Scalar Active Matter Research Articles

Strong Casimir-like Forces in Flocking Active Matter.

Confining in space the equilibrium fluctuations of statistical systems with long-range correlations is known to result into effective forces on the boundaries. Here we demonstrate the occurrence of Casimir-like forces in the nonequilibrium context provided by flocking active matter. In particular, we consider a system of aligning self-propelled particles in two spatial dimensions that are transversally confined by reflecting or partially reflecting walls. We show that in the ordered flocking phase this confined active vectorial fluid is characterized by extensive boundary layers, as opposed to the finite ones usually observed in confined scalar active matter. Moreover, a finite-size, fluctuation-induced contribution to the pressure on the wall emerges, which decays slowly and algebraically upon increasing the distance between the walls. We explain our findings-which display a certain degree of universality-within a hydrodynamic description of the density and velocity fields.

Colloquium : Inclusions, boundaries, and disorder in scalar active matter

<i>Colloquium</i> : Inclusions, boundaries, and disorder in scalar active matter

An introduction to phase ordering in scalar active matter

AbstractThese notes provide an introduction to phase ordering in dry, scalar active matter. We first briefly review Model A and Model B, the long-standing continuum descriptions of ordering in systems with a non-conserved and conserved scalar order parameter. We then contrast different ways in which the field theories can be extended so that the phase ordering persists, but in systems that are active and do not reach thermodynamic equilibrium. The active models allow a wide range of dynamical steady states not seen in their passive counterparts. These include microphase separation, active foams and travelling density bands.

Dynamic control of the Bose–Einstein-like condensation transition in scalar active matter

The dynamics of a generic class of scalar active matter exhibiting a diffusivity edge is studied in a confining potential where the amplitude is governed by a time-dependent protocol. For such non-equilibrium systems, the diffusion coefficient vanishes when the single-particle density field reaches a critical threshold, inducing a condensation transition that is formally akin to Bose–Einstein condensation. We show that this transition arises even for systems that do not reach a steady state, leading to condensation in finite time. Since the transition can be induced for a fixed effective temperature by evolving the system, we effectively show that the temporal coordinate constitutes an alternative control parameter to tune the transition characteristics. For a constant-amplitude protocol, our generalised thermodynamics reduces in the steady-state limit to earlier results. Lastly, we show numerically that for periodic modulation of the potential amplitude, the condensation transition is reentrant.

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.

Capillary action and stationary currents in scalar active matter

Active matter consists of particles (motile microorganism or active colloids) that consume nutrients or fuel and convert it into a persistent motion, has received a lot of attention due to its intrinsic out-of-equilibrium character on the microscale [1]. The simplest representatives of active matter are spherically symmetric, active Brownian particles (ABPs) [2] without alignment, however, with excluded volume interactions [3,4].

Reentrant condensation transition in a model of driven scalar active matter with diffusivity edge

The effect of a diffusivity edge is studied in a system of scalar active matter confined by a periodic potential and driven by an externally applied force. We find that this system shows qualitatively distinct stationary regimes depending on the amplitude of the driving force with respect to the potential barrier. For small driving, the diffusivity edge induces a transition to a condensed phase analogous to the Bose–Einstein-like condensation reported for the nondriven case, which is characterized by a density-independent steady state current. Conversely, large external forces lead to a qualitatively different phase diagram since in this case condensation is only possible beyond a given density threshold, while the associated transition at higher densities is found to be reentrant.

Disordered boundaries destroy bulk phase separation in scalar active matter.

We show that disordered boundaries destroy bulk phase separation in scalar active systems in dimension d<d_{c}=3. This is in strong contrast with the equilibrium case where boundaries have no impact on the bulk of phase-separated systems. The underlying mechanism is revealed by considering a localized deformation of an otherwise flat wall, from which the case of a disordered boundary can be inferred. We find long-ranged correlations of the density field as well as a cascade of eddies which we show prevent bulk phase separation in low enough dimensions. The results are derived for dilute systems as well as in the presence of interactions, under the sole condition that the density field is the unique hydrodynamic mode. Our theoretical calculations are validated by numerical simulations of microscopic active systems.

