Emergence of dynamic vortex glasses in disordered polar active fluids

Phase separation, edge currents, and Hall effect for active matter with Magnus dynamics

We examine run-and-tumble disks in two-dimensional systems where the particles also have a Magnus component to their dynamics. For increased activity, we find that the system forms a motility-induced phase-separated (MIPS) state with chiral edge flow around the clusters, where the direction of the current is correlated with the sign of the Magnus term. The stability of the MIPS state is non-monotonic as a function of increasing Magnus term amplitude, with the MIPS region first extending down to lower activities followed by a break up of MIPS at large Magnus amplitudes into a gel-like state. We examine the dynamics in the presence of quenched disorder and a uniform drive and find that the bulk flow exhibits a drive-dependent Hall angle. This is a result of the side jump effect produced by scattering from the pinning sites and is similar to the behavior found for skyrmions in chiral magnets with quenched disorder.

Topology-guided polar ordering of collective cell migration

The ability of epithelial monolayers to self-organize into a dynamic polarized state, where cells migrate in a uniform direction, is essential for tissue regeneration, development, and tumor progression. However, the mechanisms governing long-range polar ordering of motility direction in biological tissues remain unclear. Here, we investigate the self-organizing behavior of quiescent epithelial monolayers that transit to a dynamic state with long-range polar order upon growth factor exposure. We demonstrate that the heightened self-propelled activity of monolayer cells leads to formation of vortex-antivortex pairs that undergo sequential annihilation, ultimately driving the spread of long-range polar order throughout the system. A computational model, which treats the monolayer as an active elastic solid, accurately replicates this behavior, and weakening of cell-to-cell interactions impedes vortex-antivortex annihilation and polar ordering. Our findings uncover a mechanism in epithelia, where elastic solid material characteristics, activated self-propulsion, and topology-mediated guidance converge to fuel a highly efficient polar self-ordering activity.

Anisotropic run-and-tumble-turn dynamics

Run-and-tumble processes successfully model several living systems. While studies have typically focused on particles with isotropic tumbles, recent examples exhibit "tumble-turns", in which particles undergo 90° tumbles and so possess explicitly anisotropic dynamics. We study the consequences of such tumble-turn anisotropicity at both short and long-time scales. We model run-and-tumble-turn particles as self-propelled particles subjected to an angular potential that favors directions of movement parallel to Cartesian axes. Using agent-based simulations, we study the effects of the interplay between rotational diffusion and an aligning potential on the particles' trajectories, which leads to the right-angled turns. We demonstrate that the long-time effect is to alter the tumble-turn time, which governs the long-time dynamics. In particular, when normalized by this timescale, trajectories become independent of the underlying details of the potential. As such, we develop a simplified continuum theory, which quantitatively agrees with agent-based simulations. We find that the purely diffusive hydrodynamic limit still exhibits anisotropic features at intermediate times and conclude that the transition to diffusive dynamics precedes the transition to isotropic dynamics. By considering short-range repulsive and alignment particle-particle interactions, we show how the anisotropic features of a single particle are inherited by the global order of the system. We hope this work will shed light on how active systems can extend local anisotropic properties to macroscopic scales, which might be important in biological processes occurring in anisotropic environments.

Spontaneous Demixing of Binary Colloidal Flocks

Population heterogeneity is ubiquitous among active living systems, but little is known about its role in determining their spatial organization and large-scale dynamics. Combining evidence from synthetic active fluids assembled from self-propelled colloidal particles along with theoretical predictions at the continuum scale, we demonstrate the spontaneous demixing of binary polar liquids within circular confinement. Our analysis reveals how both active speed heterogeneity and nonreciprocal repulsive interactions lead to self-sorting behavior. By establishing general principles for the self-organization of binary polar liquids, our findings highlight the specificity of multicomponent active systems.

Crisscross multilayering of cell sheets

Hydrostatic skeletons such as the Hydra's consist of two stacked layers of muscle cells perpendicularly oriented. In vivo, these bilayers first assemble, and then the muscle fibers of both layers develop and organize with this crisscross orientation. In the present work, we identify an alternative mechanism of crisscross bilayering of myoblasts in vitro, which results from the prior local organization of these active cells in the initial monolayer. The myoblast sheet can be described as a contractile active nematic in which, as expected, most of the +1/2 topological defects associated with this nematic order self-propel. However, as a result of the production of extracellular matrix (ECM) by the cells, a subpopulation of these comet-like defects does not show any self-propulsion. Perpendicular bilayering occurs at these stationary defects. Cells located at the head of these defects converge toward their core where they accumulate until they start migrating on top of the tail of the first layer, while the tail cells migrate in the opposite direction under the head. Since the cells keep their initial orientations, the two stacked layers end up perpendicularly oriented. This concerted process leading to a crisscross bilayering is mediated by the secretion of ECM.

