Effective temperature concept evaluated in an active colloid mixture

The fluctuation-dissipation relation holds for a macroscopic tracer in an active bath

The fluctuation-dissipation relation (FDR) links thermal fluctuations and dissipation at thermal equilibrium through temperature. Extending it beyond equilibrium conditions in pursuit of broadening thermodynamics is often feasible, albeit with system-dependent specific conditions. We demonstrate experimentally that a generalized FDR holds for a harmonically trapped tracer colliding with self-propelled walkers. The generalized FDR remains valid across a large spectrum of active fluctuation frequencies, extending from underdamped to critically damped dynamics, which we attribute to a single primary channel for energy input and dissipation in our system.

Motility driven glassy dynamics in confluent epithelial monolayers

As wounds heal, embryos develop, cancer spreads, or asthma progresses, the cellular monolayer undergoes a glass transition between solid-like jammed and fluid-like flowing states. During some of these processes, the cells undergo an epithelial-to-mesenchymal transition (EMT): they acquire in-plane polarity and become motile. Thus, how motility drives the glassy dynamics in epithelial systems is critical for the EMT process. However, no analytical framework that is indispensable for deeper insights exists. Here, we develop such a theory inspired by a well-known glass theory. One crucial result of this work is that the confluency affects the effective persistence time-scale of active force, described by its rotational diffusivity, Deffr. Deffr differs from the bare rotational diffusivity, Dr, of the motile force due to cell shape dynamics, which acts to rectify the force dynamics: Deffr is equal to Dr when Dr is small and saturates when Dr is large. We test the theoretical prediction of Deffr and how it affects the relaxation dynamics in our simulations of the active Vertex model. This novel effect of Deffr is crucial to understanding the new and previously published simulation data of active glassy dynamics in epithelial monolayers.

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

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

Mechanical theory of nonequilibrium coexistence and motility-induced phase separation

Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both nonequilibrium and equilibrium systems. Here, we present a general mechanical theory for phase separation rooted in ideas explored nearly a half-century ago in the study of inhomogeneous fluids. The core idea is that the mechanical forces within the interface separating two coexisting phases uniquely determine coexistence criteria, regardless of whether a system is in equilibrium or not. We demonstrate the power and utility of this theory by applying it to active Brownian particles, predicting a quantitative phase diagram for motility-induced phase separation in both two and three dimensions. This formulation additionally allows for the prediction of novel interfacial phenomena, such as an increasing interface width while moving deeper into the two-phase region, a uniquely nonequilibrium effect confirmed by computer simulations. The self-consistent determination of bulk phase behavior and interfacial phenomena offered by this mechanical perspective provide a concrete path forward toward a general theory for nonequilibrium phase transitions.

Tuning nonequilibrium phase transitions with inertia

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Gas-liquid interface of a Lennard-Jones binary mixture controlled by differential activity: phase transition and interfacial stability

We perform molecular dynamics simulations of a two-dimensional binary mixture of Lennard-Jones particles, characterized by some degree of "activity" inside. Starting from a base state that features a gas-liquid interface and a completely segregated system at thermodynamic equilibrium, we introduce differential scalar activity between the two species by prescribing two different effective temperatures. The differential activity is measured as the ratio of the two temperatures. Previous studies showed segregation in a homogeneously mixed system induced by high activity. In this study, we investigate the effect of activity on a pre-existing gas-liquid interface between two separated species. Whereas a high activity ratio induces the formation of new interfaces, we show that a low activity ratio destabilizes existing ones. Moreover, the combination of a pre-existent interface with differential activity leads to partial crystallization and thus to triple phase coexistence (solid, liquid and gas), which is observed over a wide range of moderate differential activities. Findings from this idealized system can guide our understanding of interfacial behaviors in certain biological systems.

Odd viscosity-induced Hall-like transport of an active chiral fluid

Broken time-reversal and parity symmetries in active spinner fluids imply a nondissipative "odd viscosity," engendering phenomena unattainable in traditional passive or active fluids. Here we show that the odd viscosity itself can lead to a Hall-like transport when the active chiral fluid flows through a quenched matrix of obstacles, reminiscent of the anomalous Hall effect. The Hall-like velocity depends significantly on the spinner activity and longitudinal flow due to the interplay between odd viscosity and spinner-obstacle collisions. Our findings underscore the importance of odd viscosity in active chiral matter and elucidate its essential role in the anomalous Hall-like effect.

