Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks

Tunable assembly of confined Janus microswimmers in sub-kHz AC electric fields under gravity

Active systems comprising micron-sized self-propelling units, also termed microswimmers, are promising candidates for the bottom-up assembly of small structures and reconfigurable materials. Here we leverage field-driven colloidal assembly to induce structural transformations in dense layers of microswimmers driven by an alternating current (AC) electric field and confined in a microfabricated trap under the influence of gravity. By varying the electric field frequency, we realize significant structural transformations, from a gas-like state at high frequencies to dynamically rearranging dense crystalline clusters at lower frequencies, characterized by vorticity in their dynamics. We demonstrate the ability to switch between these states on-demand, showing that the clustering mechanism differs from motility-induced phase separation. Our results offer a valuable framework for designing high-density active matter systems with controllable structural properties, envisioned to advance the development of artificial materials with self-healing and reconfiguration capabilities.

Interfacial and density fluctuations in a lattice model of motility-induced phase separation

We analyze motility-induced phase separation and bubbly phase separation in a two-dimensional lattice model of self-propelled particles. We compare systems where the dense (liquid) phase has slab and droplet geometries. We find that interfacial fluctuations of the slab are well-described by capillary wave theory, despite the existence of bubbles in the dense phase. We attribute this to a separation of time scales between bubble expulsion and interfacial relaxation. We also characterize the dependence of liquid and vapor densities on the curvature of the liquid droplet, as well as the density fluctuations inside the phases. The vapor phase behaves similarly to an equilibrium system, displaying a Laplace pressure effect that shifts its density, and Gaussian density fluctuations. The liquid phase has large non-Gaussian fluctuations, but this is not accompanied by a large density shift, contrary to the equilibrium case. Nevertheless, the shift of the vapor density can be used to infer an effective surface tension that appears to also quantify capillary wave fluctuations.

Persistent exclusion process with time-periodic drive

We study a persistent exclusion process with time-periodic external potential on a one-dimensional periodic lattice through numerical simulations. A set of run-and-tumble particles move on a lattice of length L and tumbling probability γ≪1 and interact among each other via hard-core exclusion. The effect of the external potential has been modeled as a special site where the tumbling probability is 1. We call it a "defect" site and move its location along the ring lattice with speed u. In the case of γ=0 the system goes to a jammed state when there is no defect. But introduction of the moving defect creates a strongly phase-separated state where almost all active particles are present in a single large cluster, for small and moderate u. This striking effect is caused by the long-range velocity correlation of the active particles, induced by the moving defect. For large u, a single large cluster is no longer stable and breaks into multiple smaller clusters. For nonzero γ a competition develops between the timescales associated with tumbling and defect motion. While the moving defect attempts to create long-range velocity order, bulk tumbling tends to randomize the velocity alignment. If γ is comparable to u/L, then a relatively small number of tumbles take place during the time the moving defect travels through the entire system. In this case, the defect has enough time to restore the order in the system and our simulations show that the long-range order in velocity and density survive for γ values in this range. As γ increases further, long-range order is destroyed and the system develops multiple regions of high and low density. We characterize the density inhomogeneity in this case by measuring subsystem density fluctuations and present a heat map in the γ-u plane showing the regions with most pronounced density inhomogeneities.

Re-entrant percolation in active Brownian hard disks

Non-equilibrium clustering and percolation are investigated in an archetypal model of two-dimensional active matter using dynamic simulations of self-propelled Brownian repulsive particles. We concentrate on the single-phase region up to moderate levels of activity, before motility-induced phase separation (MIPS) sets in. Weak activity promotes cluster formation and lowers the percolation threshold. However, driving the system further out of equilibrium partly reverses this effect, resulting in a minimum in the critical density for the formation of system-spanning clusters and introducing re-entrant percolation as a function of activity in the pre-MIPS regime. This non-monotonic behaviour arises from competition between activity-induced effective attraction (which eventually leads to MIPS) and activity-driven cluster breakup. Using an adapted iterative Boltzmann inversion method, we derive effective potentials to map weakly active cases onto a passive (equilibrium) model with conservative attraction, which can be characterised by Monte Carlo simulations. While the active and passive systems have practically identical radial distribution functions, we find decisive differences in higher-order structural correlations, to which the percolation threshold is highly sensitive. For sufficiently strong activity, no passive pairwise potential can reproduce the radial distribution function of the active system.

Collective behavior of squirmers in thin films

Bacteria in biofilms form complex structures and can collectively migrate within mobile aggregates, which is referred to as swarming. This behavior is influenced by a combination of various factors, including morphological characteristics and propulsive forces of swimmers, their volume fraction within a confined environment, and hydrodynamic and steric interactions between them. In our study, we employ the squirmer model for microswimmers and the dissipative particle dynamics method for fluid modeling to investigate the collective motion of swimmers in thin films. The film thickness permits a free orientation of non-spherical squirmers, but constraints them to form a two-layered structure at maximum. Structural and dynamic properties of squirmer suspensions confined within the slit are analyzed for different volume fractions of swimmers, motility types (e.g., pusher, neutral squirmer, puller), and the presence of a rotlet dipolar flow field, which mimics the counter-rotating flow generated by flagellated bacteria. Different states are characterized, including a gas-like phase, swarming, and motility-induced phase separation, as a function of increasing volume fraction. Our study highlights the importance of an anisotropic swimmer shape, hydrodynamic interactions between squirmers, and their interaction with the walls for the emergence of different collective behaviors. Interestingly, the formation of collective structures may not be symmetric with respect to the two walls. Furthermore, the presence of a rotlet dipole significantly mitigates differences in the collective behavior between various swimmer types. These results contribute to a better understanding of the formation of bacterial biofilms and the emergence of collective states in confined active matter.

