Intermittent search processes in disordered medium

Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, Université Pierre et Marie Curie - 4 Place Jussieu, 75252 Paris, France

Received: 23 June 2006
Accepted: 20 November 2006

Abstract

Intermittent search processes alternate “reacting” phases, during which the searcher slowly explores its domain with a high probability to detect a target, and fast relocation phases which do not allow for target detection. This behavior, commonly observed in many situations, is studied here in the case of a Poisson distribution of targets. It is shown analytically and numerically that intermittency is useful and allows one to minimize the search time. A scaling law holds between the optimal durations of the phases, however with an exponent different from the one obtained previously for a regular distribution of targets. Furthermore, numerical simulations show that the average search time is longer for a Poisson target distribution than for regularly spaced targets. Thus, at least in the present model, order in the target distribution appears to be favorable for optimizing the search efficiency.