We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers". A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate $ω_m$. While still alive, the creeper has a finite mean frequency $ω$ of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an $ω_m$-dependent optimal frequency $ω=ω_{opt}$ that maximizes the probability of eventual target detection. We work primarily in one-dimensional ($d=1$) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in $d=2$ domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the $d=1$ case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.
Evanescent random walker on networks: Hitting times, budget renewal, and survival dynamics
Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert（索邦大学，法国国家科学研究中心，让·勒朗·达朗贝尔研究所）；Departamento de Física, Universidad Nacional de Colombia（哥伦比亚国立大学生物物理系）
Lévy walkers inside spherical shells with absorbing boundaries: Towards settling the optimal Lévy walk strategy for random searches
Federal University of Rio Grande do Norte（北里奥格兰德联邦大学）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Universidade Federal de Pernambuco（伯南布哥联邦大学）；National Institute of Science and Technology of Complex Systems, Federal University of Rio Grande do Norte（复杂系统科学与技术国家研究所，北里奥格兰德联邦大学）
Resetting mediated navigation of active Brownian searcher in a homogeneous topography
Indian Statistical Institute（印度统计研究所）；International Institute of Information Technology（国际信息技术学院）；The Institute of Mathematical Sciences（数学科学研究所）；Homi Bhabha National Institute（霍米·巴哈国家研究所）
