Related papers: Fractional Power-Law Spatial Dispersion in Electro…
Electric and magnetic self-fields can exist in the rotating plasma. A self-sustained rotation can be established in the plasma. The disturbed distribution function of rotating plasma is derived from the Vlasov equation. The propagation of…
We employ the Sagdeev pseudo-potential method to investigate the propagation of nonlinear ion waves in a relativistically degenerate electron-ion plasmas. The matching criteria for existence of such nonlinear excitations are numerically…
We consider a stochastic differential equation for a charged particle in a stochastic magnetic field, known as A-Langevin equation. The solution of the equation is found, and the Lagrange velocity correlation function is calculated in…
We examine whether the principle of detailed balance holds for the power-law distributions generated from the general Langevin equation under the generalized fluctuation-dissipation relation (FDR). With the detailed balance and the…
Competing styles in Statistical Mechanics have been introduced to investigate physico-chemical systems displaying complex structures, when one faces difficulties to handle the standard formalism in the well established Boltzmann-Gibbs…
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…
We study the influence of the space and time dispersion on the frequency dependence of the wave vectors of electromagnetic waves propagating in three-dimensional photonic crystals. Two types of structures are considered: media with weak…
Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: microphysics of electron resonant scattering by electromagnetic waves and…
The electric microfield distribution at charged particles is studied for two-component electron-ion plasmas using molecular dynamics simulation and theoretical models. The particles are treated within classical statistical mechanics using…
A relativistic quantum mechanical model to describe the quantum FEL dynamics has been developed. Neglecting the spin of electrons in the impacting beam, this model is based on the Klein-Gordon equation coupled to the Poisson equation for…
We study the viscosity of light charged particles in weakly ionized plasma with the power-law q-distributions by using the Boltzmann equation of transport and the motion equation of hydrodynamics. The nonequilibrium plasma is considered to…
Fractional differential approach to cosmic ray physics problems is discussed. A short review in this field is given, some results are represented, analyzed and criticized. A new model called the bounded anomalous diffusion model is offered.…
In this thesis we investigate how the nonlocalities affect the study of different PDEs coming from physics, and we analyze these equations under almost optimal assumptions of the nonlinearity. In particular, we focus on the fractional…
A local permittivity model is proposed to accurately characterize spatial dispersion in non-local wire-medium (WM) structures with arbitrary terminations. A closed-form expression for the local thickness-dependent permittivity is derived…
A detailed distribution of the force of electromagnetic radiation in and around dielectric media can be obtained by a direct application of the Lorentz law of force in conjunction with Maxwell's equations. We develop a theory of the force…
The dielectric susceptibility of a wide class of dielectric materials follows, over extended frequency ranges, a fractional power-law frequency dependence that is called the "universal" response. The electromagnetic fields in such…
Full orbit dynamics of charged particles in a $3$-dimensional helical magnetic field in the presence of $\alpha$-stable L\'evy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo…
The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller…
The dispersion characteristics of an circularly polarized electromagnetic wave of arbitrary amplitude, propagating in a highly (thermally and kinematically) relativistic plasma, are shown to approach those of a linear wave in an…
Using the Finite Difference Time Domain method, we solve Maxwell's equations numerically and compute the distribution of electromagnetic fields and forces inside material media. The media are generally specified by their dielectric…