Active and thermal fluctuations in multi-scale polymer structure and dynamics

The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.

Extension of Kelvin's equation to dipolar colloids

Suspensions of colloids driven out-of-equilibrium demonstrate interesting collective behavior, such as organized and directed clustering and swarming. These systems require continuous energy input, yet some of the dynamics of these driven systems resemble the equilibrium-phase behavior of molecular fluids, such as crystallization, condensation, and phase separation. Consequently, there has been significant interest in exploring the applicability of thermodynamic concepts, such as pressure and surface tension, to describe nonequilibrium phenomena. Here, we show how rotating magnetic fields can drive superparamagnetic particles to form steady-state vapor–liquid coexistence that can be analyzed with Kelvin’s equation to determine an “effective vapor pressure” for this active colloidal system. These results illustrate the convergence of statistical physics of simple liquids to nonequilibrium colloidal fluids.

Vapor pressure refers to the pressure exerted by the vapor phase in thermodynamic equilibrium with either its liquid or solid phase. An important class of active matter is field-driven colloids. A suspension of dipolar colloids placed in a high-frequency rotating magnetic field undergoes a nonequilibrium phase transition into a dilute and dense phase, akin to liquid–vapor coexistence in a simple fluid. Here, we compute the vapor pressure of this colloidal fluid. The number of particles that exist as the dilute bulk phase versus condensed cluster phases can be directly visualized. An exponential relationship between vapor pressure and effective temperature is determined as a function of applied field strength, analogous to the thermodynamic expression between vapor pressure and temperature found for pure liquids. Additionally, we demonstrate the applicability of Kelvin’s equation to this field-driven system. In principle, this appears to be in conflict with macroscopic thermodynamic assumptions due to the nonequilibrium and discrete nature of this colloidal system. However, the curvature of the vapor–liquid interface provides a mechanical equilibrium characterized by interfacial tension that connects the condensed clusters observed with these active fluids to classical colligative fluid properties.

Active Regulation of Pressure and Volume Defines an Energetic Constraint on the Size of Cell Aggregates

We explore the relationship between the nonequilibrium generation of myosin-induced active stress within the F-actin cytoskeleton and the pressure-volume relationship of cellular aggregates as models of simple tissues. We find that due to active stress, aggregate surface tension depends upon its size. As a result, both pressure and cell number density depend on size and violate equilibrium assumptions. However, the relationship between them resembles an equilibrium equation of state with an effective temperature. This suggests that bulk and surface properties of aggregates balance to yield a constant average work performed by each cell on their environment in regulating tissue size. These results describe basic physical principles that govern the size of cell aggregates.

Circular swimming motility and disordered hyperuniform state in an algae system

Active matter comprises individually driven units that convert locally stored energy into mechanical motion. Interactions between driven units lead to a variety of nonequilibrium collective phenomena in active matter. One of such phenomena is anomalously large density fluctuations, which have been observed in both experiments and theories. Here we show that, on the contrary, density fluctuations in active matter can also be greatly suppressed. Our experiments are carried out with marine algae ([Formula: see text]), which swim in circles at the air-liquid interfaces with two different eukaryotic flagella. Cell swimming generates fluid flow that leads to effective repulsions between cells in the far field. The long-range nature of such repulsive interactions suppresses density fluctuations and generates disordered hyperuniform states under a wide range of density conditions. Emergence of hyperuniformity and associated scaling exponent are quantitatively reproduced in a numerical model whose main ingredients are effective hydrodynamic interactions and uncorrelated random cell motion. Our results demonstrate the existence of disordered hyperuniform states in active matter and suggest the possibility of using hydrodynamic flow for self-assembly in active matter.

Reincarnations of the phase separation problem

Phase separation is familiar and useful, yet opportunities to manipulate it are surprisingly subtle and complex.