E-cadherin-dependent coordinated epithelial rotation on a two-dimensional discoidal pattern

In vivo, cells collectively migrate in a variety of developmental and pathological contexts. Coordinated epithelial rotation represents a unique type of collective cell migrations, which has been modeled in vitro under spatially confined conditions. Although it is known that the coordinated rotation depends on intercellular interactions, the contribution of E-cadherin, a major cell-cell adhesion molecule, has not been directly addressed on two-dimensional (2D) confined substrates. Here, using well-controlled fibronectin-coated surfaces, we tracked and compared the migratory behaviors of MDCK cells expressing or lacking E-cadherin. We observed that wild-type MDCK II cells exhibited persistent and coordinated rotations on discoidal patterns, while E-cadherin knockout cells migrated in a less coordinated manner without large-scale rotation. Our comparison of the collective dynamics between these two cell types revealed a series of changes in migratory behavior caused by the loss of E-cadherin, including a decreased global migration speed, less regularity in quantified coordination, and increased average density of topological defects. Taken together, these data demonstrate that spontaneous initiation of collective epithelial rotations depends on E-cadherin under 2D discoidal confinements.

Incompressible Polar Active Fluids with Quenched Random Field Disorder in Dimensions d>2

We present a hydrodynamic theory of incompressible polar active fluids with quenched random field disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a nonzero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions.

Packed Swarms on Dirt: Two-Dimensional Incompressible Flocks with Quenched and Annealed Disorder

We show that incompressible polar active fluids can exhibit an ordered, coherently moving phase even in the presence of quenched disorder in two dimensions. Unlike such active fluids with annealed disorder (i.e., time-dependent random white noise) only, which behave like equilibrium ferromagnets with long-range interactions, this robustness against quenched disorder is a fundamentally nonequilibrium phenomenon. The ordered state belongs to a new universality class, whose scaling laws we calculate using three different renormalization group schemes, which all give scaling exponents within 0.02 of each other, indicating that our results are quite accurate. Our predictions can be quantitatively tested in readily available artificial active systems and imply that biological systems such as cell layers can move coherently in vivo, where disorder is inevitable.

Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder

We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We obtain the large-distance, long-time scaling laws of the velocity fluctuations using three distinct dynamic renormalization group schemes. These are an uncontrolled one-loop calculation in exactly two dimensions, and two d=(d_{c}-ε) expansions to O(ε), obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a "hard" continuation which has d_{c}=7/3, and a "soft" continuation with d_{c}=5/2. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and therefore we expect the numerical values that we predict for them to be highly accurate.

Mesoscopic simulations of active nematics

Coarse-grained, mesoscale simulations are invaluable for studying soft condensed matter because of their ability to model systems in which a background solvent plays a substantial role but is not the primary interest. Such methods generally model passive solvents; however, far-from-equilibrium systems may also be composed of complex solutes suspended in an active fluid. Yet, few coarse-grained simulation methods exist to model an active medium. We introduce an algorithm to simulate active nematics, which builds on multiparticle collision dynamics (MPCD) for passive fluctuating nematohydrodynamics by introducing dipolar activity in the local collision operator. Active nematic MPCD (AN-MPCD) simulations not only exhibit the key characteristics of active nematic turbulence but, as a particle-based algorithm, also reproduce crucial attributes of active particle models. Thus, mesoscopic AN-MPCD is an approach that bridges microscopic and continuum descriptions, allowing simulations of composite active-passive systems.

Dense polar active fluids in a disordered environment

We examine the influence of quenched disorder on the flocking transition of dense polar active matter. We consider incompressible systems of active particles with aligning interactions under the effect of either quenched random forces or random dilution. The system displays a continuous disorder-order (flocking) transition, and the associated scaling behavior is described by a new universality class which is controlled by a quenched Navier-Stokes fixed point. We determine the critical exponents through a perturbative renormalization group analysis. We show that the two forms of quenched disorder, random force and random mass (dilution), belong to the same universality class, in contrast with the situation at equilibrium.

Small Obstacle in a Large Polar Flock

We show that arbitrarily large polar flocks are susceptible to the presence of a single small obstacle. In a wide region of parameter space, the obstacle triggers counterpropagating dense bands leading to reversals of the flow. In very large systems, these bands interact, yielding a never-ending chaotic dynamics that constitutes a new disordered phase of the system. While most of these results were obtained using simulations of aligning self-propelled particles, we find similar phenomena at the continuous level, not when considering the basic Toner-Tu hydrodynamic theory, but in simulations of truncations of the relevant Boltzmann equation.

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.

