Related papers: Exact mean exit time for surface-mediated diffusio…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
The purpose of this paper is to provide a formula for the effective diffusion operator obtained by projecting the 3-dimensional diffusion equation onto a 2-dimensional plane, assuming reflective boundary conditions at two surfaces in…
The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism that allows us to evaluate the…
The position $x(t)$ of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray $x=v_0 t$, where $v_0$ is the average drift. However,…
Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and…
In this paper we consider a multiparticle version of a recent probabilistic framework for studying diffusion-mediated surface reactions. The basic idea of the probabilistic approach is to consider the joint probability density or…
A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…
A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get a upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and…
By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to…
We propose a finite volume method on general meshes for the discretization of a degenerate parabolic convection-reaction-diffusion equation. Equations of this type arise in many contexts, such as the modeling of contaminant transport in…
The lateral diffusion coefficient of a Brownian particle on a two-dimensional random surface is studied in the quenched limit for which the surface configuration is time-independent. We start with the stochastic equation of motion for a…
The function of many membrane-enclosed intracellular structures relies on release of diffusing particles that exit through narrow pores or channels in the membrane. The rate of release varies with pore size, density, and length of the…
We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
Thermally activated escape of an over-damped particle from a metastable well under the action of a time-ramped force is studied. We express the mean first passage time (MFPT) as the solution to a partial differential equation, which we…
In this paper we develop some new variational principles for the exit time of non-symmetric diffusions from a domain. As applications, we give some comparison theorems and monotonicity law between different diffusions.
We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean…
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…