Statistical physics of self-propelled particles

Abstract

Self-propelled particles (SPP) are a modern topic of interdisciplinary research at the frontier between physics and biology. These entities take up energy from their environment and convert (a part of) it into motion. This ability to move autonomously enables them to generate a new variety of singular properties and of collective dynamical behaviors. Autonomous motion and the behavioral patterns associated to SPPs are inherent to many living objects but also to some engineered particles and constructs. Currently, various aspects of the physics of self-propelling particles are in the focus of scientific research. They encompass, among others, the mechanisms that bring about autonomous motion, the description of the types of motion, as well as the role played by fluctuations in the emergence of novel behaviors. Currently, the research on SPP points to three major directions, namely (i) the motion and transport of individual self-propelled objects, (ii) the motion of active particles in external and/or self-generated fields, and (iii) the collective behavior of a group of particles that act upon each other via binary interactions. Recently, an increasing number of scientific studies on SPP is observed with a main focus on the determination of the statistical properties of the motion. This is the case in studies of contemplative motion, i.e., motion where the particle is free to move without any confinements or gradients acting upon them. One of the main objectives of such studies is to assess and understand the role of fluctuations in the motion of SPPs. The statistics of such free migration may provide useful information on the efficiency of the different types of motion. Many systems, however, move either in an external gradient field, or even produce their own gradient field that, in turn, affects the motion of the SPPs. Such types of interplay may be found in biological systems where a cell or organism relays a chemoattractant, pheromone, or the like, but also in non-living systems, where the swimming of a particle may induce hydrodynamic fields that affect the swimming of the other particles. Such interactions may lead to motions, the statistics of which differ considerably from those found for free migration. Finally, systems of SPPs that are coupled to each other by binary interactions may generate interesting patterns of group dynamics, for instance, as seen in herds of sheep, schools of fish, or flocks of birds. Such collective motion may provide huge advantages for the members of the group, which adds to the scientific interest in such