Low-noise phase of a two-dimensional active nematic system

Nematic Torques in Scalar Active Matter: When Fluctuations Favor Polar Order and Persistence

We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase separation. The underlying mechanism is a fluctuation-induced renormalization of the mass of the polar field that generically arises from nematic torques. The correlations between the fluctuations of the polar and nematic fields indeed conspire to increase the particle persistence length, contrary to what phenomenological computations predict. This effect is generic and our theory also quantitatively accounts for how nematic torques enhance particle accumulation along confining boundaries and opposes demixing in mixtures of active and passive particles.

Hydrodynamics and multiscale order in confluent epithelia

We formulate a hydrodynamic theory of confluent epithelia: i.e. monolayers of epithelial cells adhering to each other without gaps. Taking advantage of recent progresses toward establishing a general hydrodynamic theory of p-atic liquid crystals, we demonstrate that collectively migrating epithelia feature both nematic (i.e. p = 2) and hexatic (i.e. p = 6) orders, with the former being dominant at large and the latter at small length scales. Such a remarkable multiscale liquid crystal order leaves a distinct signature in the system's structure factor, which exhibits two different power-law scaling regimes, reflecting both the hexagonal geometry of small cells clusters and the uniaxial structure of the global cellular flow. We support these analytical predictions with two different cell-resolved models of epithelia - i.e. the self-propelled Voronoi model and the multiphase field model - and highlight how momentum dissipation and noise influence the range of fluctuations at small length scales, thereby affecting the degree of cooperativity between cells. Our construction provides a theoretical framework to conceptualize the recent observation of multiscale order in layers of Madin-Darby canine kidney cells and pave the way for further theoretical developments.

Quantifying nematic order in the evaporation-driven self-assembly of halloysite nanotubes: nematic islands and the critical aspect ratio

Halloysite nanotubes (HNTs) are naturally occurring clay minerals found in the Earth's crust that typically exist in the form of high aspect-ratio nanometer-long rods. Here, we investigate the evaporation-driven self-assembly process of HNTs and show that a highly polydisperse collection of HNTs self-sort into a spatially inhomogeneous structure, displaying a systematic variation in the resulting nematic order. Through detailed quantification using the nematic order parameter S and nematic correlation functions, we show the existence of well-defined isotropic-nematic transitions in the emerging structures. We also show that the onset of these transitions gives rise to the formation of nematic islands, a phase resembling ordered nematic domains surrounded by an isotropic phase, which grow in size with S. Detailed image analysis indicates a strong correlation between local S and the local aspect ratio, L/D, with nematic order possible only for rods with L/D ≥ 6.5 ± 1. Finally, we conclude that the observed phenomena directly result from aspect ratio-based sorting in our system. Altogether, our results provide a unique method of tuning the local microscopic structure in self-assembled HNTs using L/D as an external parameter.

Molecular-scale substrate anisotropy, crowding and division drive collective behaviours in cell monolayers

The ability of cells to reorganize in response to external stimuli is important in areas ranging from morphogenesis to tissue engineering. While nematic order is common in biological tissues, it typically only extends to small regions of cells interacting via steric repulsion. On isotropic substrates, elongated cells can co-align due to steric effects, forming ordered but randomly oriented finite-size domains. However, we have discovered that flat substrates with nematic order can induce global nematic alignment of dense, spindle-like cells, thereby influencing cell organization and collective motion and driving alignment on the scale of the entire tissue. Remarkably, single cells are not sensitive to the substrate's anisotropy. Rather, the emergence of global nematic order is a collective phenomenon that requires both steric effects and molecular-scale anisotropy of the substrate. To quantify the rich set of behaviours afforded by this system, we analyse velocity, positional and orientational correlations for several thousand cells over days. The establishment of global order is facilitated by enhanced cell division along the substrate's nematic axis, and associated extensile stresses that restructure the cells' actomyosin networks. Our work provides a new understanding of the dynamics of cellular remodelling and organization among weakly interacting cells.

Fluctuation-induced dynamics of nematic topological defects

Topological defects are increasingly being identified in various biological systems, where their characteristic flow fields and stress patterns are associated with continuous active stress generation by biological entities. Here, using numerical simulations of continuum fluctuating nematohydrodynamics, we show that even in the absence of any specific form of active stresses associated with self-propulsion, mesoscopic fluctuations in either orientational alignment or hydrodynamics can independently result in flow patterns around topological defects that resemble the ones observed in active systems. Our simulations further show the possibility of extensile- and contractile-like motion of fluctuation-induced positive half-integer topological defects. Remarkably, isotropic stress fields also reproduce the experimentally measured stress patterns around topological defects in epithelia. Our findings further reveal that extensile- or contractile-like flow and stress patterns around fluctuation-induced defects are governed by passive elastic stresses and flow-aligning behavior of the nematics.

Spontaneous flow created by active topological defects

Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges [Formula: see text] are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.

