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, 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 [Formula: see text] 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 [Formula: see text] to [Formula: see text] (Brownian). We show that, when boundaries, barriers, and obstacles are present, the optimal search strategy depends on the topography of the environment, with [Formula: see text] 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.

Machine learning for active matter

“…Motility, navigation and search strategies are interesting for physics, biology, ecology and robotics. Like foraging animals, active particles can navigate and search complex environments 58,59 . To understand how evolution shaped search strategies of small motile organisms, one can use reinforcement learning to identify optimal and alternative strategies 60 ( Fig.…”

Enhanced propagation of motile bacteria on surfaces due to forward scattering

“…Surprisingly, even though natural bacterial habitats present characteristic features that vary on a spatial scale comparable to that of the cells' motion [7,8], experimental studies of near-surface swimming have mainly focused on smooth surfaces devoid of this natural complexity. Nonetheless, for far-from-equilibrium self-propelling particles, such as motile bacteria, both individual and collective motion dynamics can depend on environmental factors in non-intuitive ways, as recently shown for microscopic non-chiral active particles numerically [31][32][33][34][35] and experimentally [36,37]. Moreover, in environments densely packed with periodic patterns of obstacles, turning angle distributions of bacterial cells change from bulk swimming and their trajectories can be efficiently guided along open channels in the lattice [38,39].…”

Topotaxis of active Brownian particles

“…How sensitive is the performance of topotaxis with respect to the obstacles' shape [18,37,38], the type of motion (e.g., persistent random walk, run-and-tumble, Lévy walk, etc. [18,21,26,[54][55][56]), and the details of particle-obstacle interactions [29,37,[57][58][59]? Another interesting setting of the problem could be obtained by considering random arrangements of obstacles, where, unlike in the lattices studied here, particles can be trapped into convex-shaped features that can significantly alter their motion [26,28].…”

“…ABPs perform persistent self-propelled motion in the direction of the particle orientation in combination with rotational diffusion of this orientation. The motion of active particles has been explored in several complex geometries, including convex [18,19] and nonconvex [20] confinements, mazes [21], walls of funnels [22], interactions with asymmetric [23,24] and chiral [25] passive objects, porous topographies [26] and random obstacle lattices [27][28][29][30]. For a review, see Refs.…”