We consider a mixture of passive (i.e., Brownian) and active (e.g., bacterial or colloidal swimmers) particles, and analyze the stability conditions of either uniformly mixed or phase segregated steady states consisting of phases enriched with different types of particles. We show that in sufficiently dilute mixtures the system behaves as if it were exposed to two separate heat baths of uneven temperatures. It can be described within a second virial approximation neglecting three body and higher order collisions. In this approximation, we define non-equilibrium "chemical potentials" whose gradients govern diffusion fluxes and a non-equilibrium "osmotic pressure", which governs the mechanical stability of the interface.
Active Brownian particles (ABPs) with pure repulsion is an ideal model to understand the effect of nonequilibrium on collective behaviors. It has long been established that activity can create effective attractions leading to motility-induced phase separation (MIPS), whose role is similar to that of (inverse) temperature in the simplest equilibrium system with attractive inter-particle interactions. Here, our theoretical analysis based on a kinetic theory of MIPS shows that a new type of activity-induced nonequilibrium vaporization is able to hinder the formation of dense phase when activity i…
We establish the complete phase diagram of self-propelled hard disks in two spatial dimensions from the analysis of the equation of state and the statistics of local order parameters. The equilibrium melting scenario is maintained at small activities, with coexistence between active liquid and hexatic order, followed by a proper hexatic phase and a further transition to an active solid. As activity increases, the emergence of hexatic and solid order is shifted towards higher densities. Above a critical activity and for a certain range of packing fractions, the system undergoes MIPS and demixes…
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. Th…
It is well known that particles can get trapped by randomly placed obstacles when they are pushed too much. We present a model where the current in a disordered medium dies at a large external field, but is reborn when the activity is increased. By activity we mean the time-variation of the external driving at a constant time-averaged field. A different interpretation of the resurgence of the current is that the particles are capable of taking an infinite sequence of potential barriers via a mechanism similar to stochastic resonance. We add a discussion regarding the role of "shaking" in proce…
We studied a collection of chiral active particles (CAP) on a two dimensional substrate using extensive numerical study. Particles interact through soft repulsive interaction. The activity and chirality of particles is tuned by varying their self-propulsion speed and angular velocity respectively. Kinetics and steady state properties of particles are studied for different chirality and activity. The phase diagram of system on the plane of activity and chirality shows three distinct phases. For small chirality when activity is dominant, particles show enhanced dynamics and macroscopic phase sep…
Motility-induced phase separation (MIPS) leads to cohesive active matter in the absence of cohesive forces. We present, extend and illustrate a recent generalized thermodynamic formalism which accounts for its binodal curve. Using this formalism, we identify both a generalized surface tension, that controls finite-size corrections to coexisting densities, and generalized forces, that can be used to construct new thermodynamic ensembles. Our framework is based on a nonequilibrium generalization of the Cahn-Hilliard equation and we discuss its application to active particles interacting either v…
We present a numerical study of the phase behavior of repulsively interacting active polar particles that align their active velocities nematically. The amplitude of the active velocity, and the noise in its orientational alignment control the active nature of the system. At high values of orientational noise, the structural fluid undergoes a continuous nematic-isotropic transition in active orientation. This transition is well separated from an active phase separation, characterized by the formation of high density hexatic clusters, observed at lower noise strengths. With increasing activity,…
Lattice models allow for a computationally efficient investigation of motility-induced phase separation (MIPS) compared to off-lattice systems. Simulations are less demanding and thus bigger systems can be accessed with higher accuracy and better statistics. In equilibrium, lattice and off-lattice models with comparable interactions belong to the same universality class. Whether concepts of universality also hold for active particles is still a controversial and open question. Here, we examine two recently proposed active lattice systems that undergo MIPS and investigate numerically their crit…
Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis ${\bf u}$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant $\u$ until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density $ρ$ but not on ${\bf u}$, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing $v(ρ)$ causes phase separati…
We investigate the phase behavior and kinetics of a monodisperse mixture of active (\textit{i.e.}, self-propelled) and passive isometric Brownian particles through Brownian dynamics simulations and theory. As in a purely active system, motility of the active component triggers phase separation into a dense and a dilute phase; in the dense phase we further find active-passive segregation, with "rafts" of passive particles in a "sea" of active particles. We find that phase separation from an initially disordered mixture can occur with as little as 15 percent of the particles being active. Finall…
We study a system of purely repulsive spherical self-propelled particles in the minimal set-up inducing Motility-Induced Phase Separation (MIPS). We show that, even if explicit alignment interactions are absent, a growing order in the velocities of the clustered particles accompanies MIPS. Particles arrange into aligned or vortex-like domains. Their sizes increase as the persistence of the self-propulsion grows, an effect that is quantified studying the spatial correlation function of the velocities. We explain the velocity-alignment by unveiling a hidden alignment interaction of the Vicsek-li…
To study the role of torque in motility-induced phase separation (MIPS), we simulate a system of self-propelled particles whose shape varies smoothly from isotropic (disks/spheres) to weakly elongated (rods). We construct the phase diagrams of 2D active disks, 3D active spheres and 2D/3D active rods of aspect ratio $l/σ=2$. A stability analysis of the homogeneous isotropic phase allows us to predict the onset of MIPS based on the effective swimming speed and rotational diffusion of the particles. Both methods find suppression of MIPS as the particle shape is elongated. We propose a suppression…
Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence …
We present results from Langevin dynamics simulations of a glassy active-passive mixture of soft-repulsive binary colloidal disks. Activity on the smaller particles is applied according to the quorum sensing scheme, in which a smaller particle will be active for a persistence time if its local nearest neighbors are equal to or greater than a certain threshold value. We start with a passive glassy state of the system and apply activity to the smaller particles, which shows a nonmonotonous glassy character of the active particles with the persistence time of the active force, from its passive li…
We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barabási and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with chaotic neural activities exhibited by regular topologies. Periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger. The average length of the periods increases with the square root of the network size.
