Related papers: Fractional diffusion limit for a kinetic equation …
Inspired by continuum mechanical contact problems with geological fault networks, we consider elliptic second order differential equations with jump conditions on a sequence of multiscale networks of interfaces with a finite number of…
Phase field models frequently provide insight to phase transitions, and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
We derive the equations that describe adsorption of diffusing particles onto a surface followed by additional surface kinetic steps before being transported across the interface. Multistage surface kinetics occurs during membrane protein…
We study the singular limit problem referred to as the fast reaction limit. This problem has been extensively studied when the same reaction term is used in a two-component system. However, the behavior of the solution under different…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
We consider a partial exclusion process evolving on $\mathbb Z^d$ in a random trapping environment. In dimension $d\ge 2$, we derive the fractional kinetics equation \begin{equation*}\frac{\partial^\beta\rho_t}{\partial t^\beta} = \Delta…
Anomalous heat transport observed in low dimensional classical systems is associated to super-diffusive spreading of space-time correlation of the conserved fields in the system. This leads to non-local linear response relation between the…
We present a model treating the kinetics of adsorption of soluble surface-active molecules at the interface between an aqueous solution and another fluid phase. The model accounts for both the diffusive transport inside the solution and the…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e. avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual based…
This paper investigates the diffusion limit of a kinetic BGK-type equation, focusing on its relaxation to a nonlinear aggregation-diffusion equation, where the diffusion exhibits a porous-medium-type nonlinearity. Unlike previous studies by…
We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…
We consider a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with emphasis on rough interfaces which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\ boundary…
DNA denaturation, wetting in two dimensions, depinning of a flux line, and other problems map onto a phase transition with effective long range interaction. It yields giant non-universal critical indexes, arbitrarily large macroscopic…
A paradigm model is suggested for describing the diffusive limit of trajectories of two Lorentz disks moving in a finite horizon periodic configuration of smooth, strictly convex scatterers and interacting with each other via elastic…