Optimal persistent random walks

Random walks are a cornerstone of statistical physics. While Brownian motion has long been under scrutiny, there is a growing interest in a different type of motion: persistent walks. Examples abound in active matter and biological world, from self-propelled particles and crawling cells to foraging animals and a plethora of swimming micro-organisms. The statistical properties of such random motions are often unknown yet they play a key role in many vital functions of the organisms and ultimately in their survival.

One striking instance of persistent random motion is the run-and-tumble of bacteria. Bouts of persistent motion ("run") are interspersed with sudden changes of direction ("tumble"). Recent research reveals that bacteria display a fascinating repertoire of swimming patterns, which differ in their run and tumble characteristics [1,2]. Why? Which benefits come with each swimming strategy?

The goal of the internship is to address this question for confined environments, which are found in many bacterial habitats. Using an analytical approach based on a Fokker-Planck equation and numerical simulations, we will characterize the transport properties of various swimming patterns and identify which one may be optimal.

There are many facets of swimming strategies that can be explored in a PhD thesis. These include transport of bacteria in complex environments such as porous disordered media and optimization of informed swimming strategies, where the strategy is adapted dynamically. Besides, the inference of swimming patterns from experimental trajectories deserves some investigation. Finally, collective effects in assemblies of persistent random walkers, such as clustering and clogging, are also of interest.

The ideal candidate would have a strong background in statistical physics and soft or active matter. No background in biology is required.

[1] Bacteria can exploit a flagellar buckling instability to change direction Son et al, Nature Physics (2013)
[2] Generalized run-and-turn motions: From bacteria to Lévy walks. Detcheverry. Physical Review E (2017)


Keywords: theory, statistical physics, active matter, random walks, micro-organisms.

Contact: François Detcheverry francois.detcheverry@univ-lyon1.fr
Team Liquides et Interfaces, Institut Lumière Matière (Lyon)