Related papers: Large-time asymptotics for a matrix spin drift-dif…
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…
By generalizing the usual current density to a matrix with respect to spin variables, a general equation of continuity satisfied by the density matrix and current density matrix has been derived. This equation holds in arbitrary spin-orbit…
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…
We propose and analyze a decoupled time-marching scheme for the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation for the spin accumulation. This model describes the interplay of magnetization and…
By inelastic scattering of polarized neutrons near the (200)-Bragg reflection, the susceptibilities and linewidths of the spin waves and the longitudinal spin fluctuations were determined separately. By aligning the momentum transfers q…
We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed matter-type. This is done for a certain class of initial quantum states…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
We study the effect of the impurity density on lifetimes and relaxation lengths of electron spins in the presence of a static electric field in a n-type GaAs bulk. The transport of electrons and the spin dynamics are simulated by using a…
We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation…
A discrete drift-diffusion model is derived from a microscopic sequential tunneling model of charge transport in weakly coupled superlattices provided temperatures are low or high enough. Realistic transport coefficients and novel contact…
A disordered version of the one dimensional asymmetric exclusion model where the particle hopping rates are quenched random variables is studied. The steady state is solved exactly by use of a matrix product. It is shown how the phenomenon…
Using exact diagonalization numerical methods, as well as analytical arguments, we show that for the typical electron densities in chaotic and disordered dots the peak spacing distribution is not bimodal, but rather Gaussian. This is in…
A theory of spin-polarized electron transport in ferromagnet/semiconductor heterostructures, based on a unified semiclassical description of ballistic and diffusive transport in semiconductor structures, is developed. The aim is to provide…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive and based on the Helmholtz decomposition of the drift and a…
We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
In a previous paper(2021), the author studied the asymptotic behavior of coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. As a result, he proved that…