Anomalous diffusion of active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory

Quantitatively understanding the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosomes or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality f with the center cross-linker particle being ABP. We observe that the ABP cross-linker, despite its self-propelled movement, attains an active subdiffusion with the scaling ΔR2(t) ∼ tα with α ≤ 1/2, through the viscoelastic feedback from the polymer. Counter-intuitively, the apparent anomaly exponent α becomes smaller as the ABP is driven by a larger propulsion velocity, but is independent of functionality f or the boundary conditions of the polymer. We set forth an exact theory and show that the motion of the active cross-linker is a Gaussian non-Markovian process characterized by two distinct power-law displacement correlations. At a moderate Péclet number, it seemingly behaves as fractional Brownian motion with a Hurst exponent H = α/2, whereas, at a high Péclet number, the self-propelled noise in the polymer environment leads to a logarithmic growth of the mean squared displacement (∼ln t) and a velocity autocorrelation decaying as -t-2. We demonstrate that the anomalous diffusion of the active cross-linker is precisely described by a fractional Langevin equation with two distinct random noises.

Characterizing the spatiotemporal evolution of paramagnetic colloids in time-varying magnetic fields with Minkowski functionals

Phase separation processes are widely utilized to assemble complex fluids into novel materials. These separation processes can be thermodynamically driven due to changes in concentration, pressure, or temperature. Phase separation can also be induced with external stimuli, such as magnetic fields, resulting in novel nonequilibrium systems. However, how external stimuli influence the transition pathways between phases has not been explored in detail. Here, we describe the phase separation dynamics of superparamagnetic colloids in time-varying magnetic fields. An initially homogeneous colloidal suspension can transition from a continuous colloidal phase with voids to discrete colloidal clusters, through a bicontinuous phase formed via spinodal decomposition. The type of transition depends on the particle concentration and magnitude of the applied magnetic field. The spatiotemporal evolution of the microstructure during the nucleation and growth period is quantified by analyzing the morphology using Minkowski functionals. The characteristic length of the colloidal systems was determined to correlate with system variables such as magnetic field strength, particle concentration, and time in a power-law scaling relationship. Understanding the interplay between particle concentration and applied magnetic field allows for better control of the phases observed in these magnetically tunable colloidal systems.

Reconfigurable emergent patterns in active chiral fluids

Active fluids comprised of autonomous spinning units injecting energy and angular momentum at the microscopic level represent a promising platform for active materials design. The complexity of the accessible dynamic states is expected to dramatically increase in the case of chiral active units. Here, we use shape anisotropy of colloidal particles to introduce chiral rollers with activity-controlled curvatures of their trajectories and spontaneous handedness of their motion. By controlling activity through variations of the energizing electric field, we reveal emergent dynamic phases, ranging from a gas of spinners to aster-like vortices and rotating flocks, with either polar or nematic alignment of the particles. We demonstrate control and reversibility of these dynamic states by activity. Our findings provide insights into the onset of spatial and temporal coherence in a broad class of active chiral systems, both living and synthetic, and hint at design pathways for active materials based on self-organization and reconfigurability.

Competing active and passive interactions drive amoebalike crystallites and ordered bands in active colloids

Swimmers and self-propelled particles are physical models for the collective behavior and motility of a wide variety of living systems, such as bacteria colonies, bird flocks, and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behavior. Here we study colloids in a dc electric field. Our quasi-two-dimensional system of electrically driven particles exhibits a rich and exotic phase behavior exhibiting passive crystallites, motile crystallites, an active gas, and banding. Amongst these are two mesophases, reminiscent of systems with competing interactions. At low field strengths activity suppresses demixing, leading to motile crystallites. Meanwhile, at high field strengths, activity drives partial demixing to traveling bands. We parametrize a particulate simulation model which reproduces the experimentally observed phases.

Traveling bands, clouds, and vortices of chiral active matter

We consider stochastic dynamics of self-propelled particles with nonlocal normalized alignment interactions subject to phase lag. The role of the lag is to indirectly generate chirality into particle motion. To understand large-scale behavior, we derive a continuum description of an active Brownian particle flow with macroscopic scaling in the form of a partial differential equation for a one-particle probability density function. Due to indirect chirality, we find a spatially homogeneous nonstationary analytic solution for this class of equations. Our development of kinetic and hydrodynamic theories towards such a solution reveals the existence of a wide variety of spatially nonhomogeneous patterns reminiscent of traveling bands, clouds, and vortical structures of linear active matter. Our model may thereby serve as the basis for understanding the nature of chiral active media and designing multiagent swarms with designated behavior.