Motility-induced clustering and meso-scale turbulence in active polar fluids

Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large scale dynamical patterns were reproduced in a simple model of a polar fluid, assuming a constant density of active particles. Recent, more detailed studies in a variety of experimental realizations of active polar fluids revealed additional interesting aspects, such as anomalous velocity statistics and clustering phenomena. Those phenomena cannot be explained by currently available models for active polar fluids. Herein, we extend the continuum model suggested by Dunkel et al to include density variations and a local feedback between the local density and self-propulsion speed of the active polar particles. If the velocity decreases strong enough with the density, a linear stability analysis of the resulting model shows that, in addition to the short-wavelength instability of the original model, a long-wavelength instability occurs. This is typically observed for high densities of polar active particles and is analogous to the well-known phenomenon of motility-induced phase separation (MIPS) in scalar active matter. We determine a simple phase diagram indicating the linear instabilities and perform systematic numerical simulations for the various regions in the corresponding parameter space. The interplay between the well understood short-range instability (leading to meso-scale turbulence) and the long-range instability (associated with MIPS) leads to interesting dynamics and novel phenomena concerning nucleation and coarsening processes. Our simulation results display a rich variety of novel patterns, including phase separation into domains with dynamically changing irregularly shaped boundaries. Anomalous velocity statistics are observed in all phases where the system segregates into regions of high and low densities. This offers a simple explanation for their occurrence in recent experiments with bacterial suspensions.

Disorder-Induced Long-Ranged Correlations in Scalar Active Matter.

We study the impact of quenched random potentials and torques on scalar active matter. Microscopic simulations reveal that motility-induced phase separation is replaced in two dimensions by an asymptotically homogeneous phase with anomalous long-ranged correlations and nonvanishing steady-state currents. Using a combination of phenomenological models and a field-theoretical treatment, we show the existence of a lower-critical dimension d_{c}=4, below which phase separation is only observed for systems smaller than an Imry-Ma length scale. We identify a weak-disorder regime in which the structure factor scales as S(q)∼1/q^{2}, which accounts for our numerics. In d=2, we predict that, at larger scales, the behavior should cross over to a strong-disorder regime. In d>2, these two regimes exist separately, depending on the strength of the potential.

Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model

Pair interactions between active particles need not follow Newton's third law. In this work we propose a continuum model of pattern formation due to non-reciprocal interaction between multiple species of scalar active matter. The classical Cahn-Hilliard model is minimally modified by supplementing the equilibrium Ginzburg-Landau dynamics with particle number conserving currents which cannot be derived from a free energy, reflecting the microscopic departure from action-reaction symmetry. The strength of the asymmetry in the interaction determines whether the steady state exhibits a macroscopic phase separation or a traveling density wave displaying global polar order. The latter structure, which is equivalent to an active self-propelled smectic phase, coarsens via annihilation of defects, whereas the former structure undergoes Ostwald ripening. The emergence of traveling density waves, which is a clear signature of broken time-reversal symmetry in this active system, is a generic feature of any multi-component mixture with microscopic non-reciprocal interactions.

Bose–Einstein-like condensation due to diffusivity edge under periodic confinement

A generic class of scalar active matter, characterized at the mean field level by the diffusivity vanishing above some threshold density, was recently introduced [Golestanian R 2019 Phys. Rev. E 100 010601(R)]. In the presence of harmonic confinement, such ‘diffusivity edge’ was shown to lead to condensation in the ground state, with the associated transition exhibiting formal similarities with Bose–Einstein condensation (BEC). In this work, the effect of a diffusivity edge is addressed in a periodic potential in arbitrary dimensions, where the system exhibits coexistence between many condensates. Using a generalized thermodynamic description of the system, it is found that the overall phenomenology of BEC holds even for finite energy barriers separating each neighbouring pair of condensates. Shallow potentials are shown to quantitatively affect the transition, and introduce non-universality in the values of the scaling exponents.

Statistical field theory and effective action method for scalar active matter

We employ Statistical Field Theory techniques for coarse-graining the steady-state properties of Active Ornstein-Uhlenbeck particles. The computation is carried on in the framework of the Unified Colored Noise approximation that allows an effective equilibrium picture. We thus develop a mean-field theory that allows to describe in a unified framework the phenomenology of scalar Active Matter. In particular, we are able to describe through spontaneous symmetry breaking mechanism two peculiar features of Active Systems that are (i) The accumulation of active particles at the boundaries of a confining container, and (ii) Motility-Induced Phase Separation (MIPS). \textcolor{black}{We develop a mean-field theory for steric interacting active particles undergoing to MIPS and for Active Lennard-Jones (ALJ) fluids.} \textcolor{black}{Within this framework}, we discuss the universality class of MIPS and ALJ \textcolor{black}{showing that it falls into Ising universality class.} We \textcolor{black}{thus} compute analytically the critical line $T_c(\tau)$ for both models. In the case of MIPS, $T_c(\tau)$ gives rise to a reentrant phase diagram compatible with an inverse transition from liquid to gas as the strength of the noise decreases. \textcolor{black}{However, in the case of particles interacting through anisotropic potentials, } the field theory acquires a $\varphi^3$ term that, \textcolor{black}{in general, cannot be canceled performing the expansion around the critical point.} In this case, the \textcolor{black}{Ising} critical point might \textcolor{black}{be replaced} by a first-order phase transition \textcolor{black}{region}.