Percolation of nonequilibrium assemblies of colloidal particles in active chiral liquids

The growing interest in the non-equilibrium assembly of colloidal particles in active liquids is driven by the motivation to create novel structures endowed with tunable properties unattainable within the confines of equilibrium systems. Here, we present an experimental investigation of the structural features of colloidal assemblies in active liquids of chiral E. coli. The colloidal particles form dynamic clusters due to the effective interaction mediated by active media. The activity and chirality of the swimmers strongly influence the dynamics and local ordering of colloidal particles, resulting in clusters with persistent rotation, whose structure differs significantly from those in equilibrium systems with attractive interactions, such as colloid-polymer mixtures. Our colloid-bacteria mixture displays several hallmark features of a percolation transition at a critical density, where the clusters span the system size. A closer examination of the critical exponents associated with cluster size distribution, the average cluster size, and the correlation length in the vicinity of the critical density shows deviations from the prediction of the standard continuum percolation model. Therefore, our experiments reveal a richer phase behavior of colloidal assemblies in active liquids.

Kinetic Theory of Motility Induced Phase Separation for Active Brownian Particles

When two active Brownian particles collide, they slide along each other until they can continue their free motion. For persistence lengths much larger than the particle diameter, the directors do not change, but the collision can be modeled as producing a net displacement on the particles compared to their free motion in the absence of the encounter. With these elements, a Boltzmann-Enskog-like kinetic theory is built. A linear stability analysis of the homogeneous state predicts a density instability resulting from the effective velocity reduction of tagged particles predicted by the theory.

Time-dependent properties of run-and-tumble particles: Density relaxation

We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient D(ρ,γ) for arbitrary density ρ and tumbling rate γ, in systems on a d-dimensional periodic lattice. We study two minimal models of RTPs: Model I is the standard version of hardcore RTPs introduced in [Phys. Rev. E 89, 012706 (2014)10.1103/PhysRevE.89.012706], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion, an analytically tractable variant of model I. We calculate the bulk-diffusion coefficient analytically for model II and numerically for model I through an efficient Monte Carlo algorithm; notably, both models have qualitatively similar features. In the strong-persistence limit γ→0 (i.e., dimensionless ratio r_{0}γ/v→0), with v and r_{0} being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales: (i) persistence length l_{p}=v/γ and (ii) a "mean free path," being a measure of the average empty stretch or gap size in the hopping direction. We find that the bulk-diffusion coefficient varies as a power law in a wide range of density: D∝ρ^{-α}, with exponent α gradually crossing over from α=2 at high densities to α=0 at low densities. As a result, the density relaxation is governed by a nonlinear diffusion equation with anomalous spatiotemporal scaling. In the thermodynamic limit, we show that the bulk-diffusion coefficient-for ρ,γ→0 with ρ/γ fixed-has a scaling form D(ρ,γ)=D^{(0)}F(ρav/γ), where a∼r_{0}^{d-1} is particle cross section and D^{(0)} is proportional to the diffusion coefficient of noninteracting particles; the scaling function F(ψ) is calculated analytically for model II (LLG) and numerically for model I. Our arguments are independent of dimensions and microscopic details.

Bridging the gap between collective motility and epithelial-mesenchymal transitions through the active finite voronoi model

We introduce an active version of the recently proposed finite Voronoi model of epithelial tissue. The resultant Active Finite Voronoi (AFV) model enables the study of both confluent and non-confluent geometries and transitions between them, in the presence of active cells. Our study identifies six distinct phases, characterized by aggregation-segregation, dynamical jamming-unjamming, and epithelial-mesenchymal transitions (EMT), thereby extending the behavior beyond that observed in previously studied vertex-based models. The AFV model with rich phase diagram provides a cohesive framework that unifies the well-observed progression to collective motility via unjamming with the intricate dynamics enabled by EMT. This approach should prove useful for challenges in developmental biology systems as well as the complex context of cancer metastasis. The simulation code is also provided.

Inertia changes evolution of motility-induced phase separation in active matter across particle activity

The effects of inertia in active matter and motility-induced phase separation (MIPS) have attracted growing interest but still remain poorly studied. We studied MIPS behavior in the Langevin dynamics across a broad range of particle activity and damping rate values with molecular dynamic simulations. Here we show that the MIPS stability region across particle activity values consists of several domains separated by discontinuous or sharp changes in susceptibility of mean kinetic energy. These domain boundaries have fingerprints in the system's kinetic energy fluctuations and characteristics of gas, liquid, and solid subphases, such as the number of particles, densities, or the power of energy release due to activity. The observed domain cascade is most stable at intermediate damping rates but loses its distinctness in the Brownian limit or vanishes along with phase separation at lower damping values.

