Related papers: First Invader Dynamics in Diffusion-Controlled Abs…
Cover times measure the speed of exhaustive searches which require the exploration of an entire spatial region(s). Applications include the immune system hunting pathogens, animals collecting food, robotic demining or cleaning, and computer…
Consider a one dimensional diffusion process on the diffusion interval $I$ originated in $x_0\in I$. Let $a(t)$ and $b(t)$ be two continuous functions of $t$, $t>t_0$ with bounded derivatives and with $a(t)<b(t)$ and $a(t),b(t)\in I$,…
The Schr\"odinger integral-equation approach for calculating the classical first-passage time (C-fpt) probability density is extended to the case of quantum first-passage time (Q-fpt). Using this extension, we have calculated analytically…
In this paper, a diffusion-based molecular communication channel is modeled in presence of a probabilistic absorber. The probabilistic absorber is an absorber which absorbs molecules upon collision with probability q. With random walk…
The escape dynamics of sticky particles from textured surfaces is poorly understood despite importance to various scientific and technological domains. In this work, we address this challenge by investigating the escape time of adsorbates…
For a given barrier $S$ and a one-dimensional jump-diffusion process $X(t),$ starting from $x<S,$ we study the probability distribution of the integral $A_S(x)= \int_0 ^ {\tau_S(x)}X(t) \ dt$ determined by $X(t)$ till its first-crossing…
We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted "onion-shell" geometry bounded by two nested membranes of…
We establish general moment estimates for the discrete and continuous exit times of a general It\^o process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the…
Initial conditions for star formation in clusters are estimated for protostars whose masses follow the initial mass function (IMF) from 0.05 to 10 solar masses. Star-forming infall is assumed equally likely to stop at any moment, due to gas…
We investigate a stochastic process consisting of a two-dimensional particle with anisotropic diffusion, mortality rate and a drift velocity, in the presence of an absorbing boundary. After the particle has encountered the boundary, the…
We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle.…
In this chapter, we review our recent work on first passage time (FPT) problems for absorption by a target whose interface is semipermeable. For pedagogical reasons, we focus on a single Brownian particle searching for a single target in a…
Using dark matter only N-body cosmological simulations, we measure the pericentre distance of dark matter halos on their first infall into group and cluster halos. We find that the pericentre distance (R$_{\rm{peri}}$) is an important…
A granular system confined in a quasi two-dimensional box that is vertically vibrated can transit to an absorbing state in which all particles bounce vertically in phase with the box, with no horizontal motion. In principle, this state can…
The release of a gas limited by surface desorption, or by diffusion from the bulk of spherical pebbles is revisited. A method is proposed to identify the release limiting process, by comparing a partial temperature ramp, up to slightly…
We present an analytical framework to study the first-passage (FP) and first-return (FR) distributions for the broad family of models described by the one-dimensional Fokker-Planck equation in finite domains, identifying general properties…
We propose an approach for estimating the probability that a given small target, among many, will be the first to be reached in a molecular dynamics simulation. Reaching small targets out of a vast number of possible configurations…
We study the survival probability and the corresponding first passage time density of fractional Brownian motion confined to a two-dimensional open wedge domain with absorbing boundaries. By analytical arguments and numerical simulation we…
We consider a Brownian particle, with diffusion constant D, moving inside an expanding d-dimensional sphere whose surface is an absorbing boundary for the particle. The sphere has initial radius L_0 and expands at a constant rate c. We…
We explore the effect of stochastic resetting on the first-passage properties of space-dependent diffusion in presence of a constant bias. In our analytically tractable model system, a particle diffusing in a linear potential…