Capillary Action in Scalar Active Matter.

We study the capacity of active matter to rise in thin tubes against gravity and other related phenomena like wetting of vertical plates and spontaneous imbibition, where a wetting liquid is drawn into a porous medium. This capillary action or capillarity is well known in classical fluids and originates from attractive interactions between the liquid molecules and the container walls, and from the attraction of the liquid molecules among each other. We observe capillarity in a minimal model for scalar active matter with purely repulsive interactions, where an effective attraction emerges due to slowdown during collisions between active particles and between active particles and walls. Simulations indicate that the capillary rise in thin tubes is approximately proportional to the active sedimentation length λ and that the wetting height of a vertical plate grows superlinear with λ. In a disordered porous medium the imbibition height scales as ⟨h⟩∝λϕ_{m}, where ϕ_{m} is its packing fraction. These predictions are highly relevant for suspensions of sedimenting active colloids or motile bacteria in a porous medium under the influence of a constant force field.

Collective forces in scalar active matter.

Large-scale collective behavior in suspensions of active particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the application of collective forces in synthetic active matter, as well as their role in living active matter.

Bose-Einstein-like condensation in scalar active matter with diffusivity edge.

Due to their remarkable properties, systems that exhibit self-organization of their components resulting from intrinsic microscopic activity have been extensively studied in the last two decades. In a generic class of active matter, the interactions between the active components are represented via an effective density-dependent diffusivity in a mean-field single-particle description. Here, a class of scalar active matter is proposed by incorporating a diffusivity edge into the dynamics: when the local density of the system surpasses a critical threshold, the diffusivity vanishes. The effect of the diffusivity edge is studied under the influence of an external potential, which introduces the ability to control the behavior of the system by changing an effective temperature, which is defined in terms of the single-particle diffusivity and mobility. At a critical effective temperature, a system that is trapped by a harmonic potential is found to undergo a condensation transition, which manifests formal similarities to Bose-Einstein condensation.

From bulk to microphase separation in scalar active matter: a perturbative renormalization group analysis

We consider a dynamical field theory (Active Model B+) that minimally extends the equilibrium Model B for diffusive phase separation of a scalar field, by adding leading-order terms that break time-reversal symmetry. It was recently shown that such active terms can cause the bulk phase separation of Model B to be replaced by a steady state of microphase separation at a finite length scale. This phenomenon was understood at mean-field level as due to the activity-induced reversal of the Ostwald ripening mechanism, which provides the kinetic pathway to bulk phase separation in passive fluids. This reversal occurs only in certain ranges for the activity parameters. In this paper we go beyond such a mean-field analysis and develop a -loop renormalisation group (RG) approach. We first show that, in the parameter range where bulk phase separation is still present, the critical point belongs formally to the same (Wilson–Fisher) universality class as the passive Model B. In contrast, in a parameter range associated with microphase separation, we find that an unstable non-equilibrium fixed point of the RG flow arises for , colliding with the Wilson–Fisher point in and making it unstable in . At large activity, the flow in this region is towards strong coupling. We argue that the phase transition to microphase separation in active systems, in the physically relevant dimensions and , very probably belongs to a new non-equilibrium universality class. Because it is governed by the strong-coupling regime of the RG flow, our perturbative analysis leaves open the quantitative characterization of this new class.

Generalized thermodynamics of phase equilibria in scalar active matter.

Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high densities. Starting from a continuum description of scalar active matter akin to a generalized Cahn-Hilliard equation, we give a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrodynamics scale, to extremizing an effective free energy. We illustrate our approach on two well-known models: self-propelled particles interacting either through a density-dependent propulsion speed or via direct pairwise forces. Our theory accounts quantitatively for their phase diagrams, providing a unified description of MIPS.