First-Passage Times ind-Dimensional Heterogeneous Media

Abstract

Although there are many theoretical studies of the mean first-passage time (MFPT), most neglect the diffusive heterogeneity of real systems. We present exact analytical expressions for the MFPT and residence times of a pointlike particle diffusing in a spherically symmetric d-dimensional heterogeneous system composed of two concentric media with different diffusion coefficients with an absorbing inner boundary (target) and a reflecting outer boundary. By varying the convention, e.g., Itō, Stratonovich, or isothermal, chosen to interpret the overdamped Langevin equation with multiplicative noise describing the diffusion process, we find different predictions and counterintuitive results for the residence time in the outer region and hence for the MFPT, while the residence time in the inner region is independent of the convention. This convention dependence of residence times and the MFPT could provide insights about the heterogeneous diffusion in a cell or in a tumor, or for animal and insect searches inside their home range.

Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces

“…On the other hand, homogenization techniques were used to substitute piecewise constant reactivity κ(s) by an effective homogeneous reactivity [31][32][33][51][52][53][54][55][56][57][58]. More recent works investigated how the mean reaction time is affected by a finite lifetime of diffusing particles [59][60][61], by partial reactivity and interactions [63,64], by target aspect ratio [65], by reversible target-binding kinetics [66,67] and surface-mediated diffusion [68][69][70][71], by heterogeneous diffusivity [72], and by rapid re-arrangments of the medium [73][74][75]. Some of the related effects onto the whole distribution of reaction times were analyzed [76][77][78][79][80].…”

Interlacing relaxation and first-passage phenomena in reversible discrete and continuous space Markovian dynamics

“…In a broader context, first passage concepts were invoked in studies of kinetics in complex media, such as reactions in fractal-like [12,13] and planar domains [14,15], in inhomogeneous cellular environments [16][17][18][19], in the study of neural networks [20,21], ultra cold atoms [22], as well as in diverse narrow escape problems [23][24][25][26][27][28] and so-called intermittent search strategies involving searching agents with internal dynamics [29,30] (see also [31] for a review).…”

Survival probability of stochastic processes beyond persistence exponents

“…In order to determine the time it takes for a random walker to find a target, or the probability that a stochastic signal has not reached a threshold up to time t, it is required to analyse the First-Passage Time (FPT) statistics. This has attracted considerable attention from physicists and mathematicians in the last decades [1][2][3][4][5][6] notably because of the relevance of FPT related quantities in contexts as varied as diffusion controlled reactions, finance, search processes, or biophysics [7,8].…”