Coarsening, condensates, and extremes in aggregation-fragmentation models

We use extreme value statistics to study the dynamics of coarsening in aggregation-fragmentation models which form condensates in the steady state. The dynamics is dominated by the formation of local condensates on a coarsening length scale which grows in time in both the zero range process and conserved mass aggregation model. The local condensate mass distribution exhibits scaling, which implies anomalously large fluctuations, with mean and standard deviation both proportional to the coarsening length. Remarkably, the state of the system during coarsening is governed not by the steady state, but rather a preasymptotic state in which the condensate mass fluctuates strongly.

Emergent collective behavior of active Brownian particles with visual perception

Systems comprised of self-steering active Brownian particles are studied via simulations for a minimal cognitive flocking model. The dynamics of the active Brownian particles is extended by an orientational response with limited maneuverability to an instantaneous visual input of the positions of neighbors within a vision cone and a cut-off radius. The system exhibits large-scale self-organized structures, which depend on selected parameter values, and, in particular, the presence of excluded-volume interactions. The emergent structures in two dimensions, such as worms, worm-aggregate coexistence, and hexagonally close-packed structures, are analysed and phase diagrams are constructed. The analysis of the particle's mean-square displacement shows ABP-like dynamics for dilute systems and the worm phase. In the limit of densely packed structures, the active diffusion coefficient is significantly smaller and depends on the number of particles in the cluster. Our analysis of the cluster-growth dynamics shows distinct differences to processes in systems of short-range attractive colloids in equilibrium. Specifically, the characteristic time for the growth and decay of clusters of a particular size is longer than that of isotropically attractive colloids, which we attribute to the non-reciprocal nature of the directed visual perception. Our simulations reveal a strong interplay between ABP-characteristic interactions, such as volume exclusion and rotational diffusion, and cognitive-based interactions and navigation.

Effect of anisotropy on the formation of active particle films

Active colloids belong to a class of nonequilibrium systems where energy uptake, conversion, and dissipation occur at the level of individual colloidal particles, which can lead to particles' self-propelled motion and surprising collective behavior. Examples include coexistence of vapor- and liquid-like steady states for active particles with repulsive interactions only, phenomena known as motility-induced phase transitions. Similarly to motile unicellular organisms, active colloids tend to accumulate at confining surfaces forming dense adsorbed films. In this work, we study the structure and dynamics of aggregates of self-propelled particles near confining solid surfaces, focusing on the effects of the particle anisotropic interactions. We performed Langevin dynamics simulations of two complementary models for active particles: ellipsoidal particles interacting through the Gay-Berne potential and rodlike particles composed of several repulsive Lennard-Jones beads. We observe a nonmonotonic behavior of the structure of clusters formed along the confining surface as a function of the particle aspect ratio, with a film spreading when particles are near-spherical, compact clusters with hedgehog-like particle orientation for more elongated active particles, and a complex dynamical behavior for an intermediate aspect ratio. The stabilization time of cluster formation along the confining surface also displays a nonmonotonic dependence on the aspect ratio, with a local minimum at intermediate values. Additionally, we demonstrate that the hedgehog-like aggregates formed by Gay-Berne ellipsoids exhibit higher structural stability as compared to the ones formed by purely repulsive active rods, which are stable due to the particle activity only.

Motile Topological Defects Hinder Dynamical Arrest in Dense Liquids of Active Ellipsoids

Recent numerical studies have identified the persistence time of active motion as a critical parameter governing glassy dynamics in dense active matter. Here we studied dynamics in liquids of granular active ellipsoids with tunable persistence and velocity. We show that increasing the persistence time at moderate supercooling is equivalent to increasing the strength of attraction in equilibrium liquids and results in reentrant dynamics not just in the translational degrees of freedom, as anticipated, but also in the orientational ones. However, at high densities, motile topological defects, unique to active liquids of elongated particles, hindered dynamical arrest. Most remarkably, for the highest activity, we observed intermittent dynamics due to the jamming-unjamming of these defects for the first time.

Enhanced diffusivity in microscopically reversible active matter

The physics of self-propelled objects at the nanoscale is a rapidly developing research field where recent experiments have focused on the motion of individual catalytic enzymes. Contrary to the experimental advancements, theoretical understanding of the possible self-propulsion mechanisms at these scales is limited. A particularly puzzling question concerns the origins of the reportedly high diffusivities of the individual enzymes. Here we start with the fundamental principle of microscopic reversibility (MR) of chemical reactions powering self-propulsion and demonstrate that MR can lead to an increase of the particle mobility and of the short- and long-time diffusion coefficients as compared to dynamics where MR is neglected. Furthermore, the derived diffusion coefficients are enhanced due to the action of an external force. These results can shed new light on interpretations of the measured diffusivities and help to test the relevance of MR for the active motion of individual nanoswimmers.

Active interaction switching controls the dynamic heterogeneity of soft colloidal dispersions

We employ Reactive Dynamical Density Functional Theory (R-DDFT) and Reactive Brownian Dynamics (R-BD) simulations to investigate the dynamics of a suspension of active soft Gaussian colloids with binary interaction switching, i.e., a one-component colloidal system in which every particle stochastically switches at predefined rates between two interaction states with different mobility. Using R-DDFT we extend a theory previously developed to access the dynamics of inhomogeneous liquids [Archer et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 75, 040501] to study the influence of the switching activity on the self and distinct part of the Van Hove function in bulk solution, and determine the corresponding mean squared displacement of the switching particles. Our results demonstrate that, even though the average diffusion coefficient is not affected by the switching activity, it significantly modifies the non-equilibrium dynamics and diffusion coefficients of the individual particles, leading to a crossover from short to long times, with a regime for intermediate times showing anomalous diffusion. In addition, the self-part of the van Hove function has a Gaussian form at short and long times, but becomes non-Gaussian at intermediates ones, having a crossover between short and large displacements. The corresponding self-intermediate scattering function shows the two-step relaxation patters typically observed in soft materials with heterogeneous dynamics such as glasses and gels. We also introduce a phenomenological Continuous Time Random Walk (CTRW) theory to understand the heterogeneous diffusion of this system. R-DDFT results are in excellent agreement with R-BD simulations and the analytical predictions of CTRW theory, thus confirming that R-DDFT constitutes a powerful method to investigate not only the structure and phase behavior, but also the dynamical properties of non-equilibrium active switching colloidal suspensions.

