in the case of small, energy supercritical…
We derive a system of coupled partial differential equations for the equal-time Wigner function in an arbitrary strong electromagnetic field using the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a 3+1-system of…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…
Fractional electromagnetic field theory describes electromagnetic wave propagation through the complex, nonlocal, dissipative, fractal and also recent artificially engineered materials know as fractional metamaterials. In this theory using…
The structure of the electric field in a plasma has been elucidated for the skin effect problem. An expression for the distribution function in the half-space and the electric field profile have been obtained in the explicit form. The…
The before described general principles and methodology of calculating electron wave propagation in homogeneous isotropic half-infinity slab of Maxwellian plasma with indefinite but in principal value sense taken integrals in characteristic…
We study the dispersion properties of surface plasmon oscillations in a semi-bounded semiconductor plasma with the effects of the Coulomb exchange force associated with the spin polarization of electrons and holes as well as the effects of…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
Non-linear electrodynamic models are re-assessed in this paper to pursue an investigation of the kinematics of the Compton effect in a magnetic background. Before considering specific models, we start off by presenting a general non-linear…
We express the electromagnetic field propagating in an arbitrary time-independent non-dispersive medium in terms of an operator that turns out to be pseudo-Hermitian for Hermitian dielectric and magnetic permeability tensors Epsilon and Mu.…
We consider the fractional Laplace framework and provide models and theorems related to nonlocal diffusion phenomena. Some applications are presented, including: a simple probabilistic interpretation, water waves, crystal dislocations,…
By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is…
Examination of equilibrium radiation in plasma media shows that the spectral the energy distribution of such radiation is different from the Planck equilibrium radiation. Using the previously obtained general relations for the spectral…
Using the Langevin approach and the multiscale technique, a kinetic theory of the time and space nonlocal fluctuations in the collisional plasma is constructed. In local equilibrium a generalized version of the Callen-Welton theorem is…
We study the diffusion and thermal conductivity of charged particles in the weakly ionized plasma with the power-law q-distributions in nonextensive statistics and without the magnetic field. Electrons and ions have different q-parameters…
We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove…
A hydrodynamic theory of screening in a generic electron gas of arbitrary dimensionality is given that encompasses all previously studied cases and clarifies the predictions of the many-body approach. We find that long-wavelength plasma…
In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics,…
A general theoretical framework for investigating nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or…