Traveling bands, clouds, and vortices of chiral active matter

Spontaneous generation of angular momentum in chiral active crystals

We study a two-dimensional chiral active crystal composed of underdamped chiral active particles. These particles, characterized by intrinsic handedness and persistence, interact via linear forces derived from harmonic potentials. Chirality plays a pivotal role in shaping the system's behavior: it reduces displacement and velocity fluctuations while inducing cross-spatial correlations among different Cartesian components of velocity. These features distinguish chiral crystals from their non-chiral counterparts, leading to the emergence of net angular momentum, as predicted analytically. This angular momentum, driven by the torque generated by the chiral active force, exhibits a non-monotonic dependence on the degree of chirality. Additionally, it contributes to the entropy production rate, as revealed through a path-integral analysis. We investigate the dynamic properties of the crystal in both Fourier and real space. Chirality induces a non-dispersive peak in the displacement spectrum, which underlies the generation of angular momentum and oscillations in time-dependent autocorrelation functions or mean-square displacement, all of which are analytically predicted.

Spontaneous oscillation in collective microswimmers: Insights from a chiral self-propelled rod model

Active systems exhibit fascinating self-organized structures and rich motility patterns, yet the underlying mechanisms governing their emergence and characteristics remain elusive. Here, we develop a chiral self-propelled rod (CSPR) model with mechanical contact-induced quorum sensing to investigate the spatiotemporal dynamics of dense bacteria populations. Our findings show that the CSPR model showcases spontaneous nonequilibrium oscillatory clustering of active systems. The motion characteristics of these clusters depend on colony features (microswimmers' morphology and density) and mechanical contact-induced sensing mechanisms (polarization alignment and angular velocity alignment of CSPR). Interestingly, reinforced strength of polar alignment accelerates the formation of stable oscillations, while decreased density and angular velocity alignment strength modify their emergence pattern. Significantly, our study identifies three distinct oscillation patterns: global stable oscillation, bistable oscillation, and multistable oscillation, and reveals that their phase transitions are driven by variations in the spatial correlation of CSPR. These insights provide a new perspective on understanding the intricate evolution of active matter, opening possible avenues for emerging applications.

Spontaneous separation of attractive chiral mixtures

The separation of chiral matter has garnered significant attention due to its wide-ranging applications in biological and chemical processes. In prior researches, particle interactions were predominantly repulsive, but the indiscriminate attraction among particles under attractive interactions makes the separation of mixtures more difficult. The question of whether chiral mixed particles, characterized by attractive effects, can undergo spontaneous separation, remains unresolved. We study a binary mixture of chiral (counterclockwise or clockwise) active particles with attractive interactions. It is demonstrated that attractive chiral particles can undergo spontaneous separation without the aid of any specific strategies. The key factor driving the separation is the attractive interactions, enabling the formation of stable clusters of particles with same chirality. There exist optimal parameters (self-propelled velocity, angular velocity, and packing fraction) at which the separation is optimal. Our results may contribute to a deeper understanding of the mechanisms behind chiral matter separation and potentially catalyze further experimental investigations in this field.

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.

Order, chaos, and dimensionality transition in a system of swarmalators

Similarly to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces. We show that several static and active collective states can emerge and derive necessary conditions for each to show up as the model parameters are varied. These conditions elucidate, in some cases, the displaying of multistability among states. Notably, in the active regime, the system exhibits hyperchaos, maintaining spatial correlation under certain conditions and breaking it under others on what we interpret as a dimensionality transition.

Chiral active matter in external potentials

We investigate the interplay between chirality and confinement induced by the presence of an external potential. For potentials having radial symmetry, the circular character of the trajectories induced by the chiral motion reduces the spatial fluctuations of the particle, thus providing an extra effective confining mechanism, that can be interpreted as a lowering of the effective temperature. In the case of non-radial potentials, for instance, with an elliptic shape, chirality displays a richer scenario. Indeed, the chirality can break the parity symmetry of the potential that is always fulfilled in the non-chiral system. The probability distribution displays a strong non-Maxwell-Boltzmann shape that emerges in cross-correlations between the two Cartesian components of the position, that vanishes in the absence of chirality or when radial symmetry of the potential is restored. These results are obtained by considering two popular models in active matter, i.e. chiral Active Brownian particles and chiral active Ornstein-Uhlenbeck particles.

Collision-induced torque mediates the transition of chiral dynamic patterns formed by active particles

Controlling the patterns formed by self-propelled particles through dynamic self-organization is a challenging task. Although varieties of patterns associated with chiral self-propelled particles have been reported, essential factors that determine the morphology of the patterns have remained unclear. Here, we explore theoretically how torque formed upon collision of the particles affects the dynamic self-organization of the particles and determine the patterns. Based on a particle-based model with collision-induced torque and torque associated with self-propulsion, we find that introducing collision-induced torque turns the homogeneous bi-directionally aligned particles into rotating mono-polar flocks, which helps resolve a discrepancy in the earlier observations in microfilament gliding assays.

Deformable active nematic particles and emerging edge currents in circular confinements

We consider a microscopic field theoretical approach for interacting active nematic particles. With only steric interactions the self-propulsion strength in such systems can lead to different collective behaviour, e.g. synchronized self-spinning and collective translation. The different behaviour results from the delicate interplay between internal nematic structure, particle shape deformation and particle-particle interaction. For intermediate active strength an asymmetric particle shape emerges and leads to chirality and self-spinning crystals. For larger active strength the shape is symmetric and translational collective motion emerges. Within circular confinements, depending on the packing fraction, the self-spinning regime either stabilizes positional and orientational order or can lead to edge currents and global rotation which destroys the synchronized self-spinning crystalline structure.

Synchronized oscillations in swarms of nematode Turbatrix aceti

There is a recent surge of interest in the behavior of active particles that can at the same time align their direction of movement and synchronize their oscillations, known as swarmalators. While theoretical and numerical models of such systems are now abundant, no real-life examples have been shown to date. We present an experimental investigation of the collective motion of the nematode Turbatrix aceti that self-propel by body undulation. We discover that these nematodes can synchronize their body oscillations, forming striking traveling metachronal waves, which produces strong fluid flows. We uncover that the location and strength of this collective state can be controlled through the shape of the confining structure; in our case the contact angle of a droplet. This opens a way for producing controlled work such as on-demand flows or displacement of objects. We illustrate this by showing that the force generated by this state is sufficient to change the physics of evaporation of fluid droplets, by counteracting the surface-tension force, which allow us to estimate its strength. The relatively large size and ease of culture make Turbatrix aceti a promising model organism for experimental investigation of swarming and oscillating active matter capable of producing controllable work.

Emergent vortices and phase separation in systems of chiral active particles with dipolar interactions

Using Brownian dynamics (BD) simulations we investigate the self-organization of a monolayer of chiral active particles with dipolar interactions. Each particle is driven by both, translational and rotational self-propulsion, and carries a permanent point dipole moment at its center. The direction of the translational propulsion for each particle is chosen to be parallel to its dipole moment. Simulations are performed at high dipolar coupling strength and a density below that related to motility-induced phase separation in simple active Brownian particles. Despite this restriction, we observe a wealth of phenomena including formation of two types of vortices, phase separation, and flocking transitions. To understand the appearance and disappearance of vortices in the many-particle system, we further investigate the dynamics of simple ring structures under the impact of self-propulsion.

Solitary states in the mean-field limit

We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second-order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise. By studying this limit, we establish second-order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite-size models.