Volume 77, Number 2, January 2007
Article Number 20006
Number of page(s) 6
Section General
Published online 18 January 2007
EPL, 77 (2007) 20006
DOI: 10.1209/0295-5075/77/20006

Intermittent search processes in disordered medium

M. 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