概要：Collective pattern formations of self-propelled particles are ubiquitous such as flocks of bird, fish school, and bacterial swarming, and it is expected that there exist the unified descriptions of the collective motions. Along this spirit, Vicsek et al. proposed a minimal multi-agent model, which is called the Vicsek model, in 1995. In the Vicsek model, each point particle which has its own moving direction is subject to temporally uncorrelated random directional noise. Each particle aligns to the neighbors, namely only short-range orientational interaction works. Using multi-agent models including the Vicsek model, global directional order in 2D and anomalous density fluctuations, which are called giant number fluctuations, in the ordered phase were predicted in collective motions of self-propelled particles with short-range directional interaction. Indeed, using E. coli elongated with an antibiotic, these two properties were observed in the real system [1]. The particles in the Vicsek model change their direction with no memory. However, there are various kinds of self-propelled particle that keeps its rotation rate for a long time and shows a circular trajectory such as an E. coli close to a wall and a mycoplasma on a glass plate. Using a multi-agent model like the Vicsek model, we elucidated the role of memory of rotation rate. We found that vortices filled the whole area only when the rotation rate of each particle was kept for a while [2]. It is known that microtubules driven by dyneins on a glass plate [3] and C. elegans [4] also have a long memory of rotation rate. Both the self-propelled particles formed many vortices, which are commonly well reproduced by the model in the upper paragraph. This indicates that there exists the unified description of self- propelled particles with memory of rotation rate and short-range directional interaction.
1. D. Nishiguchi, K. H. Nagai, et al., Phys. Rev. E (2017). 2. K. H. Nagai, et al., Phys. Rev. Lett. (2015).
3. Y. Sumino, et al., Nature (2012).
4. T. Sugi, et al., Nat. Commun. (2019).