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Optimal search strategies of space-time coupled random walkers with finite lifetimes

D. Campos1,*, E. Abad2, V. Méndez1, S. B. Yuste3, and K. Lindenberg4

  • 1Grup de Física Estadística, Departament de Física, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
  • 2Departamento de Física Aplicada and Instituto de Computación Científica Avanzada (ICCAEX), Centro Universitario de Mérida, Universidad de Extremadura, E-06800 Mérida, Spain
  • 3Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEX), Universidad de Extremadura, E-06071 Badajoz, Spain
  • 4Department of Chemistry and Biochemistry, and BioCircuits Institute, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, USA

  • *Daniel.Campos@uab.cat
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Phys. Rev. E 91, 052115 – Published 11 May, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.052115

Abstract

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 ωm. 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 ωm-dependent optimal frequency ω=ωopt 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.

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Phys. Rev. E 91, 052115– Published 11 May, 2015
  • Received 9 March 2015
Article part of CHORUS

©2015 American Physical Society

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