Related papers: Diffusion models for atomic scale electron current…
We study the problem of electronic conduction in mesoscopic systems when the electrons are allowed to interact not only with static impurities, but also with a scatterer (a phase breaker(PB)) that possesses internal degrees of freedom. We…
In the conventional theory of hopping transport the positions of localized electronic states are assumed to be fixed, and thermal fluctuations of atoms enter the theory only through the notion of phonons. On the other hand, in 1D and 2D…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
A model is developed for describing the transport of charged colloidal particles in an evaporating sessile droplet on the electrified metal substrate in the presence of a solvent flow. The model takes into account the electric charge of…
The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of…
A recent description of the motion of atoms in a classical monatomic system in liquid and supercooled liquid states divides the motion into two parts: oscillations within a given many-particle potential valley, and transit motion which…
Predicting atomic-scale crack propagation in aluminum nitride (AlN) is critical for semiconductor reliability but remains prohibitively expensive via molecular dynamics (MD). We develop a diffusion-based generative machine learning model to…
Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially…
Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
The symmetric part of the distribution of the electrons in a semiconductor submicron film, placed between a heater and refrigeration unit, is derived and analyzed. It is shown that, in general, it is of non-Fermi (non-Maxwellian) nature. A…
We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the…
Quasi-one dimensional electron systems have been created using a suspended helium film on a structured substrate. The electron mobility along the channel is calculated by taking into account the essential scattering processes of electrons…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We show that in the linear response approximation only entropy provides coupling between thermal and electric phenomena. The dissipationless quantum currents -- magnetization, superconducting, persistent and topological edge currents -- do…
We generalize Einstein's master equation for random walk processes by considering that the probability for a particle at position $r$ to make a jump of length $j$ lattice sites, $P_j(r)$ is a functional of the particle distribution function…
The relationship between excess entropy and diffusion is revisited by means of large-scale computer simulation combined to supervised learning approach to determine the excess entropy for the Lennard-Jones potential. Results reveal that it…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
Several algorithms have been used for mass transfer between particles undergoing advective and macro-dispersive random walks. The mass transfer between particles is required for general reactions on, and among, particles. The mass transfer…