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

Volpe, G; Volpe, G; (2017) The topography of the environment alters the optimal search strategy for active particles. Proceedings of the National Academy of Sciences of the United States of America , 114 (43) pp. 11350-11355. 10.1073/pnas.1711371114. Green open access

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Abstract

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 α 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.

Type: Article
Title: The topography of the environment alters the optimal search strategy for active particles
Open access status: An open access version is available from UCL Discovery
DOI: 10.1073/pnas.1711371114
Publisher version: http://dx.doi.org/10.1073/pnas.1711371114
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: optimal search strategy, complex topographies, active particles, Lévy walks, anomalous diffusion
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Chemistry
URI: https://discovery.ucl.ac.uk/id/eprint/10025947
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