Search

The authors study an intermittent search process combining diffusion and "teleportation" phases in a d-dimensional spherical continuous system and in a regular lattice. The searcher alternates diffusive phases, during which targets can be discovered, and fast phases (teleportation) which randomly relocate the searcher, but do not allow for target detection. The authors show that this alternation can be favorable for minimizing the time of first discovery, and that this time can be optimized by a convenient choice of the mean waiting times of each motion phase. The optimal search strategy is explicitly derived in the continuous case and in the lattice case. Arguments are given to show that much more general intermittent motions do provide optimal search strategies in d dimensions. These results can be useful in the context of heterogeneous catalysis or in various biological examples of transport through membrane pores.

What is the fastest way of finding a randomly hidden target? Experimental observations reveal that the search behavior of foraging animals is generally intermittent: active search phases randomly alternate with phases of fast ballistic motion. Here, we study the efficiency of this two state search strategy by calculating analytically the mean first passage time at the target. We model the perception mechanism involved in the active search phase by a diffusive process. We show that the search strategy is optimal when the average duration of "motion phases" varies like the power either 3/5 or 2/3 of the average duration of "search phases" depending on the regime. This scaling accounts for experimental data over a wide range of species, which suggests that the kinetics of search trajectories is a determining factor optimized by foragers and that the perception activity is adequately described by a diffusion process.