Micro-flock patterns and macro-clusters in chiral active Brownian disks

Collective Hall current in chiral active fluids: Coupling of phase and mass transport through traveling bands

Active fluids composed of constituents that are constantly driven away from thermal equilibrium can support spontaneous currents and can be engineered to have unconventional transport properties. Here, we report the emergence of (meta)stable traveling bands in computer simulations of aligning circle swimmers. These bands are different from polar flocks and, through coupling phase with mass transport, induce a bulk particle current with a component perpendicular to the propagation direction, thus giving rise to a collective Hall (or Magnus) effect. Traveling bands require sufficiently small orbits and undergo a discontinuous transition into a synchronized state with transient polar clusters for large orbital radii. Within a minimal hydrodynamic theory, we show that the bands can be understood as nondispersive soliton solutions fully accounting for the numerically observed properties.

Hydrodynamic Synchronization of Chiral Microswimmers

We study synchronization in bulk suspensions of spherical microswimmers with chiral trajectories using large scale numerics. The model is generic. It corresponds to the lowest order solution of a general model for self-propulsion at low Reynolds numbers, consisting of a nonaxisymmetric rotating source dipole. We show that both purely circular and helical swimmers can spontaneously synchronize their rotation. The synchronized state corresponds to velocity alignment with high orientational order in both the polar and azimuthal directions. Finally, we consider a racemic mixture of helical swimmers where intraspecies synchronization is observed while the system remains as a spatially uniform fluid. Our results demonstrate hydrodynamic synchronization as a natural collective phenomenon for microswimmers with chiral trajectories.

Resonant Diffusion of a Gravitactic Circle Swimmer

We investigate the dynamics of a single chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations reveal an arbitrarily strong increase of the long-time diffusivity of the gravitactic agent when the external torque approaches the intrinsic angular drift. We provide analytic expressions for the mean-square displacement in terms of eigenfunctions and eigenvalues of the noisy-driven-pendulum problem. The pronounced maximum in the diffusivity is then rationalized by the vanishing of the lowest eigenvalues of the Fokker-Planck equation for the angular motion as the rotational diffusion decreases and the underlying classical bifurcation is approached. A simple harmonic-oscillator picture for the barrier-dominated motion provides a quantitative description for the onset of the resonance while its range of validity is determined by the crossover to a critical-fluctuation-dominated regime.

Dynamical clustering interrupts motility-induced phase separation in chiral active Brownian particles

One of the most intriguing phenomena in active matter has been the gas-liquid-like motility-induced phase separation (MIPS) observed in repulsive active particles. However, experimentally, no particle can be a perfect sphere, and the asymmetric shape, mass distribution, or catalysis coating can induce an active torque on the particle, which makes it a chiral active particle. Here, using computer simulations and dynamic mean-field theory, we demonstrate that the large enough torque of circle active Brownian particles in two dimensions generates a dynamical clustering state interrupting the conventional MIPS. Multiple clusters arise from the combination of the conventional MIPS cohesion, and the circulating current caused disintegration. The nonvanishing current in non-equilibrium steady states microscopically originates from the motility "relieved" by automatic rotation, which breaks the detailed balance at the continuum level. This suggests that no equilibrium-like phase separation theory can be constructed for chiral active colloids even with tiny active torque, in which no visible collective motion exists. This mechanism also sheds light on the understanding of dynamic clusters observed in a variety of active matter systems.

Phase separation of self-propelled disks with ferromagnetic and nematic alignment

We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and motility-induced phase separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a closed set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in motility-induced phase separation.

Layered Chiral Active Matter: Beyond Odd Elasticity

In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this Letter, starting from active model H^{*}, the general hydrodynamics of a pseudoscalar in a momentum-conserving fluid, we demonstrate that chirality qualitatively modifies the dynamics of layered liquid crystals in active systems in both two and three dimensions due to an active "odder" elasticity. In three dimensions, we demonstrate that the hydrodynamics of active cholesterics differs fundamentally from smectic-A liquid crystals, unlike their equilibrium counterpart. This distinction can be used to engineer a columnar array of vortices, with an antiferromagnetic vorticity alignment, that can be switched on and off by external strain. A two-dimensional chiral layered state-an array of lines on an incompressible, freestanding film of chiral active fluid with a preferred normal direction-is generically unstable. However, this instability can be tuned in easily realizable experimental settings when the film is either on a substrate or in an ambient fluid.

Emergent stereoselective interactions and self-recognition in polar chiral active ellipsoids

In many active matter systems, particle trajectories have a well-defined handedness or chirality. Whether such chiral activity can introduce stereoselective interactions between particles is not known. Here, we developed a strategy to tune the nature of chiral activity of three-dimensionally printed granular ellipsoids without altering their shape or size. In vertically agitated monolayers of these particles, we observed two types of dimers form depending on the chirality of the pairing monomers. Heterochiral dimers moved collectively as a single achiral active unit, while homochiral ones formed a translationally immobile spinner. In active racemic mixtures, the former was more abundant than the latter, indicating that interactions were stereoselective. Through dimer lifetime measurements, we further provide evidence for chiral self-recognition in mixtures of particles with different chiral activities. We lastly show that, at fixed particle number density, changing the net chirality of a dense active liquid fundamentally alters the nature of collective relaxation.

