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We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The… (More)

The asymptotic behavior for the Vlasov–Poisson–Fokker–Planck system in bounded domains is analyzed in this paper. Boundary conditions defined by a scattering kernel are considered. It is proven that the distribution of particles tends for large time to a Maxwellian determined by the solution of the Poisson–Boltzmann equation with Dirichlet boundary… (More)

In this paper, a stochastic model [5] for the turbulent fiber lay-down in the industrial production of nonwoven materials is extended by including a moving conveyor belt. In the hydrodynamic limit corresponding to large noise values, the transient and stationary joint probability distributions are determined using the method of multiple scales and the… (More)

Charge transport in semiconductor superlattices can be described through a discrete drift-diffusion model. In this model, we identify some small parameter h > 0, related to the ratio between the length of a superlattice period and the observation length scale. Specifically, we investigate a regime where the length of the superlattice period is small while… (More)

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems… (More)

Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy principle can be used to close the… (More)