Polar Fluctuations Lead to Extensile Nematic Behavior in Confluent Tissues

How can a collection of motile cells, each generating contractile nematic stresses in isolation, become an extensile nematic at the tissue level? Understanding this seemingly contradictory experimental observation, which occurs irrespective of whether the tissue is in the liquid or solid states, is not only crucial to our understanding of diverse biological processes, but is also of fundamental interest to soft matter and many-body physics. Here, we resolve this cellular to tissue level disconnect in the small fluctuation regime by using analytical theories based on hydrodynamic descriptions of confluent tissues, in both liquid and solid states. Specifically, we show that a collection of microscopic constituents with no inherently nematic extensile forces can exhibit active extensile nematic behavior when subject to polar fluctuating forces. We further support our findings by performing cell level simulations of minimal models of confluent tissues.

Swarming Bottom Feeders: Flocking at Solid-Liquid Interfaces

We present the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface, and many of its predictions for experiment. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations," which grow as the 3/4th power of the mean number. Stable systems also exhibit anomalous rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction perpendicular to the plane is not anomalous. In the remaining parameter space, the system becomes unstable.

Alignment destabilizes crystal order in active systems

We combine numerical and analytical methods to study two-dimensional active crystals formed by permanently linked swimmers and with two distinct alignment interactions. The system admits a stationary phase with quasi-long-range translational order, as well as a moving phase with quasi-long-range active force director and velocity order. The translational order in the moving phase is significantly influenced by alignment interaction. For Vicsek-like alignment, the translational order is short ranged, whereas the bond-orientational order is quasi-long ranged, implying a moving hexatic phase. For elasticity-based alignment, the translational order is quasi-long ranged parallel to the motion and short ranged in the perpendicular direction, whereas the bond orientational order is long ranged. We also generalize these results to higher dimensions.

Hydrodynamic theory of flocking at a solid-liquid interface: Long-range order and giant number fluctuations

We construct the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface. The polar order parameter and concentration of a collection of "active" (self-propelled) particles at a planar interface between a passive, isotropic bulk fluid and a solid surface are dynamically coupled to the bulk fluid. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations," i.e., large fluctuations of the number of active particles in a fixed large area. Specifically, these number fluctuations grow as the 3/4th power of the mean number within the area. Stable systems also exhibit anomalously rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction perpendicular to the plane is nonanomalous. In other parameter regimes, the system becomes unstable.

Long-Range Nematic Order in Two-Dimensional Active Matter

Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond ℓ_{r}, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured. Below ℓ_{r}, nematic order is long-range. We construct and study a hydrodynamic theory for this de facto phase and show that its structure and symmetries differ from conventional descriptions of active nematics. We check numerically our theoretical predictions, in particular the presence of π-symmetric propagative sound modes, and provide estimates of all scaling exponents governing long-range space-time correlations.

Emergence of dynamic vortex glasses in disordered polar active fluids

In equilibrium, disorder conspires with topological defects to redefine the ordered states of matter in systems as diverse as crystals, superconductors, and liquid crystals. Far from equilibrium, however, the consequences of quenched disorder on active condensed matter remain virtually uncharted. Here, we reveal a state of strongly disordered active matter with no counterparts in equilibrium: a dynamical vortex glass. Combining microfluidic experiments and theory, we show how colloidal flocks collectively cruise through disordered environments without relaxing the topological singularities of their flows. The resulting state is highly dynamical but the flow patterns, shaped by a finite density of frozen vortices, are stationary and exponentially degenerated. Quenched isotropic disorder acts as a random gauge field turning active liquids into dynamical vortex glasses. We argue that this robust mechanism should shape the collective dynamics of a broad class of disordered active matter, from synthetic active nematics to collections of living cells exploring heterogeneous media.

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.

Moving, Reproducing, and Dying Beyond Flatland: Malthusian Flocks in Dimensions d>2

We show that "Malthusian flocks"-i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion-belong to a new universality class in spatial dimensions d>2. We calculate the universal exponents and scaling laws of this new universality class to O(ε) in an ε=4-d expansion, and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks in d>2. Our expansion should be quite accurate in d=3, allowing precise quantitative comparisons between our theory, simulations, and experiments.

Phases and excitations of active rod-bead mixtures: simulations and experiments

We present a large-scale numerical study, supplemented by experimental observations, on a quasi-two-dimensional active system of polar rods and spherical beads confined between two horizontal plates and energised by vertical vibration. For a low rod concentration Φr, our observations are consistent with a direct phase transition, as bead concentration Φb is increased, from the isotropic phase to a homogeneous flock. For Φr above a threshold value, an ordered band dense in both rods and beads occurs between the disordered phase and the homogeneous flock, in both experiments and simulations. Within the size ranges accessible, we observe only a single band, whose width increases with Φr. Deep in the ordered state, we observe broken-symmetry "sound" modes and giant number fluctuations. The direction-dependent sound speeds and the scaling of fluctuations are consistent with the predictions of field theories of flocking; sound damping rates show departures from such theories, but the range of wavenumbers explored is modest. At very high densities, we see phase separation into rod-rich and bead-rich regions, both of which move coherently.

