Related papers: Gas diffusion in nanoporous thin films
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
The flow of ions through permeable channels causes voltage drop in physiological nanodomains such as synapses, dendrites and dendritic spines, and other protrusions. How the voltage changes around channels in these nanodomains has remained…
We consider the generalized Milne problem in non-conservative plane-parallel optically thick atmosphere consisting of two components - the free electrons and small dust particles. Recall, that the traditional Milne problem describes the…
Boundary value problems for diffusion in singularly perturbed domains (domains with small holes removed from the interior) is a topic of considerable current interest. Applications include intracellular diffusive transport and the spread of…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
The paper addresses the single-file diffusion in the presence of an absorbing boundary. The emphasis is on an interplay between the hard-core interparticle interaction and the absorption process. The resulting dynamics exhibits several…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
Three problems are considered in which inhomogeneous broadening can yield unusual consequences. One problem involves the energy levels of atoms moving within nanopores of nearly cylindrical cross section. A second involves atomic or…
Freezing of dispersions is omnipresent in science and technology. While the passing of a freezing front over a solid particle is reasonably understood, this is not so for soft particles. Here, using an oil-in-water emulsion as a model…
Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…
Plasmonic nanoparticles resonantly couple to and confine light below the diffraction limit. This mechanism has enabled a modern renaissance in optical materials, with potential applications ranging from sensing and circuitry to renewable…
Large-scale molecular dynamics simulations are used to simulate a layer of nanoparticles diffusing on the surface of a liquid. Both a low viscosity liquid, represented by Lennard-Jones monomers, and a high viscosity liquid, represented by…
In Physica A vol 387(24) (2008) pp6079-6094 [1], a kinetic equation for gas flows was proposed that leads to a set of four macroscopic conservation equations, rather than the traditional set of three equations. The additional equation…
The propagation and transmission of Bessel beams through nano-layered structures has been discussed recently. Within this framework we recognize the formation of unguided diffraction-free waves with the spot size approaching and…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
We consider a diffusion process under a local weak H\"{o}rmander condition on the coefficients. We find Gaussian estimates for the density in short time and exponential lower and upper bounds for the probability that the diffusion remains…
We study axisymmetric accretion of slowly rotating matter onto a gravitation center. The process of the flow restructuring is presented as the angular velocity of accreting gas approaches the Keplerian velocity. For spherically-symmetric…