Alignment interactions drive structural transitions in biological tissues

Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a nonequilibrium phase transition into a quasihexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of the alignment coupling. In this regime, the dynamics of cell centers and shape fluctuation show features typical of glassy systems.

Diversity of self-propulsion speeds reduces motility-induced clustering in confined active matter

Self-propelled swimmers such as bacteria agglomerate into clusters as a result of their persistent motion. In 1D, those clusters do not coalesce macroscopically and the stationary cluster size distribution (CSD) takes an exponential form. We develop a minimal lattice model for active particles in narrow channels to study how clustering is affected by the interplay between self-propulsion speed diversity and confinement. A mixture of run-and-tumble particles with a distribution of self-propulsion speeds is simulated in 1D. Particles can swap positions at rates proportional to their relative self-propulsion speed. Without swapping, we find that the average cluster size L_c decreases with diversity and follows a non-arithmetic power mean of the single-component L_c's, unlike the case of tumbling-rate diversity previously studied. Effectively, the mixture is thus equivalent to a system of identical particles whose self-propulsion speed is the harmonic mean self-propulsion speed of the mixture. With swapping, particles escape more quickly from clusters. As a consequence, L_c decreases with swapping rates and depends less strongly on diversity. We derive a dynamical equilibrium theory for the CSDs of binary and fully polydisperse systems. Similarly to the clustering behaviour of one-component models, our qualitative results for mixtures are expected to be universal across active matter. Using literature experimental values for the self-propulsion speed diversity of unicellular swimmers known as choanoflagellates, which naturally differentiate into slower and faster cells, we predict that the error in estimating their L_cvia one-component models which use the conventional arithmetic mean self-propulsion speed is around 30%.

Dynamics of flowing 2D skyrmions

We investigate, numerically, the effects of externally imposed material flows on the structure and temporal evolution of liquid crystal (LC) skyrmions. The dynamics of a 2D system of skyrmions is modeled using the Ericksen-Leslie theory, which is based on two coupled equations, one for material flow and the other for the director field. As the time scales of the velocity and director fields differ by several orders of magnitude for realistic values of the system parameters, we have simplified the calculations by assuming that the velocity relaxes instantaneously when compared to the relaxation of the director field. Thus, we have used a finite-differences method known as artificial compressibility with adaptive time step to solve the velocity field and a fourth-order Runge-Kutta method for the director field. We characterized the skyrmion shape or configuration as a function of the time and the average velocity of the flow field. We found that for velocities above a certain threshold, the skyrmions stretch in the direction perpendicular to the flow, by contrast to the regime of weak flows where the skyrmions stretch along the streamlines of the flow field. These two regimes are separated by an abrupt (first-order) dynamical transition, which is robust with respect to e.g., the LC elastic anisotropy. Additionally, we have found how the presence of a second skyrmion affects the evolution of the shape of the skyrmions, by comparing the evolution of pairs of skyrmions to the evolution of a single-skyrmion.

Kinetic Monte Carlo Algorithms for Active Matter Systems

We study kinetic Monte Carlo (KMC) descriptions of active particles. We show that, when they rely on purely persistent, active steps, their continuous-time limit is ill-defined, leading to the vanishing of trademark behaviors of active matter such as the motility-induced phase separation, ratchet effects, as well as to a diverging mechanical pressure. We then show how, under an appropriate scaling, mixing passive steps with active ones leads to a well-defined continuous-time limit that however differs from standard active dynamics. Finally, we propose new KMC algorithms whose continuous-time limits lead to the dynamics of active Ornstein-Uhlenbeck, active Brownian, and run-and-tumble particles.

Effect of polydispersity on the dynamics of active Brownian particles

We numerically study the dynamics and the phases of self-propelled disk-shaped particles of different sizes with soft repulsive potential in two dimensions. Size diversity is introduced by the polydispersity index (PDI) ε, which is the width of the uniform distribution of the particle's radius. The self-propulsion speed of the particles controls the activity v. We observe enhanced dynamics for large size diversity among the particles. We calculate the effective diffusion coefficient D_{eff} in the steady state. The system exhibits four distinct phases, jammed phase with small D_{eff} for small activity and liquid phase with enhanced D_{eff} for large activity. The number fluctuation is larger and smaller than the equilibrium limit in the liquid and jammed phases, respectively. Further, the jammed phase is of two types: solid jammed and liquid jammed for small and large PDI. Whereas the liquid phase is called motility induced phase separation (MIPS) liquid for small PDI and for large PDI, we find enhanced diffusivity and call it the pure liquid phase. The system is studied for three packing densities ϕ, and the response of the system for polydispersity is the same for all ϕ's. Our study can help understand the behavior of cells of various sizes in a tissue, artificial self-driven granular particles, or living organisms of different sizes in a dense environment.