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.

A practical guide to active colloids: choosing synthetic model systems for soft matter physics research

Synthetic active colloids that harvest energy stored in the environment and swim autonomously are a popular model system for active matter. This emerging field of research sits at the intersection of materials chemistry, soft matter physics, and engineering, and thus cross-talk among researchers from different backgrounds becomes critical yet difficult. To facilitate this interdisciplinary communication, and to help soft matter physicists with choosing the best model system for their research, we here present a tutorial review article that describes, in appropriate detail, six experimental systems of active colloids commonly found in the physics literature. For each type, we introduce their background, material synthesis and operating mechanisms and notable studies from the soft matter community, and comment on their respective advantages and limitations. In addition, the main features of each type of active colloid are summarized into two useful tables. As materials chemists and engineers, we intend for this article to serve as a practical guide, so those who are not familiar with the experimental aspects of active colloids can make more informed decisions and maximize their creativity.

Phase transition and emergence of active temperature in an active Brownian system in underdamped background

We explore the role of inertia in the properties of active Brownian particles (ABPs) immersed in an underdamped background in two dimensions using Langevin dynamics computer simulation. Similar to an equilibrium two-dimensional passive interacting particle system, the system of ABPs transits from a liquid phase to a solid phase with the change in the coupling parameter, which is the ratio of interaction potential energy and thermal energy of the background solvent. Important qualitative and quantitative differences are found in the liquid-solid phase transition with increasing strength of activity as compared to those found in the conventional overdamped background limit. In the underdamped background, inherent activity is found to lead to a temperature, called the active temperature and defined by average velocity fluctuations of the ABPs, that is different from the fixed background solvent temperature. A new scaling law for active temperature as a function of activity strength is found near the liquid-solid boundary. Active temperature, which behaves similar to the thermodynamic equilibrium temperature, is also found to depend upon the interaction strength between the active particles and the strength of the background dissipation. With an increase in background dissipation, the difference between active temperature and the background solvent temperature decreases and the difference is found to eventually vanish in the overdamped limit, demonstrating the correctness of the calculation.

Frequency Response of Induced-Charge Electrophoretic Metallic Janus Particles

The ability to manipulate and control active microparticles is essential for designing microrobots for applications. This paper describes the use of electric and magnetic fields to control the direction and speed of induced-charge electrophoresis (ICEP) driven metallic Janus microrobots. A direct current (DC) magnetic field applied in the direction perpendicular to the electric field maintains the linear movement of particles in a 2D plane. Phoretic force spectroscopy (PFS), a phase-sensitive detection method to detect the motions of phoretic particles, is used to characterize the frequency-dependent phoretic mobility and drag coefficient of the phoretic force. When the electric field is scanned over a frequency range of 1 kHz-1 MHz, the Janus particles exhibit an ICEP direction reversal at a crossover frequency at ~30 kH., Below this crossover frequency, the particle moves in a direction towards the dielectric side of the particle, and above this frequency, the particle moves towards the metallic side. The ICEP phoretic drag coefficient measured by PFS is found to be similar to that of the Stokes drag. Further investigation is required to study microscopic interpretations of the frequency at which ICEP mobility switched signs and the reason why the magnitudes of the forward and reversed modes of ICEP are so different.

Activity-modulated phase transition in a two-dimensional mixture of active and passive colloids

We study a two-dimensional binary mixture of active and passive colloids as an idealized model of an hybrid aggregate of living cells and inert particles. We perform molecular dynamics simulations of this system using two different thermostats, and we systematically investigate the effect of varying these two effective temperatures on the system behavior, as characterized by its density, structure and thermoelastic properties. Our results indicate that the presence of active colloids shifts the mixture towards the liquid state and renders it more deformable. Such system softening and melting effects due to the addition of active particles are larger than expected from a linear combination of temperatures of the active and passive components. This heightened effect becomes more pronounced as the effective temperature difference between the two components becomes larger. The binary mixture remains homogeneous for moderate colloidal activity, but segregation arises for large effective temperature difference. Our results provide insights to guide future experimental hybrid aggregate studies with promising biomedical applications.

