Related papers: Capture of a diffusive prey by multiple predators …
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we…
In this chapter, we consider the problem of a non-Markovian random walker (displaying memory effects) searching for a target. We review an approach that links the first passage statistics to the properties of trajectories followed by the…
Many physical, chemical, and biological systems depend on the first passage time (FPT) of a diffusive searcher to a target. Typically, this FPT is much slower than the characteristic diffusion timescale. For example, this is the case if the…
First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
In this paper we study some aspects of search for an immobile target by a swarm of N non-communicating, randomly moving searchers (numbered by the index k, k = 1, 2,..., N), which all start their random motion simultaneously at the same…
We analyze predator-prey dynamics in one dimension in which a Brownian predator adopts a chasing strategy that consists in stochastically resetting its current position to locations previously visited by a diffusive prey. We study three…
We develop a model to compute the first-passage time of a random walker in a crowded environment. Hard-core particles with the same size and diffusion coefficient than the tracer diffuse, and the model allows to compute the first passage…
The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two-…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
First passage times (FPTs) are often used to study timescales in physical, chemical, and biological processes. FPTs generically describe the time it takes a random "searcher" to find a "target." In many systems, the important timescale is…
Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
Finding a target in a complex environment is a fundamental challenge in nature, from chemical reactions to sperm reaching an egg. An effective strategy to reduce the time needed to reach a target is to deploy many searchers, increasing the…
Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between…
We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
How long does it take a random walker to reach a given target point? This quantity, known as a first passage time (FPT), has led to a growing number of theoretical investigations over the last decade1. The importance of FPTs originates from…
Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two…
We consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive…