Related papers: Exact mean exit time for surface-mediated diffusio…
The narrow escape problem concerns the time needed for a diffusing particle to exit a confining domain through a small hole in the boundary. While this problem is now well-understood, determining the escape time for a particle that must…
The time dependency of the diffusion coefficient of particles in porous media is an efficient probe of their geometry. The analysis of this quantity, measured e.g. by nuclear magnetic resonance (PGSE-NMR), can provide rich information…
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…
The out-of-equilibrium character of active particles, responsible for accumulation at boundaries in confining domains, determines not-trivial effects when considering escape processes. Non-monotonous behavior of exit times with respect to…
In this paper we consider a star-shaped hypersurface flow by mean curvature. Without any assumption on the convexity, we give a new proof of gradient estimate for a short time. As an application, we also give a lower bound for the blowing…
We consider a particle diffusing along the links of a general graph possessing some absorbing vertices. The particle, with a spatially-dependent diffusion constant D(x) is subjected to a drift U(x) that is defined in every point of each…
In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We study the problem of optimal stopping of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a…
We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by one- or multi-dimensional Ornstein-Uhlenbeck process. We start by recalling the main derivation steps of a…
By an extension of the Bethe ansatz method used by Gwa and Spohn, we obtain an exact expression for the large deviation function of the time averaged current for the fully asymmetric exclusion process in a ring containing $N$ sites and $p$…
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…
We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a…
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete…
It is given an effective upper estimate of expectation of |T_1-T_2|, where T_1 and T_2 are the first exit times from a region for two vector diffusion processes.
We study mixing times of the symmetric and asymmetric simple exclusion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well…
We propose a mathematical model for computing drug release from multi-layer capsules. The diffusion problem in such heterogeneous layer-by-layer composite medium is described by a system of coupled partial differential equations, which we…
The concept of a mean first passage time is used to study the time lapse over which a fissioning system may emit light particles. The influence of the "transient" and "saddle to scission times" on this emission are critically examined. It…
We derive an expression for the mean square displacement of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, $t$, and Planck's constant, $\hbar$, and allows a…
A knowledge of the particle escape time from the acceleration regions of many space and astrophysical sources is of critical importance in the analysis of emission signatures produced by these particles and in the determination of the…