Dynamical self-assembly of dipolar active Brownian particles in two dimensions

Based on Brownian Dynamics (BD) simulations, we study the dynamical self-assembly of active Brownian particles with dipole-dipole interactions, stemming from a permanent point dipole at the particle center. The propulsion direction of each particle is chosen to be parallel to its dipole moment. We explore a wide range of motilities and dipolar coupling strengths and characterize the corresponding behavior based on several order parameters. At low densities and low motilities, the most important structural phenomenon is the aggregation of the dipolar particles into chains. Upon increasing the particle motility, these chain-like structures break, and the system transforms into a weakly correlated isotropic fluid. At high densities, we observe that the motility-induced phase separation is strongly suppressed by the dipolar coupling. Once the dipolar coupling dominates the thermal energy, the phase separation disappears, and the system rather displays a flocking state, where particles form giant clusters and move collective along one direction. We provide arguments for the emergence of the flocking behavior, which is absent in the passive dipolar system.

Hydrodynamics of random-organizing hyperuniform fluids

Disordered hyperuniform structures are locally random while uniform like crystals at large length scales. Recently, an exotic hyperuniform fluid state was found in several nonequilibrium systems, while the underlying physics remains unknown. In this work, we propose a nonequilibrium (driven-dissipative) hard-sphere model and formulate a hydrodynamic theory based on Navier-Stokes equations to uncover the general mechanism of the fluidic hyperuniformity (HU). At a fixed density, this model system undergoes a smooth transition from an absorbing state to an active hyperuniform fluid and then, to the equilibrium fluid by changing the dissipation strength. We study the criticality of the absorbing-phase transition. We find that the origin of fluidic HU can be understood as the damping of a stochastic harmonic oscillator in q space, which indicates that the suppressed long-wavelength density fluctuation in the hyperuniform fluid can exhibit as either acoustic (resonance) mode or diffusive (overdamped) mode. Importantly, our theory reveals that the damping dissipation and active reciprocal interaction (driving) are the two ingredients for fluidic HU. Based on this principle, we further demonstrate how to realize the fluidic HU in an experimentally accessible active spinner system and discuss the possible realization in other systems.

Directional Stepping Model for Yeast Dynein: Longitudinal- and Side-Step Distributions

Motor proteins are biological machines that convert chemical energy stored in ATP to mechanical work. Kinesin and dynein are microtubule (MT)-associated motor proteins that, among other functions, facilitate intracellular transport. Here, we focus on dynein motility. We deduce the directional step distribution of yeast dynein motor protein on the MT surface by combing intrinsic features of the dynein and MTs. These include the probability distribution of the separation vector between the two microtubule-binding domains, the angular probability distribution of a single microtubule-binding domain translation, the existence of an MT seam defect, MT-binding sites, and theoretical extension that accounts for a load force on the motor. Our predictions are in excellent accord with the measured longitudinal step size distributions at various load forces. Moreover, we predict the side-step distribution and its dependence on longitudinal load forces, which shows a few surprising features. First, the distribution is broad. Second, in the absence of load, we find a small right-handed bias. Third, the side-step bias is susceptible to the longitudinal load force; it vanishes at a load equal to the motor stalling force and changes to a left-hand bias above that value. Fourth, our results are sensitive to the ability of the motor to explore the seam several times during its walk. Although available measurements of side-way distribution are limited, our findings are amenable to experimental check and, moreover, suggest a diversity of results depending on whether the MT seam is viable to motor sampling.

On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems

We review generalized fluctuation-dissipation relations, which are valid under general conditions even in "nonstandard systems," e.g., out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperturbed dynamics. In these relations, typically, one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.