Susceptibility of Orientationally Ordered Active Matter to Chirality Disorder

We investigate the susceptibility of long-range ordered phases of two-dimensional dry aligning active matter to population disorder, taken in the form of a distribution of intrinsic individual chiralities. Using a combination of particle-level models and hydrodynamic theories derived from them, we show that while in finite systems all ordered phases resist a finite amount of such chirality disorder, the homogeneous ones (polar flocks and active nematics) are unstable to any amount of disorder in the infinite-size limit. On the other hand, we find that the inhomogeneous solutions of the coexistence phase (bands) may resist a finite amount of chirality disorder even asymptotically.

Active matter shepherding and clustering in inhomogeneous environments

We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.

Defect Superdiffusion and Unbinding in a 2D XY Model of Self-Driven Rotors

We consider a nonequilibrium extension of the 2D XY model, equivalent to the noisy Kuramoto model of synchronization with short-range coupling, where rotors sitting on a square lattice are self-driven by random intrinsic frequencies. We study the static and dynamic properties of topological defects (vortices) and establish how self-spinning affects the Berezenskii-Kosterlitz-Thouless phase transition scenario. The nonequilibrium drive breaks the quasi-long-range ordered phase of the 2D XY model into a mosaic of ordered domains of controllable size and results in self-propelled vortices that generically unbind at any temperature, featuring superdiffusion ⟨r^{2}(t)⟩∼t^{3/2} with a Gaussian distribution of displacements. Our work provides a simple framework to investigate topological defects in nonequilibrium matter and sheds new light on the problem of synchronization of locally coupled oscillators.

Clogging, dynamics, and reentrant fluid for active matter on periodic substrates

We examine the collective states of run-and-tumble active matter disks driven over a periodic obstacle array. When the drive is applied along a symmetry direction of the array, we find a clog-free uniform liquid state for low activity, while at higher activity, the density becomes increasingly heterogeneous and an active clogged state emerges in which the mobility is strongly reduced. For driving along nonsymmetry or incommensurate directions, there are two different clogging behaviors consisting of a drive-dependent clogged state in the low activity thermal limit and a drive-independent clogged state at high activity. These regimes are separated by a uniform flowing liquid at intermediate activity. There is a critical activity level above which the thermal clogged state does not occur, as well as an optimal activity level that maximizes the disk mobility. Thermal clogged states are dependent on the driving direction while active clogged states are not. In the low activity regime, diluting the obstacles produces a monotonic increase in the mobility; however, for large activities, the mobility is more robust against obstacle dilution. We also examine the velocity-force curves for driving along nonsymmetry directions and find that they are linear when the activity is low or intermediate but become nonlinear at high activity and show behavior similar to that found for the plastic depinning of solids. At higher drives, the active clustering is lost. For low activity, we also find a reentrant fluid phase, where the system transitions from a high mobility fluid at low drives to a clogged state at higher drives and then back into another fluid phase at very high drives. We map the regions in which the thermally clogged, partially clogged, active uniform fluid, clustered fluid, active clogged, and directionally locked states occur as a function of disk density, drift force, and activity.

Breakdown of Ergodicity and Self-Averaging in Polar Flocks with Quenched Disorder

We show that spatial quenched disorder affects polar active matter in ways more complex and far reaching than heretofore believed. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we find in particular that ergodicity is lost in the ordered phase, the nature of which we show to depend qualitatively on the type of quenched disorder: for random couplings, it remains long-range ordered, but qualitatively different from the pure (disorderless) case. For random scatterers, polar order varies with system size but we find strong non-self-averaging, with sample-to-sample fluctuations dominating asymptotically, which prevents us from elucidating the asymptotic status of order.

Jamming, fragility and pinning phenomena in superconducting vortex systems

We examine driven superconducting vortices interacting with quenched disorder under a sequence of perpendicular drive pulses. As a function of disorder strength, we find four types of behavior distinguished by the presence or absence of memory effects. The fragile and jammed states exhibit memory, while the elastic and pinning dominated regimes do not. In the fragile regime, the system organizes into a pinned state during the first pulse, flows during the second perpendicular pulse, and then returns to a pinned state during the third pulse which is parallel to the first pulse. This behavior is the hallmark of the fragility proposed for jamming in particulate matter. For stronger disorder, we observe a robust jamming state with memory where the system reaches a pinned or reduced flow state during the perpendicular drive pulse, similar to the shear jamming of granular systems. We show signatures of the different states in the spatial vortex configurations, and find that memory effects arise from coexisting elastic and pinned components of the vortex assembly. The sequential perpendicular driving protocol we propose for distinguishing fragile, jammed, and pinned phases should be general to the broader class of driven interacting particles in the presence of quenched disorder.