Vortex with fourfold defect lines in a simple model of self-propelled particles

Abstract

We studied formation of vortex with four-fold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observed five other phases in the system: homogeneous gaseous phase, band structures, moving clumps, moving clusters and vibrating rings. All six phases emerge from controlling strength of noise and contribution of repulsion and alignment interactions. We studied shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion interactions between particles are necessary to form such patterns. Finally, we derived hydrodynamical equations for our model and compared them with the results of both computer simulations and Quincke rotors. A good agreement between the three is observed.

Active Brownian particles and run-and-tumble particles separate inside a maze

“…Our work also has biomedical relevance for separating bacteria from other microorganisms or passive objects such as blood cells. In future work it will be interesting to study the collective behavior of active particles in these strongly confining complex structures6566 and to explore their potential for optimal search strategies386367.…”

Gaussian theory for spatially distributed self-propelled particles

“…( 23)], the GA method [Eq. ( 22)], and a method with the assumption that the orientation of the particles has very small deviation from the mean value [82] -The third and higher moments of the distribution are negligible -, which is called small deviation [61]. Homogeneous solution of this method is a slowly declining line with a transition point at D r = 2.0.…”

“…One can also write the general form of transport coefficients in terms of the trigonometric moments of the probability distribution, but each moment depends on higher orders [56][57][58], and still a closure is required. Truncating the series of angular Fourier coefficients of particles distribution is vastly used in active matter to obtain the continuum equations [34,[59][60][61]. This method has a reasonable accuracy in determining the phase boundaries.…”

“…Nevertheless, the accuracy of this method for low noise depends on the truncation level. For example, a second order truncation gives transport coefficients that diverge for vanishing noise [34,60,61]. To achieve better results one has to raise the cut-off for the truncation which can be done numerically [54].…”

“…To achieve better results one has to raise the cut-off for the truncation which can be done numerically [54]. Similar to an expansion of the transport coefficients in terms of trigonometric moments [56][57][58], we recently tried to obtain transport coefficients in terms of polynomial moments of the distribution, and the closure was done by neglecting higher moments what appeared to be valid for sharp distributions [61]. Although one can obtain finite transport coefficients for vanishing noise in this limit, the continuum equations are not able to predict accurately the transition point of the system.…”