Active microrheology, Hall effect, and jamming in chiral fluids

We examine the motion of a probe particle driven through a chiral fluid composed of circularly swimming disks. We find that the probe particle travels in both the longitudinal direction, parallel to the driving force, and in the transverse direction, perpendicular to the driving force, giving rise to a Hall angle. Under constant driving force, we show that the probe particle velocity in both the longitudinal and transverse directions exhibits nonmonotonic behavior as a function of the activity of the circle swimmers. The Hall angle is maximized when a resonance occurs between the frequency of the chiral disks and the motion of the probe particle. As the density of the chiral fluid increases, the Hall angle gradually decreases before reaching zero when the system enters a jammed state. We show that the onset of jamming depends on the chiral particle swimming frequency, with a fluid state appearing at low frequencies and a jammed solid occurring at high frequencies.

Aggregation dynamics of active rotating particles in dense passive media

Active matter systems are able to exhibit emergent non-equilibrium behavior due to activity-induced effective interactions between the active particles. Here we study the aggregation and dynamical behavior of active rotating particles, spinners, embedded in 2D passive colloidal monolayers. Using both experiments and simulations we observe aggregation of active particles or spinners whose behavior resembles classical 2D Cahn-Hilliard coarsening. The aggregation behavior and spinner attraction depend on the mechanical properties of the passive monolayer and the activity of spinners. Spinner aggregation only occurs when the passive monolayer behaves elastically and when the spinner activity exceeds a minimum activity threshold. Interestingly, for the spinner concentrations investigated here, the spinner concentration does not seem to change the dynamics of the aggregation behavior. There is a characteristic cluster size which maximizes spinner aggregation by minimizing the drag through the passive monolayer and maximizing the stress applied on the passive medium. We also show a ternary mixture of passive particles and co-rotating and counter-rotating spinners that aggregate into clusters of co and counter-rotating spinners respectively.

Topological Waves in Fluids with Odd Viscosity

Fluids in which both time reversal and parity are broken can display a dissipationless viscosity that is odd under each of these symmetries. Here, we show how this odd viscosity has a dramatic effect on topological sound waves in fluids, including the number and spatial profile of topological edge modes. Odd viscosity provides a short-distance cutoff that allows us to define a bulk topological invariant on a compact momentum space. As the sign of odd viscosity changes, a topological phase transition occurs without closing the bulk gap. Instead, at the transition point, the topological invariant becomes ill defined because momentum space cannot be compactified. This mechanism is unique to continuum models and can describe fluids ranging from electronic to chiral active systems.

Inhomogeneous assembly of driven nematic colloids

We present a quantitative analysis of the nonequilibrium assembly of colloidal particles dispersed in a nematic liquid crystal. The driven particles assemble into reconfigurable circular clusters by liquid-crystal-enabled electrokinetic phenomena generated by an AC electric field that provides propulsion along the local director. We identify the coexistence of different aggregation states, including a central, jammed core, where short-range elastic attraction dominates, surrounded by a liquid-like corona where particles retain their mobility but reach a mechanical equilibrium that we rationalize in terms of a balance between centripetal phoretic drive and pairwise repulsion. An analysis of the compressible liquid-like region reveals a linear density profile that can be tuned with the field frequency, and a bond-orientational order that reaches a maximum at intermediate packing densities, where elastic effects are minimized. Since the phoretic propulsion force acts also on assembled particles, we compute the mechanical pressure and show that a hard-disk equation of state can be used to describe the assembly of this driven system.

Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations

Disordered hyperuniform structures are an exotic state of matter having vanishing long-wavelength density fluctuations similar to perfect crystals but without long-range order. Although its importance in materials science has been brought to the fore in past decades, the rational design of experimentally realizable disordered strongly hyperuniform microstructures remains challenging. Here we find a new type of nonequilibrium fluid with strong hyperuniformity in two-dimensional systems of chiral active particles, where particles perform independent circular motions of the radius R with the same handedness. This new hyperuniform fluid features a special length scale, i.e., the diameter of the circular trajectory of particles, below which large density fluctuations are observed. By developing a dynamic mean-field theory, we show that the large local density fluctuations can be explained as a motility-induced microphase separation, while the Fickian diffusion at large length scales and local center-of-mass-conserved noises are responsible for the global hyperuniformity.

