The fastest of N independent power-law-jump walkers reaches a target at distance X in time X/v + (⟨t⟩/N)(X/(v t0))^α, giving a 1/N speed-up over Brownian search with a crossover at α_c ~ 2 + ln N / ln(X/(v t0)).
Intermittent Run Motility of Bacteria in Gels Exhibits Power-Law Distributed Dwell Times
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While bacterial swimming has been well characterized in uniform liquid environments, only little is known about how bacteria propagate through complex environments, such as gel-like matrices or porous media that are typically encountered in tissue or soil. Here, we study swimming motility of the soil bacterium Pseudomonas putida (P. putida) in polysaccharide matrices formed by different concentrations of agar. P. putida cells display intermittent run-motility in the gel, where run times are exponentially distributed and intermittently occurring dwell times follow a waiting-time distribution with a power-law decay. An analysis of the turn angle distribution suggests that both, flagella mediated turning as well as mechanical trapping in the agar matrix play a role in the overall swimming pattern. Based on the experimentally observed motility pattern and measured waiting-time distributions, we propose a minimal active particle model which correctly describes the observed time dependence of the mean square displacement of the bacterial swimmers.
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Rare Events and Redundancy in Random Walkers Target Search in a Finite Domain
The fastest of N independent power-law-jump walkers reaches a target at distance X in time X/v + (⟨t⟩/N)(X/(v t0))^α, giving a 1/N speed-up over Brownian search with a crossover at α_c ~ 2 + ln N / ln(X/(v t0)).