Related papers: Diffusion equations in inhomogeneous solid having …
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…
Particle scattering and vacuum instability in a constant inhomogeneous electric field of particular peak configuration that consists of two (exponentially increasing and exponentially decreasing) independent parts are studied. It presents a…
Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional,…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
We examine the validity of the kinetic description of wave turbulence for a model quadratic equation. We focus on the space-inhomogeneous case, which had not been treated earlier; the space-homogeneous case is a simple variant. We determine…
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,…
We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a…
We consider a particle moving with equation of motion $\dot x=f(t)$, where $f(t)$ is a random function with statistics which are independent of $x$ and $t$, with a finite drift velocity $v=\langle f\rangle$ and in the presence of a…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
The Fokker-Planck Equation, applied to transport processes in fusion plasmas, can model several anomalous features, including uphill transport, scaling of confinement time with system size, and convective propagation of externally induced…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
The characterization of the formation mechanisms of amorphous solids is a large avenue for research, since understanding its non-Arrhenius behavior is challenging to overcome. In this context, we present one path toward modeling the…
We consider a kinetic equation describing evolution of a particle distribution function in a system with nonlinear wave-particle interactions (trappings into a resonance and nonlinear scatterings). We study properties of its solutions and…
A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account…
In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the autors [1], which takes into account nonlinear effects, the role of the cubic in concentration…
The kinetics of the deposition of colloidal particles onto a solid surface is analytically studied. We take into account both the diffusion of particles from the bulk as well as the geometrical aspects of the layer of adsorbed particles. We…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at…
The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the existence of…