Wetting of a solid surface by active matter

A lattice model is used to study repulsive active particles at a planar surface. A rejection-free Kinetic Monte Carlo method is employed to characterize the wetting behaviour. The model predicts a motility-induced phase separation of active particles, and the bulk coexistence of dense liquid-like and dilute vapour-like steady states is determined. An "ensemble", with a varying number of particles, analogous to a grand canonical ensemble in equilibrium, is introduced. The formation and growth of the liquid film between the solid surface and the vapour phase is investigated. At constant activity, as the system is brought towards coexistence from the vapour side, the thickness of the adsorbed film exhibits a divergent behaviour regardless of the activity. This suggests a complete wetting scenario along the full coexistence curve.

Active mixtures in a narrow channel: motility diversity changes cluster sizes

The persistent motion of bacteria produces clusters with a stationary cluster size distribution (CSD). Here we develop a minimal model for bacteria in a narrow channel to assess the relative importance of motility diversity (i.e. polydispersity in motility parameters) and confinement. A mixture of run-and-tumble particles with a distribution of tumbling rates (denoted generically by α) is considered on a 1D lattice. Particles facing each other cross at constant rate, rendering the lattice quasi-1D. To isolate the role of diversity, the global average α stays fixed. For a binary mixture with no particle crossing, the average cluster size (Lc) increases with the diversity as lower-α particles trap higher-α ones for longer. At finite crossing rate, particles escape from the clusters sooner, making Lc smaller and the diversity less important, even though crossing can enhance demixing of particle types between the cluster and gas phases. If the crossing rate is increased further, the clusters become controlled by particle crossing. We also consider an experiment-based continuous distribution of tumbling rates, revealing similar physics. Using parameters fitted from experiments with Escherichia coli bacteria, we predict that the error in estimating Lc without accounting for polydispersity is around 60%. We discuss how to find a binary system with the same CSD as the fully polydisperse mixture. An effective theory is developed and shown to give accurate expressions for the CSD, the effective α, and the average fraction of mobile particles. We give reasons why our qualitative results are expected to be valid for other active matter models and discuss the changes that would result from polydispersity in the active speed rather than in the tumbling rate.

Statistical mechanics of active Ornstein-Uhlenbeck particles

We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.

Frictional active Brownian particles

Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles and their motility-induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional systems become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility-induced phase diagram by tuning the roughness of the particles.

Frictional active Brownian particles

Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles and their motility-induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional systems become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility-induced phase diagram by tuning the roughness of the particles.

Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems

We study the stationary dynamics of an active interacting Brownian particle system. We measure the violations of the fluctuation dissipation theorem, and the corresponding effective temperature, in a locally resolved way. Quite naturally, in the homogeneous phases the diffusive properties and effective temperature are also homogeneous. Instead, in the inhomogeneous phases (close to equilibrium and within the MIPS sector) the particles can be separated in two groups with different diffusion properties and effective temperatures. Notably, at fixed activity strength the effective temperatures in the two phases remain distinct and approximately constant within the MIPS region, with values corresponding to the ones of the whole system at the boundaries of this sector of the phase diagram. We complement the study of the globally averaged properties with the theoretical and numerical characterization of the fluctuation distributions of the single-particle diffusion, linear response, and effective temperature in the homogeneous and inhomogeneous phases. We also distinguish the behavior of the (time-delayed) effective temperature from the (instantaneous) kinetic temperature, showing that the former is independent of the friction coefficient.

Hydrodynamics, superfluidity, and giant number fluctuations in a model of self-propelled particles

We derive hydrodynamics of a prototypical one-dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients-the hardcore interaction and the competing mechanisms of short- and long-range hopping. We calculate two density-dependent transport coefficients-the bulk-diffusion coefficient and the conductivity, the ratio of which, despite violation of detailed balance, is connected to particle-number fluctuation by an Einstein relation. In the limit of infinite-range hopping, the model exhibits, upon tuning density ρ (or activity), a "superfluidlike" transition from a finitely conducting fluid phase to an infinitely conducting "superfluid" phase, characterized by a divergence in conductivity χ(ρ)∼(ρ-ρ_{c})^{-1} with ρ_{c} being the critical density. The diverging conductivity greatly increases particle (or vacancy) mobility and thus induces "giant" number fluctuations in the system.

Unjamming of active rotators

Active particle assemblies can exhibit a wide range of interesting dynamical phases depending on internal parameters such as density, adhesion strength or self-propulsion. Active self-rotations are rarely studied in this context, although they can be relevant for active matter systems, as we illustrate by analyzing the motion of Chlamydomonas reinhardtii algae under different experimental conditions. Inspired by this example, we simulate the dynamics of a system of interacting active disks endowed with active torques and self-propulsive forces. At low packing fractions, adhesion causes the formation of small rotating clusters, resembling those observed when algae are stressed. At higher densities, the model shows a jamming to unjamming transition promoted by active torques and hindered by adhesion. We also study the interplay between self-propulsion and self-rotation and derive a phase diagram. Our results yield a comprehensive picture of the dynamics of active rotators, providing useful guidance to interpret experimental results in cellular systems where rotations might play a role.