As a result of nonequilibrium forces, purely repulsive self-propelled particles undergo macrophase separation between a dense and a dilute phase. We present a thorough study of the ordering kinetics of such motility-induced phase separation (MIPS) in active Brownian particles in two dimensions, and we show that it is generically accompanied by microphase separation. The growth of the dense phase follows a law akin to the one of liquid-gas phase separation. However, it is made of a mosaic of hexatic microdomains whose size does not coarsen indefinitely, leaving behind a network of extended topo…
Dense active systems are widespread in nature, examples range from bacterial colonies to biological tissues. Dense clusters of active particles can be obtained by increasing the packing fraction of the system or taking advantage of a peculiar phenomenon named motility-induced phase separation (MIPS). In this work, we explore the phase diagram of a two-dimensional model of active glass and show that disordered active materials develop a rich collective behaviour encompassing both MIPS and glassiness. We find that, although the glassy state is almost indistinguishable from that of equilibrium gl…
Active colloids exhibit persistent motion, which can lead to motility-induced phase separation (MIPS). However, there currently exists no microscopic theory to account for this phenomenon. We report a first-principles theory, free of fit parameters, for active spherical colloids, which shows explicitly how an effective many-body interaction potential is generated by activity and how this can rationalize MIPS. For a passively repulsive system the theory predicts phase separation and pair correlations in quantitative agreement with simulation. For an attractive system the theory shows that phase…
A collection of self-propelled particles with volume exclusion interactions can exhibit the phenomenology of gas-liquid phase separation, known as motility-induced phase separation (MIPS). The non-equilibrium nature of the system is fundamental to the phase transition, however, it is unclear whether MIPS at criticality contributes a novel universality class to non-equilibrium 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.
The thermodynamics of a lattice regularized asymmetric Anderson impurity in a correlated host is obtained by an exact solution. The crossover from the Anderson- to the Kondo-regime is studied, thus making contact with predictions by scaling theory. On the basis of the exact solution, the transition to universal Kondo behavior is shown to be realized by a graduate separation of the energy scales of spin and charge excitations.
Phase diagram of the phenomenon of motility induced phase separation (MIPS) for a collection of self-propelled interacting disks is explored using Langevin dynamics simulation with particular emphasis on disk wall softness and the range of interaction amongst disks. We bring out important changes in the MIPS phase diagram both due to softness and inertia of the disks. Specifically, we show that overdamped softer disks phase separate while MIPS becomes possible only for harder disks in the inertial limit. Unlike most of the earlier studies on MIPS which consider hard-core disks, our findings ma…
The motility-induced phase separation (MIPS) is the spontaneous aggregation of active particles, while equilibrium phase separation (EPS) is thermodynamically driven by attractive interactions between passive particles. Despite such difference in the microscopic mechanism, similarities between MIPS and EPS like free energy structure and critical phenomena have been discussed. Here we introduce and analyze a 2D lattice gas model that undergoes both MIPS and EPS by tuning activity and interaction parameters. Based on simulations and mean-field theory, we find that the MIPS and EPS critical point…
We study the phase behavior of polar Active Brownian Particles moving in two-spatial dimensions and interacting through volume exclusion and velocity alignment. We combine particle-based simulations of the microscopic model with a simple mean-field kinetic model to understand the impact of velocity alignment on the motility-induced phase separation of self-propelled disks. We show that, as the alignment strength is increased, approaching the onset of collective motion from below, orientational correlations grow, rendering the diffusive reorientation dynamics slower. As a consequence, the tende…
A crowd of nonequilibrium entities can show phase transition behaviors that are prohibited in conventional equilibrium setups. An interesting question is whether similar activity-driven phase transitions also occur in pure quantum systems. Here we introduce a minimally simple quantum many-body model that undergoes quantum phase transitions induced by non-Hermiticity. The model is based on a classical anisotropic lattice gas model that undergoes motility-induced phase separation (MIPS), and the quantum phase diagram includes other active phases such as the flocking phase. The quantum phase tran…
Spontaneous persistent motions driven by active processes play a central role to maintain the living cells far from equilibrium. In the majority of the research works, the steady state dynamics of an active system has been described in terms of an effective temperature. In the majority of the research works, the steady state dynamics of an active system has been described in terms of an effective temperature. By contrast, we have examined a prototype model for diffusion in an activity-induced rugged energy landscape to describe the slow dynamics of a tagged particle in a dense active environme…
Spatially uniform electric fields have been used to induce instabilities in liquids and polymers, and to orient and deform ordered phases of block-copolymers. Here we discuss the demixing phase transition occurring in liquid mixtures when they are subject to spatially nonuniform fields. Above the critical value of potential, a phase-separation transition occurs, and two coexisting phases appear separated by a sharp interface. Analytical and numerical composition profiles are given, and the interface location as a function of charge or voltage is found. The possible influence of demixing on the…
