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The topography of the environment alters the optimal search strategy for active particles

Journal article
Authors Giorgio Volpe
Giovanni Volpe
Published in Proceedings of the National Academy of Sciences of the United States of America
Volume 114
Issue 43
Pages 11350-11355
ISSN 0027-8424
Publication year 2017
Published at Department of Physics (GU)
Pages 11350-11355
Language en
Keywords Active particles, Anomalous diffusion, Complex topographies, Lévy walks, Optimal search strategy
Subject categories Physical Sciences


In environments with scarce resources, adopting the right search strategy can make the difference between succeeding and failing, even between life and death. At different scales, this applies to molecular encounters in the cell cytoplasm, to animals looking for food or mates in natural landscapes, to rescuers during search and rescue operations in disaster zones, and to genetic computer algorithms exploring parameter spaces. When looking for sparse targets in a homogeneous environment, a combination of ballistic and diffusive steps is considered optimal; in particular, more ballistic Lévy flights with exponent α ≤1 are generally believed to optimize the search process. However, most search spaces present complex topographies. What is the best search strategy in these more realistic scenarios? Here, we show that the topography of the environment significantly alters the optimal search strategy toward less ballistic and more Brownian strategies. We consider an active particle performing a blind cruise search for nonregenerating sparse targets in a 2D space with steps drawn from a Lévy distribution with the exponent varying from α= 1 to α= 2 (Brownian). We show that, when boundaries, barriers, and obstacles are present, the optimal search strategy depends on the topography of the environment, with assuming intermediate values in the whole range under consideration.We interpret these findings using simple scaling arguments and discuss their robustness to varying searcher's size. Our results are relevant for search problems at different length scales from animal and human foraging to microswimmers' taxis to biochemical rates of reaction.

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