A lattice kinetic Monte-Carlo method for simulating chromosomal dynamics and other (non-)equilibrium bio-assemblies

Biological assemblies in living cells such as chromosomes constitute large many-body systems that operate in a fluctuating, out-of-equilibrium environment. Since a brute-force simulation of that many degrees of freedom is currently computationally unfeasible, it is necessary to perform coarse-grained stochastic simulations. Here, we develop all tools necessary to write a lattice kinetic Monte-Carlo (LKMC) algorithm capable of performing such simulations. We discuss the validity and limits of this approach by testing the results of the simulation method in simple settings. Importantly, we illustrate how at large external forces Metropolis-Hastings kinetics violate the fluctuation-dissipation and steady-state fluctuation theorems and discuss better alternatives. Although this simulation framework is rather general, we demonstrate our approach using a DNA polymer with interacting SMC condensin loop-extruding enzymes. Specifically, we show that the scaling behavior of the loop-size distributions that we obtain in our LKMC simulations of this SMC-DNA system is consistent with that reported in other studies using Brownian dynamics simulations and analytic approaches. Moreover, we find that the irreversible dynamics of these enzymes under certain conditions result in frozen, sterically jammed polymer configurations, highlighting a potential pitfall of this approach.

Tuning the self-organization of confined active particles by the steepness of the trap

We consider the collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with small rotational fluctuations. They also interact with each other via soft, isotropic, repulsive potentials. The particles are confined in a circular trap. The steepness of the trap is tuneable. The average packing fraction of the particles is low. When the trap is steep, particles flock along its boundary. They form a polar cluster that spreads over the boundary. The cluster is not spatially ordered. We show that when the steepness is decreased beyond a threshold value, the cluster becomes round and compact and eventually spatial order (hexagonal) emerges in addition to the pre-established polar order. We investigate the kinetics of such ordering. We find that while rotating around the centre of the trap along its circular boundary, the cluster needs to roll around its centre of mass to be spatially ordered. We have studied the stability of the order when the trap is suddenly switched off. We find that for the particles with velocity alignment interaction, the decay of the spatial order is much slower than the particles without the alignment interaction.

Clustering and anisotropic correlated percolation in polar flocks

We study clustering and percolation phenomena in the Vicsek model, taken here in its capacity of prototypical model for dry aligning active matter. Our results show that the order-disorder transition is not related in any way to a percolation transition, contrary to some earlier claims. We study geometric percolation in each of the phases at play, but we mostly focus on the ordered Toner-Tu phase, where we find that the long-range correlations of density fluctuations give rise to an anisotropic percolation transition.

Interrupted Motility Induced Phase Separation in Aligning Active Colloids

Switching on high activity in a relatively dense system of active Janus colloids, we observe fast clustering, followed by cluster aggregation towards full phase separation. The phase separation process is however interrupted when large enough clusters start breaking apart. Following the cluster size distribution as a function of time, we identify three successive dynamical regimes. Tracking both the particle positions and orientations, we characterize the structural ordering and alignment in the growing clusters and thereby unveil the mechanisms at play in these regimes. In particular, we identify how alignment between the neighboring particles is responsible for the interruption of the full phase separation. Our large scale quantification of the phase separation kinetics in active colloids points towards the new physics observed when both alignment and short-range repulsions are present.

Critical Motility-Induced Phase Separation Belongs to the Ising Universality Class

A collection of self-propelled particles with volume exclusion interactions can exhibit the phenomenology of a gas-liquid phase separation, known as motility-induced phase separation (MIPS). The nonequilibrium nature of the system is fundamental to the phase transition; however, it is unclear whether MIPS at criticality contributes a novel universality class to nonequilibrium physics. We demonstrate here that this is not the case by showing that a generic critical MIPS belongs to the Ising universality class with conservative dynamics.

Thermodynamic phases in two-dimensional active matter

Active matter has been much studied for its intriguing properties such as collective motion, motility-induced phase separation and giant fluctuations. However, it has remained unclear how the states of active materials connect with the equilibrium phases. For two-dimensional systems, this is also because the understanding of the liquid, hexatic, and solid equilibrium phases and their phase transitions is recent. Here we show that two-dimensional self-propelled point particles with inverse-power-law repulsions moving with a kinetic Monte Carlo algorithm without alignment interactions preserve all equilibrium phases up to very large activities. Furthermore, at high activity within the liquid phase, a critical point opens up a gas–liquid motility-induced phase separation region. In our model, two-step melting and motility-induced phase separation are thus independent phenomena. We discuss the reasons for these findings to be common to a wide class of two-dimensional active systems.

Adapting statistical physics tools to study active systems is challenging due to their non-equilibrium nature. Here the authors use simulations to present a phase diagram of a 2D active system, showing a two-step melting scenario far from equilibrium along with gas-liquid motility-induced phase separation.

Phase separation in binary mixtures of active and passive particles

We study binary mixtures of small active and big passive athermal particles interacting via soft repulsive forces on a frictional substrate. Athermal self propelled particles are known to phase separate into a dense aggregate and a dilute gas-like phase at fairly low packing fractions. Known as motility induced phase separation, this phenomenon governs the behaviour of binary mixtures for small to intermediate size ratios of the particle species. An effective attraction between passive particles, due to the surrounding active medium, leads to true phase separation for large size ratios and volume fractions of active particles. The effective interaction between active and passive particles can be attractive or repulsive at short range depending on the size ratio and volume fractions of the particles. This affects the clustering of passive particles. We find three distinct phases based on the spatial distribution of passive particles. The cluster size distribution of passive particles decays exponentially in the homogeneous phase. It decays as a power law with an exponential cutoff in the clustered phase and tends to a power law as the system approaches the transition to the phase separated state. We present a phase diagram in the plane defined by the size ratio and volume fraction of passive particles.