We present a hydrodynamic theory for systems of dipolar active Brownian particles which, in the regime of weak dipolar coupling, predicts the onset of motility-induced phase separation (MIPS), consistent with Brownian dynamics (BD) simulations. The hydrodynamic equations are derived by explicitly coarse-graining the microscopic Langevin dynamics, thus allowing for a quantitative comparison of parameters entering the coarse-grained model and particle-resolved simulations. Performing BD simulations at fixed density, we find that dipolar interactions tend to hinder MIPS, as first reported in [Lia…
Collectives of actively-moving particles can spontaneously separate into dilute and dense phases -- a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly-moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS -- in some cases, arresting or completely suppressing phase separation, or …
Active systems, or active matter, are self-driven systems which live, or function, far from equilibrium - a paradigmatic example which we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The nonequilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one which has recently been the subject of intense interest among biological and soft matter physici…
Microphase separation in polymeric systems provides a bottom-up strategy to fabricate nanostructures. Polymers that are reported to undergo microphase separation usually include block copolymers or polyelectrolytes. Neutral homopolymers, which are comparatively easy to synthesize, are thought to be incapable of microphase separation. Here, using a minimal model that accounts for ion solvation, we show that microphase separation is possible in neutral homopolymer blends with sufficient dielectric contrast, upon a tiny amount of salt-doping. The driving force for the microphase separation is the…
Nonequilibrium processes occurring in functional materials can significantly impact device efficiencies and are often difficult to characterize due to the broad range of length and time scales involved. In particular, mixed halide hybrid perovskites are promising for optoelectronics, yet the halides reversibly phase separate when photo-excited, significantly altering device performance. By combining nanoscale imaging and multiscale modeling, we elucidate the mechanism underlying this phenomenon, demonstrating that local strain induced by photo-generated polarons promotes halide phase separatio…
Turbulence in driven stratified active matter is considered. The relevant parameters characterizing the problem are the Reynolds number Re and an active matter Richardson-like number,R. In the mixing limit,Re>>1, R<<1, we show that the standard Kolmogorov energy spectrum 5/3 law is realized. On the other hand, in the stratified limit, Re>>1,R>>1, there is a new turbulence universality class with a 7/5 law. The crossover from one regime to the other is discussed in detail. Experimental predictions and probes are also discussed.
Motility-induced phase separation, MIPS, is arguably the most well-studied collective phenomenon occurring in active matter without alignment interactions (scalar active matter). Its basic origin is simple: since self-propelled particles accumulate where they move slowly, having a propulsion speed that decreases steeply enough with density, due to collisions or chemical interactions, leads to a feedback loop that induces the formation of a dense phase. In these notes, I will discuss some of the main theoretical and computational efforts that have been made over the last decade in understanding…
Adhesion between membranes is studied using a phenomenological model, where the inter-membrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both for adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. We mainly consider the case where the sticker molecules form bridges and adhere directly to both membranes. The calculated mean-field phase diagrams show an upward shift of the transition temperature indicating that the lateral phase separation in the membrane is …
Self-propelled particles include both self-phoretic synthetic colloids and various micro-organisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: the steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density, for either biochemical or steric reasons. This creates positive feedback which can lead to motility-induced phase separation (MIPS) between dense and dilute f…
Nanosecond kinetics of phase separation in binary fluid studied by a combination of Laser-induced temperature jump and Forster Resonant Excitation Transfer probing
An effective approach to isolation of sub-micro sized particles is desired to separate cancer and healthy cells or in therapy of Parkinson's and Alzheimer's disease. However, since bioparticles span a large size range comprising several orders of magnitude, development of an adequate separation method is a challenging task. We consider a collection of non-interacting Brownian particles of various sizes moving in a symmetric periodic potential and subjected to an external unbiased harmonic driving as well as a constant bias. We reveal a nonintuitive, yet efficient, separation mechanism based on…
Recently, there has been much interest in activity-induced phase separations in concentrated suspensions of "active Brownian particles" (ABPs), self-propelled spherical particles whose direction of motion relaxes through thermal rotational diffusion. To date, almost all these studies have been restricted to 2 dimensions. In this work we study activity-induced phase separation in 3D and compare the results with previous and new 2D simulations. To this end, we performed state-of-the-art Brownian dynamics simulations of up to 40 million ABPs -- such very large system sizes are unavoidable to evad…
