Related papers: Analysis of a generalised Boltzmann equation for a…
This study unveils the time-space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time-space fabric on physical behaviors and accordingly derive…
We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
An analytical formula is derived for particle and energy densities of fermions and bosons, and their ballistic momentum and energy currents for anisotropic energy dispersions in generalized dimensions. The formulation considerably…
A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz…
The general equation for the flux of an electrolyte in solution in the presence of an external magnetic field was derived mathematically in accordance with the Onsager formalism of irreversible thermodynamics. The time reversal symmetry was…
Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of…
Transport surrounding is full of all kinds of fields, like particle potential, external potential. Under these conditions, how elements work and how position and momentum redistribute in the diffusion? For enriching the Fick law in…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
We discuss the kinetics of the disordered interacting Bose gas using the Boltzmann transport equation. The theory may serve as a unifying framework for studying questions of dynamics of the expanding Bose gas at different stages of 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…
We study Lorentz processes in two different settings. Both cases are characterized by infinite expectation of the free-flight times, contrary to what happens in the classical Gallavotti-Spohn models. Under a suitable Boltzmann-Grad type…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
We investigate in this article the long-time behaviour of the solutions to the energy-dependant, spatially-homogeneous, inelastic Boltzmann equation for hard spheres. This model describes a diluted gas composed of hard spheres under…
We study a fuzzy Boltzmann equation, where particles interact via delocalised collisions, in contrast to classical Boltzmann equations. We discuss the existence and uniqueness of solutions and provide a natural variational characterisation…
We investigate the transport behavior of finite modular quantum systems. Such systems have recently been analyzed by different methods. These approaches indicate diffusive behavior even and especially for finite systems. Inspired by these…