Title: The topography of the environment alters the optimal search strategy for active particles,
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, as well as 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 {\alpha} <= 1 are generally believed to optimize the search process.
However, most search spaces present complex topographies, with boundaries,
barriers and obstacles. 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 towards less ballistic and
more Brownian strategies. We consider an active particle performing a blind
search in a two-dimensional space with steps drawn from a Lévy distribution
with exponent varying from {\alpha} = 1 to {\alpha} = 2 (Brownian). We
demonstrate that the optimal search strategy depends on the topography of the
environment, with {\alpha} assuming intermediate values in the whole range
under consideration. We interpret these findings in terms of a simple
theoretical model, and discuss their robustness to the addition of Brownian
diffusion to the searcher's motion. Our results are relevant for search
problems at different length scales, from animal and human foraging to
microswimmers' taxis, to biochemical rates of reaction.