Intermittent search processes in disordered mediumM. Moreau, O. Bénichou, C. Loverdo and R. Voituriez
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 in final form 20 November 2006; published January 2007
published online 18 January 2007
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.
05.40.Fb - Random walks and Levy flights .
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion .
02.50.-r - Probability theory, stochastic processes, and statistics .
© Europhysics Letters Association 2007