Two types of exclusion interactions for self-propelled objects and collective motion induced by their combination

Exclusive interactions between self-driven objects may play crucial roles in their collective behavior, e.g., in collective migration of living cells. Here, such collective behavior is studied based on a simple but sufficient model taking account the exclusion effects, which incorporate the following two distinct kinds of exclusion interactions in two dimensions: The first is the mechanical exclusion wherein two objects mechanically repel each other when they overlap. The second is the scattering exclusion, wherein the directions along which each object tries to move are modulated to avoid overlapping. We propose a theoretical model based on two principles: (1) Each object maintains its own polarity with a fixed strength and attempts to move into the polarity direction and (2) objects interact with each other through the abovementioned exclusions. Based on this model, we look at the difference of consequences and combinatory effects of these two kinds of exclusions. Furthermore, we calculate the polar order of polarity directions without an external directional bias. Our results suggest that the combination of these two kinds of exclusions leads to effectively inelastic scattering of two objects, which eventually gives rise to global polar ordering. We also find that the traveling band can arise by this mechanism of alignment at the intermediate density, as generally seen in collective motion with polar alignment and investigated in various earlier works. Characteristics of transitions among disordered, traveling band, and homogeneously ordered states of the presented model are investigated, and their similarities and differences with those given by the explicit alignment interaction are discussed.