Collective Behavior of Chiral Active Matter: Pattern Formation and Enhanced Flocking

Abstract

We generalize the Vicsek model to describe the collective behaviour of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise ratio as for linear swimmers, as we show, circular motion enhances the polarization in the ordered phase (enhanced flocking) and induces secondary instabilities leading to structure formation. Slow rotations promote phase separation whereas fast rotations generate patterns consisting of phase synchronized microflocks with a controllable selflimited size. Our results defy the viewpoint that monofrequent rotations form a vapid extension of the Vicsek model and establish a generic route to pattern formation in chiral active matter with possible applications to control coarsening and to design rotating microflocks.Among the most remarkable features of active matter systems is their ability to spontaneously form selfsustained nonequilibrium structures, without requiring external driving. These active structures range from motility-induced phase separation of self-propelled particles into a dense and a dilute phase [1, 2] and clusters of self-limited size [3][4][5][6][7] in isotropic active matter, to long range ordered flocks and travelling bands in 2D polar active matter [8][9][10][11][12]. Despite their phenomenological diversity most of these (and other) activity-induced structures can be observed in a small class of archetypical minimal models allowing to explore their universality. For linear self-propelled particles which change their swimming direction only by diffusion (and alignment interactions), the Active Brownian Particle model and the Vicsek model have become standard models representing isotropic and polar active matter.Besides such linear swimmers, there is now a strong interest in a new class of self-propelled particles which change their direction of motion autonomously. This class of chiral active matter includes a variety of biological circle swimmers, such as E.coli which swim circularly when close to walls and interfaces [13][14][15][16], as well as sperm cells [17,18], and magnetotactic bacteria in rotating external fields [19,20]. Following the general principle that any deviation between the self-propulsion direction of the particle and its symmetry axis couples its translational and rotational degrees of freedom, it has also been possible to design synthetic circle swimmers; examples being L-shaped self-phoretic swimmers [21,22] and actuated colloids allowing to design radius and frequency of circular trajectories on demand. While these synthetic examples have supported the recent boost of interest in chiral active matter, as the recent reviews [23,24] Therefore, following the spirit of formulating minimal models for the collective behaviour of linear active matter, we introduce here the 'rotating Vicsek model ' (RVM) to describe the collective behaviour of polar circle swimmers. This model describes overdamped self-propelled particles changing their dir...

Active particles in noninertial frames: How to self-propel on a carousel

“…[46]. Again, in the overdamped limit (ζ → ∞), the expression (52) reduces to (18). For a constantly accelerated frame R 0 (t) =ê x a 0 t 2 /2, the mean-square displacement is "superballistic" and will grow with a power law for long times ( r(t) − r(0)) 2 a 2 t 4 /4 resulting from the acceleration.…”

“…The latter type of swimmers experiences also a torque which steadily changes the direction of self-propulsion. These chiral swimmers were studied in various environ-ments [14][15][16][17][18][19][20].…”

Dynamical density functional theory for circle swimmers

“…Apart from that, near surfaces bent self-propelled objects tend to follow circular trajectories [42,43]. In modeling approaches, circle swimmers are often realized by simply imposing an effective torque or rotational drive in addition to the self-propulsion mechanism [15,31,35,[44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59].…”

Configuration dynamics of a flexible polymer chain in a bath of chiral active particles

“…Compared to the active crowder without dynamic chirality, the chiral one is affected not only by the active force but also by an extra torque, leading to a circular motion in two dimensional space or a helical motion in three dimensional space. It has been found that the chiral feature of active particles can affect significantly the collective dynamics including transport [53][54][55][56], separation [57,58], sorting [59,60], and so on. However, to the best of our knowledge, how the dynamic chirality of active crowders would influence the configuration change of a polymer chain has not been studied yet.…”