Target search of active particles in complex environments

Abstract

Microswimmers are microscopic active agents capable of harvesting energy from the surrounding environment and converting it into self-propulsion and directed motion. This peculiar feature characterizes them as out-of-equilibrium systems that break microscopic reversibility. The problem of finding a specific target in a complex environment is essential for these agents since it is employed for a variety of purposes, from foraging nourishment to escaping potential threats. Here, we provide a detailed study of the target search process for microswimmers exploring complex environments. To this end, we generalize Transition Path Theory, the rigorous statistical mechanics description of transition processes, to the target-search problem. One of the main results of this thesis is the generalization to non-equilibrium systems of the Transition Path Sampling (TPS) algorithm, which was originally designed to simulate rare transitions in passive systems. The TPS algorithm relies on microscopic reversibility for its functioning, therefore its generalization to out-of-equilibrium systems lacking detailed balance and microscopic reversibility has remained a major challenge. Within this work, we generalize the TPS algorithm to the case of an active Brownian particle, i.e. a paradigmatic model for microswimmers, and we obtain a first insight into the counterintuitive target-search pathways explored by these agents. The second result of this thesis is a systematic characterization of the target-search path ensemble for an active particle exploring an energy landscape. The third and final original contribution of this Ph.D. thesis is the generalization of the concept of the committor function to target-search problems, with a validation of our theory against experiments of a camphor self-propelled disk.