Giant number fluctuations in dry active polar fluids: A shocking analogy with lightning rods

It has been shown [H. Chaté et al., Phys. Rev. E 77, 046113 (2008) and F. Ginelli, Eur. Phys. J.: Spec. Top. 225, 2099 (2016)] that the hydrodynamic equations of dry active polar fluids (i.e., moving flocks without momentum conservation) imply giant number fluctuations. Specifically, the rms fluctuations ⟨(δN)²⟩ of the number N of active particles in a region containing a mean number of active particles ⟨N⟩ scale according to the law ⟨(δN)²⟩=K^'⟨N⟩^ϕ(d) with ϕ(d)=710+15d in d ≤ 4 spatial dimensions. This is much larger than the "law of large numbers" scaling ⟨(δN)²⟩=K⟨N⟩ found in most equilibrium and nonequilibrium systems. In this paper, it is demonstrated that giant number fluctuations also depend singularly on the shape of the box in which one counts the particles, vanishing in the limit of very thin and very fat boxes. These fluctuations arise not from large density fluctuations-indeed, the density fluctuations in polar ordered dry active fluids are not in general particularly large-but from long ranged spatial correlations between those fluctuations. These are shown to be closely related in two spatial dimensions to the electrostatic potential near a sharp upward pointing conducting wedge of opening angle 3π4=135° and in three dimensions to the electrostatic potential near a sharp upward pointing charged cone of opening angle 37.16°. This very precise prediction can be stringently tested by alternative box counting experiments that directly measure the direction dependence, as well as the scaling with distance, of the density-density correlation function.

Dynamical subclasses of dry active nematics

We show that the dominant mode of alignment plays an important role in dry active nematics, leading to two dynamical subclasses defined by the nature of the instability of the nematic bands that characterize, in these systems, the coexistence phase separating the isotropic and fluctuating nematic states. In addition to the well-known instability inducing long undulations along the band, another stronger instability leading to the breakup of the band in many transversal segments may arise. We elucidate the origin of this strong instability for a realistic model of self-propelled rods and determine the high-order nonlinear terms responsible for it at the hydrodynamic level.

Defect Unbinding in Active Nematics

We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the nonequilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane that separates the quasi-long-range ordered (nematic) and disordered (isotropic) phases. Below a critical activity, defects remain bound as rotational noise decorrelates the directed dynamics of +1/2 defects, stabilizing the quasi-long-range ordered nematic state. This activity threshold vanishes at low temperature, leading to a reentrant transition. At large enough activity, active forces always exceed thermal ones and the perturbative result fails, suggesting that in this regime activity will always disorder the system. Crucially, rotational diffusion being a two-dimensional phenomenon, defect unbinding cannot be described by a simplified one-dimensional model.

Isotropic-nematic transition of self-propelled rods in three dimensions

Using overdamped Brownian dynamics simulations we investigate the isotropic-nematic (IN) transition of self-propelled rods in three spatial dimensions. For two well-known model systems (Gay-Berne potential and hard spherocylinders) we find that turning on activity moves to higher densities the phase boundary separating an isotropic phase from a (nonpolar) nematic phase. This active IN phase boundary is distinct from the boundary between isotropic and polar-cluster states previously reported in two-dimensional simulation studies and, unlike the latter, is not sensitive to the system size. We thus identify a generic feature of anisotropic active particles in three dimensions.

Self-Propelled Particles with Velocity Reversals and Ferromagnetic Alignment: Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order

We introduce and study in two dimensions a new class of dry, aligning active matter that exhibits a direct transition to orientational order, without the phase-separation phenomenology usually observed in this context. Characterized by self-propelled particles with velocity reversals and a ferromagnetic alignment of polarities, systems in this class display quasi-long-range polar order with continuously varying scaling exponents, yet a numerical study of the transition leads to conclude that it does not belong to the Berezinskii-Kosterlitz-Thouless universality class but is best described as a standard critical point with an algebraic divergence of correlations. We rationalize these findings by showing that the interplay between order and density changes the role of defects.

A nonequilibrium force can stabilize 2D active nematics

Suspensions of actively driven anisotropic objects exhibit distinctively nonequilibrium behaviors, and current theories predict that they are incapable of sustaining orientational order at high activity. By contrast, here we show that nematic suspensions on a substrate can display order at arbitrarily high activity due to a previously unreported, potentially stabilizing active force. This force moreover emerges inevitably in theories of active orientable fluids under geometric confinement. The resulting nonequilibrium ordered phase displays robust giant number fluctuations that cannot be suppressed even by an incompressible solvent. Our results apply to virtually all experimental assays used to investigate the active nematic ordering of self-propelled colloids, bacterial suspensions, and the cytoskeleton and have testable implications in interpreting their nonequilibrium behaviors.