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The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is…
The optimization of the usual entropy $S_1[p]=-\int du p(u) ln p(u)$ under appropriate constraints is closely related to the Gaussian form of the exact time-dependent solution of the Fokker-Planck equation describing an important class of…
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global well-posedness result with instantaneous smoothness effect,…
The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail is reexamined from a fundamental statistical point of view making use of the division of particle orbits into waiting…
A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
The properties of the nonextensive parameter q and the Tsallis distribution for self-gravitating systems are studied. A mathematical expression of q is deduced based on the generalized Boltzmann equation, the q-H theorem and the generalized…
We study the collision frequencies of particles in the weakly and highly ionized plasmas with the power-law q-distributions in nonextensive statistics. We derive the average collision frequencies of neutral-neutral particle,…
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as…
Using generic (non)extensive statistics, in which the underlying system autonomously manifests its extensive and nonextensive statistical nature, we extract various fit parameters from the CMS experiment and compare these to the…
We point out a connection between anomalous quantum transport in an optical lattice and Tsallis' generalized thermostatistics. Specifically, we show that the momentum equation for the semiclassical Wigner function that describes atomic…
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For…
This paper is devoted to the anomalous diffusion limit of kinetic equations with a fractional Fokker-Planck collision operator in a spatially bounded domain. We consider two boundary conditions at the kinetic scale: absorption and specular…
Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter $q$. A number of possible sources of such distributions are presented in more detail. It is further…
Nonthermal relativistic plasmas are ubiquitous in astrophysical systems like pulsar wind nebulae and active galactic nuclei, as inferred from their emission spectra. The underlying nonthermal particle acceleration (NTPA) processes have…
In this letter, a theoretical method for the analysis of diffusive flux/current to limited scale self-affine random fractals is presented and compared with experimentally measured electrochemical current for such roughness. The theory…
The temporal Fokker-Planck equation is analytically integrated in an arbitrary number of spatial dimensions but with the 2D and 3D results highlighted. It is shown that a temporal power-law ansatz for the anisotropic diffusion coefficients…
Deviations from an idealized equilibrium phase transition picture in nuclear multifragmentation is studied in terms of the entropic index. We investigate different heat-capacity features in the canonical quantum statistical model of nuclear…
We investigate the multiplicity fluctuations observed in high-energy nuclear collisions attributing them to intrinsic fluctuations of temperature of the hadronizing system formed in such processes. To account for these fluctuations we…
We report studies on first-order Fermi acceleration in parallel modified shock waves with a large scattering center compression ratio expected from turbulence transmission models. Using a Monte Carlo technique we have modeled particle…