Chiral Active Hexatics: Giant Number Fluctuations, Waves, and Destruction of Order

Active materials, composed of internally driven particles, have properties that are qualitatively distinct from matter at thermal equilibrium. However, the most spectacular departures from equilibrium phase behavior are thought to be confined to systems with polar or nematic asymmetry. In this Letter, we show that such departures are also displayed by more symmetric phases such as hexatics if, in addition, the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density have giant number fluctuations. If the rotation rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large length scale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them nonmutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

Rectification and separation of mixtures of active and passive particles driven by temperature difference

Transport and separation of binary mixtures of active and passive particles are investigated in the presence of temperature differences. It is found that temperature differences can strongly affect the rectification and separation of the mixtures. For active particles, there exists an optimal temperature difference at which the rectified efficiency is maximal. Passive particles are not propelled and move by collisions with active particles, so the response to temperature differences is more complicated. By changing the system parameters, active particles can change their directions, while passive particles always move in the same direction. The simulation results show that the separation of mixtures is sensitive to the system parameters, such as the angular velocity, the temperature difference, and the polar alignment. The mixed particles can be completely separated under certain conditions.

Simultaneous phase separation and pattern formation in chiral active mixtures

Chiral active particles, or self-propelled circle swimmers, from sperm cells to asymmetric Janus colloids, form a rich set of patterns, which are different from those seen in linear swimmers. Such patterns have mainly been explored for identical circle swimmers, while real-world circle swimmers typically possess a frequency distribution. Here we show that even the simplest mixture of (velocity-aligning) circle swimmers with two different frequencies hosts a complex world of superstructures: The most remarkable example comprises a microflock pattern, formed in one species, while the other species phase separates and forms a macrocluster, coexisting with a gas phase. Here one species microphase separates and selects a characteristic length scale, whereas the other one macrophase separates and selects a density. A second notable example, here occurring in an isotropic system, are patterns comprising two different characteristic length scales, which are controllable via frequency and swimming speed of the individual particles.

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

Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion, and fluctuations occur relative to a noninertial frame and thereby the active Brownian motion model is generalized to noninertial frames. First, analytical solutions are presented for the overdamped case, both for linear swimmers and for circle swimmers. For a frame rotating with constant angular velocity ("carousel"), the resulting noise-free trajectories in the static laboratory frame are trochoids if these are circles in the rotating frame. For systems governed by inertia, such as vibrated granulates or active complex plasmas, centrifugal and Coriolis forces become relevant. For both linear and circling self-propulsion, these forces lead to out-spiraling trajectories which for long times approach a spira mirabilis. This implies that a self-propelled particle will typically leave a rotating carousel. A navigation strategy is proposed to avoid this expulsion, by adjusting the self-propulsion direction at will. For a particle, initially quiescent in the rotating frame, it is shown that this strategy only works if the initial distance to the rotation center is smaller than a critical radius R_{c} which scales with the self-propulsion velocity. Possible experiments to verify the theoretical predictions are discussed.

Rectification of chiral active particles driven by transversal temperature difference

Rectification of chiral active particles driven by transversal temperature difference is investigated in a two-dimensional periodic channel. Chiral active particles can be rectified by transversal temperature difference. Transport behaviors are qualitatively different for different wall boundary conditions. For the sliding boundary condition, the direction of transport completely depends on the chirality of particles. The average velocity is a peaked function of angular velocity or temperature difference. The average velocity increases linearly with the self-propulsion speed, while it decreases monotonically with the increase in the packing fraction. For randomized boundary condition, the transport behaviors become complex. When self-propulsion speed is small, in contrast with the sliding boundary condition, particles move in the opposite direction. However, for large self-propulsion speed, current reversals can occur by continuously changing the system parameters (angular velocity, temperature difference, packing fraction, and width of the channel).

Spontaneous rotation can stabilise ordered chiral active fluids

Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases are by now well established, the effect of chirality on these phases is much less studied. In this paper, we present a complete dynamical theory of orientationally ordered chiral particles in two-dimensional incompressible systems. We show that phase-coherent states of rotating chiral particles are remarkably stable in both momentum-conserved and non-conserved systems in contrast to their non-rotating counterparts. Furthermore, defect separation-which drives chaotic flows in non-rotating active fluids-is suppressed by intrinsic rotation of chiral active particles. We thus establish chirality as a source of dramatic stabilisation in active systems, which could be key in interpreting the collective behaviors of some biological tissues, cytoskeletal systems and collections of bacteria.

Transport of particles driven by the traveling obstacle arrays

Transport of three types of particles (passive particles, active particles without polar interaction, and active particles with polar interaction) is numerically investigated in the presence of traveling obstacle arrays. The transport behaviors are different for different types of particles. For passive particles, there exists an optimal traveling speed (or the translational diffusion) at which the average velocity of particles takes its maximum value. For active particles without polar interaction, the average velocity of particles is a peaked function of the obstacle traveling speed. The average velocity decreases monotonically with increase of the rotational diffusion for large driving speed, while it is a peaked function of the rotational diffusion for small driving speed. For active particles with polar interaction, interestingly, within particular parameter regimes, active particles can move in the opposite direction to the obstacles. The average velocity of particles can change its direction by changing the system parameters (the obstacles driving speed, the polar interaction strength, and the rotational diffusion).