Modeling persistence of motion in a crowded environment: The diffusive limit of excluding velocity-jump processes

Persistence of motion is the tendency of an object to maintain motion in a direction for short time scales without necessarily being biased in any direction in the long term. One of the most appropriate mathematical tools to study this behavior is an agent-based velocity-jump process. In the absence of agent-agent interaction, the mean-field continuum limit of the agent-based model (ABM) gives rise to the well known hyperbolic telegraph equation. When agent-agent interaction is included in the ABM, a strictly advective system of partial differential equations (PDEs) can be derived at the population level. However, no diffusive limit of the ABM has been obtained from such a model. Connecting the microscopic behavior of the ABM to a diffusive macroscopic description is desirable, since it allows the exploration of a wider range of scenarios and establishes a direct connection with commonly used statistical tools of movement analysis. In order to connect the ABM at the population level to a diffusive PDE at the population level, we consider a generalization of the agent-based velocity-jump process on a two-dimensional lattice with three forms of agent interaction. This generalization allows us to take a diffusive limit and obtain a faithful population-level description. We investigate the properties of the model at both the individual and population levels and we elucidate some of the models' key characteristic features. In particular, we show an intrinsic anisotropy inherent to the models and we find evidence of a spontaneous form of aggregation at both the micro- and macroscales.

Vitrification and gelation in sticky spheres

Glasses and gels are the two dynamically arrested, disordered states of matter. Despite their importance, their similarities and differences remain elusive, especially at high density, where until now it has been impossible to distinguish them. We identify dynamical and structural signatures which distinguish the gel and glass transitions in a colloidal model system of hard and "sticky" spheres. It has been suggested that "spinodal" gelation is initiated by gas-liquid viscoelastic phase separation to a bicontinuous network and the resulting densification leads to vitrification of the colloid-rich phase, but whether this phase has sufficient density for arrest is unclear [M. A. Miller and D. Frenkel, Phys. Rev. Lett. 90, 135702 (2003) and P. J. Lu et al., Nature 435, 499-504 (2008)]. Moreover alternative mechanisms for arrest involving percolation have been proposed [A. P. R. Eberle et al., Phys. Rev. Lett. 106, 105704 (2011)]. Here we resolve these outstanding questions, beginning by determining the phase diagram. This, along with demonstrating that percolation plays no role in controlling the dynamics of our system, enables us to confirm spinodal decomposition as the mechanism for gelation. We are then able to show that gels can be formed even at much higher densities than previously supposed, at least to a volume fraction of ϕ = 0.59. Far from being networks, these gels apparently resemble glasses but are still clearly distinguished by the "discontinuous" nature of the transition and the resulting rapid solidification, which leads to the formation of inhomogeneous (with small voids) and far-from-equilibrium local structures. This is markedly different from the glass transition, whose continuous nature leads to the formation of homogeneous and locally equilibrated structures. We further reveal that the onset of the attractive glass transition in the form of a supercooled liquid is in fact interrupted by gelation. Our findings provide a general thermodynamic, dynamic, and structural basis upon which we can distinguish gelation from vitrification.

Collective motion of active Brownian particles with polar alignment

We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles. We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (active brownian particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.

Aggregation-fragmentation and individual dynamics of active clusters

A remarkable feature of active matter is the propensity to self-organize. One striking instance of this ability to generate spatial structures is the cluster phase, where clusters broadly distributed in size constantly move and evolve through particle exchange, breaking or merging. Here we propose an exhaustive description of the cluster dynamics in apolar active matter. Exploiting large statistics gathered on thousands of Janus colloids, we measure the aggregation and fragmentation rates and rationalize the resulting cluster size distribution and fluctuations. We also show that the motion of individual clusters is entirely consistent with a model positing random orientation of colloids. Our findings establish a simple, generic model of cluster phase, and pave the way for a thorough understanding of clustering in active matter.

Mode-coupling theory for active Brownian particles

We present a mode-coupling theory (MCT) for the slow dynamics of two-dimensional spherical active Brownian particles (ABPs). The ABPs are characterized by a self-propulsion velocity v_{0} and by their translational and rotational diffusion coefficients D_{t} and D_{r}, respectively. Based on the integration-through-transients formalism, the theory requires as input only the equilibrium static structure factors of the passive system (where v_{0}=0). It predicts a nontrivial idealized-glass-transition diagram in the three-dimensional parameter space of density, self-propulsion velocity, and rotational diffusivity that arise because at high densities, the persistence length of active swimming ℓ_{p}=v_{0}/D_{r} interferes with the interaction length ℓ_{c} set by the caging of particles. While the low-density dynamics of ABPs is characterized by a single Péclet number Pe=v_{0}^{2}/D_{r}D_{t}, close to the glass transition the dynamics is found to depend on Pe and ℓ_{p} separately. At fixed density, increasing the self-propulsion velocity causes structural relaxation to speed up, while decreasing the persistence length slows down the relaxation. The active-MCT glass is a nonergodic state that is qualitatively different from the passive glass. In it, correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions.

