Abstract
AbstractWe theoretically address minimal search strategies of self‐propelled particles towards hidden targets in three‐dimensional space. The particles can sense if targets are close, e. g., by detecting released signaling molecules, but they cannot deduce directional cues. We investigate composite search strategies, where particles switch between extensive outer search and intensive inner search; inner search is started when proximity of a target is detected and ends when a certain inner search time has elapsed. In the simplest strategy, active particles move ballistically during outer search, and transiently reduce their directional persistence during inner search. In a second, adaptive strategy, particles exploit a dynamic scattering effect by reducing directional persistence only outside a well‐defined target zone. These two search strategies require only minimal information processing capabilities, yet increase target encounter rates substantially. The optimal inner search time scales as power‐law with exponent −2/3 with target density, reflecting a trade‐off between exploration and exploitation.
Highlights
We theoretically address minimal search strategies of active, self-propelled particles towards hidden targets in three-dimensional space
We propose a minimal model of an Active Brownian Particle (ABP) that regulates its directional persistence in response to local cues
(ii) Adaptive inner search: During inner search, the ABP uses a position-dependent rotational diffusion coefficient Drot(x) that depends on its distance R from the nearest target: the agent uses ballistic motion with Drot = D1 = 0 if the target is within the detection radius with R ≤ R1, while the agent moves with reduced directional persistence with Drot = D2 > 0 for R > R1
Summary
We will assume ballistic motion for outer search. Directional persistence is a key kinetic parameter of self-propelled microswimmers, which is set by a competition between swimming speed and directional fluctuations; directional fluctuations can be of thermal origin or originate from active fluctuations of the propulsion mechanism itself. (ii) Adaptive inner search: During inner search, the ABP uses a position-dependent rotational diffusion coefficient Drot(x) that depends on its distance R from the nearest target: the agent uses ballistic motion with Drot = D1 = 0 if the target is within the detection radius with R ≤ R1, while the agent moves with reduced directional persistence with Drot = D2 > 0 for R > R1. This strategy exploits a generic scattering effect that provides ABPs with multiple search attempts [5]. ABP that head away from the target will switch to motion with low directional persistence as soon as they move beyond distance R1, which results in a high probability to reverse direction and enter the target (a) (b) First passage time distribution
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