Hugues Meyer (Theoretical Physics department, Saarland University, Germany)
Optimizing search strategies with memory: general results and application to autochemotactic walkers
The term search process refers to any process in which agents are looking for targets in a well-defined domain. This general definition encompasses a broad scope of phenomena, from foraging in animal species to the search of toxic bodies by immune cells. In most cases, the searching agents need to optimize their strategy in order to maximize the search efficiency, often quantified in terms of first-passage times in statistical physics. In this talk, we will discuss how a search can be optimized if the agents have memory of the locations they have previously visited. This question can be formalized and solved in general terms in order to infer the very optimal strategy for a searcher with a given memory time and to define a lower bound for the mean first-passage time. We will then discuss the concrete case of autochemotactic particles, i.e. agents that generate a self-repeling chemical cue. This phenomenon is for instance observed in ants looking for food, or in some immune cells searching for organisms to eliminate. The chemical information that they produce can be effectively used as a way to memorize the previously visited locations and as a non-local communication channel between particles. For such systems, we will first evaluate how search efficiency can be optimized in the low density regime, and how it compares to the theoretically optimal efficiency. Then, we will show how the search process is impacted as the density of searchers increases. While one might intuitively think that search should be more efficient with more searchers, the formation of bands under certain conditions can make it particularly inefficient. We will discuss the mechanism and conditions for such bands to form.