Active Brownian equation of state: metastability and phase coexistence

As a result of the competition between self-propulsion and excluded volume interactions, purely repulsive self-propelled spherical particles undergo a motility-induced phase separation (MIPS). We carry out a systematic computational study, considering several interaction potentials, systems confined by hard walls or with periodic boundary conditions, and different initial conditions. This approach allows us to identify that, despite its non-equilibrium nature, the equations of state of Active Brownian Particles (ABP) across MIPS verify the characteristic properties of first-order liquid-gas phase transitions, meaning, equality of pressure of the coexisting phases once a nucleation barrier has been overcome and, in the opposite case, hysteresis around the transition as long as the system remains in the metastable region. Our results show that the equations of state of ABPs account for their phase behaviour, providing a firm basis to describe MIPS as an equilibrium-like phase transition.

Collective Behavior of Chiral Active Matter: Pattern Formation and Enhanced Flocking

We generalize the Vicsek model to describe the collective behavior of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise ratio as for linear swimmers, as we show, circular motion enhances the polarization in the ordered phase (enhanced flocking) and induces secondary instabilities leading to structure formation. Slow rotations promote macroscopic droplets with late time sizes proportional to the system size (indicating phase separation) whereas fast rotations generate patterns consisting of phase synchronized microflocks with a controllable characteristic size proportional to the average single-particle swimming radius. Our results defy the viewpoint that monofrequent rotations form a vapid extension of the Vicsek model and establish a generic route to pattern formation in chiral active matter with possible applications for understanding and designing rotating microflocks.

Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles

We present a mode coupling theory study for the relaxation and glassy dynamics of a system of strongly interacting self-propelled particles, wherein the self-propulsion force is described by Ornstein-Uhlenbeck colored noise and thermal noises are included. Our starting point is an effective Smoluchowski equation governing the distribution function of particle positions, from which we derive a memory function equation for the time dependence of density fluctuations in nonequilibrium steady states. With the basic assumption of the absence of macroscopic currents and standard mode coupling approximation, we can obtain expressions for the irreducible memory function and other relevant dynamic terms, wherein the nonequilibrium character of the active system is manifested through an averaged diffusion coefficient D[combining macron] and a nontrivial structural function S₂(q) with q being the magnitude of wave vector q. D[combining macron] and S₂(q) enter the frequency term and the vertex term for the memory function, and thus influence both the short time and the long time dynamics of the system. With these equations obtained, we study the glassy dynamics of this thermal self-propelled particle system by investigating the Debye-Waller factor f_q and relaxation time τ_α as functions of the persistence time τ_p of self-propulsion, the single particle effective temperature T_eff as well as the number density ρ. Consequently, we find the critical density ρ_c for given τ_p shifts to larger values with increasing magnitude of propulsion force or effective temperature, in good accordance with previously reported simulation work. In addition, the theory facilitates us to study the critical effective temperature T for fixed ρ as well as its dependence on τ_p. We find that T increases with τ_p and in the limit τ_p → 0, it approaches the value for a simple passive Brownian system as expected. Our theory also well recovers the results for passive systems and can be easily extended to more complex systems such as active-passive mixtures.

Morphology of clusters of attractive dry and wet self-propelled spherical particle suspensions

In order to assess the effect of hydrodynamics in the assembly of active attractive spheres, we simulate a semi-dilute suspension of attractive self-propelled spherical particles in a quasi-two dimensional geometry comparing the case with and without hydrodynamics interactions. To start with, independent of the presence of hydrodynamics, we observe that depending on the ratio between attraction and propulsion, particles either coarsen or aggregate forming finite-size clusters. Focusing on the clustering regime, we characterize two different cluster parameters, i.e. their morphology and orientational order, and compare the case when active particles behave either as pushers or pullers (always in the regime where inter-particle attractions compete with self-propulsion). Studying cluster phases for squirmers with respect to those obtained for active Brownian disks (indicated as ABPs), we have shown that hydrodynamics alone can sustain a cluster phase of active swimmers (pullers), while ABPs form cluster phases due to the competition between attraction and self-propulsion. The structural properties of the cluster phases of squirmers and ABPs are similar, although squirmers show sensitivity to active stresses. Active Brownian disks resemble weakly pusher squirmer suspensions in terms of cluster size distribution, structure of the radius of gyration on the cluster size and degree of cluster polarity.

Collective transport for active matter run-and-tumble disk systems on a traveling-wave substrate

We examine numerically the transport of an assembly of active run-and-tumble disks interacting with a traveling-wave substrate. We show that as a function of substrate strength, wave speed, disk activity, and disk density, a variety of dynamical phases arise that are correlated with the structure and net flux of disks. We find that there is a sharp transition into a state in which the disks are only partially coupled to the substrate and form a phase-separated cluster state. This transition is associated with a drop in the net disk flux, and it can occur as a function of the substrate speed, maximum substrate force, disk run time, and disk density. Since variation of the disk activity parameters produces different disk drift rates for a fixed traveling-wave speed on the substrate, the system we consider could be used as an efficient method for active matter species separation. Within the cluster phase, we find that in some regimes the motion of the cluster center of mass is in the opposite direction to that of the traveling wave, while when the maximum substrate force is increased, the cluster drifts in the direction of the traveling wave. This suggests that swarming or clustering motion can serve as a method by which an active system can collectively move against an external drift.