Lifetime of a target in the presence of N independent walkers

TL;DR

This paper investigates the survival probability and mean lifetime of a target surrounded by multiple diffusing walkers, analyzing effects of initial distribution, trap quality, and search optimization strategies in various spatial settings.

Contribution

It provides a comprehensive analysis of target lifetime considering multiple factors, including number of walkers, initial conditions, and intermittent search strategies, extending previous single-walker models.

Findings

Mean target lifetime depends on the number and initial distribution of walkers.

Imperfect trapping affects the target survival probability.

Intermittent motion can optimize search efficiency.

Abstract

We study the survival probability of an immobile target in presence of N independent diffusing walkers. We address the problem of the Mean Target Lifetime and its dependence on the number and initial distribution of the walkers when the trapping is perfect or imperfect. We consider the diffusion on lattices and in the continuous space and we address the bulk limit corresponding to a density of diffusing particles and only one isolated trap. Also, we use intermittent motion for optimization of search strategies.