Théorique, numérique
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. Why? Which benefits come with each swimming strategy? The goal of the internship is to understand theoretically the statistical properties of run-and-tumble motion and assess their optimality.