Stationary superstatistics distributions of trapped run-and-tumble particles

We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides an original insight on the link between the intrinsic nonequilibrium nature of active motion and the well-known concept of local equilibrium used in nonequilibrium statistical mechanics and contributes to the understanding of the validity of the concept of effective temperature. Particular cases of interest, regarding specific trapping potentials used in other theoretical or experimental studies, are discussed. We point out as an unprecedented effect, the emergence of new modes of the stationary distribution as a consequence of the coupling of persistent motion in a trapping potential that varies highly enough with position.

Clustering and phase separation of circle swimmers dispersed in a monolayer

We perform Brownian dynamics simulations in two dimensions to study the collective behavior of circle swimmers, which are driven by both, an (effective) translational and rotational self-propulsion, and interact via steric repulsion. We find that active rotation generally opposes motility-induced clustering and phase separation, as demonstrated by a narrowing of the coexistence region upon increase of the propulsion angular velocity. Moreover, although the particles are intrinsically assigned to rotate counterclockwise, a novel state of clockwise vortices emerges at an optimal value of the effective propulsion torque. We propose a simple gear-like model to capture the underlying mechanism of the clockwise vortices.

Active apolar doping determines routes to colloidal clusters and gels

Collections of polar active particles have been unable to form stable and long-living structures due to the presence of self-propulsion. We solve this timely issue by introducing the concept of “active doping” and show that a few light-activated apolar, i.e., non–self-propelling, units can be used to rapidly trigger the formation of solid clusters and gels composed of passive colloidal particles. Our active doping can be used to assemble disparate microscopic objects, including synthetic or biological ones, paving the way toward the extension of fundamental concepts of gel and glass formation to active out-of-equilibrium systems.

Collections of interacting active particles, self-propelling or not, have shown remarkable phenomena including the emergence of dynamic patterns across different length scales, from animal groups to vibrated grains, microtubules, bacteria, and chemical- or field-driven colloids. Burgeoning experimental and simulation activities are now exploring the possibility of realizing solid and stable structures from passive elements that are assembled by a few active dopants. Here we show that such an elusive task may be accomplished by using a small amount of apolar dopants, namely synthetic active but not self-propelling units. We use blue light to rapidly assemble 2D colloidal clusters and gels via nonequilibrium diffusiophoresis, where microscopic hematite dockers form long-living interstitial bonds that strongly glue passive silica microspheres. By varying the relative fraction of doping, we uncover a rich phase diagram including ordered and disordered clusters, space-filling gels, and bicontinuous structures formed by filamentary dockers percolating through a solid network of silica spheres. We characterize the slow relaxation and dynamic arrest of the different phases via correlation and scattering functions. Our findings provide a pathway toward the rapid engineering of mesoscopic gels and clusters via active colloidal doping.

Active Atoms and Interstitials in Two-Dimensional Colloidal Crystals

We study experimentally and numerically the motion of a self-phoretic active particle in two-dimensional loosely packed colloidal crystals at fluid interfaces. Two scenarios emerge depending on the interactions between the active particle and the lattice: the active particle either navigates throughout the crystal as an interstitial or is part of the lattice and behaves as an active atom. Active interstitials undergo a run-and-tumble-like motion, with the passive colloids of the crystal acting as tumbling sites. Instead, active atoms exhibit an intermittent motion, stemming from the interplay between the periodic potential landscape of the passive crystal and the particle's self-propulsion. Our results constitute the first step towards the realization of non-close-packed crystalline phases with internal activity.

Energy dissipation and fluctuations in a driven liquid

Minimal models of active and driven particles have recently been used to elucidate many properties of nonequilibrium systems. However, the relation between energy consumption and changes in the structure and transport properties of these nonequilibrium materials remains to be explored. We explore this relation in a minimal model of a driven liquid that settles into a time periodic steady state. Using concepts from stochastic thermodynamics and liquid state theories, we show how the work performed on the system by various nonconservative, time-dependent forces-this quantifies a violation of time reversal symmetry-modifies the structural, transport, and phase transition properties of the driven liquid.

Active colloids with collective mobility status and research opportunities

The collective mobility of active matter (self-propelled objects that transduce energy into mechanical work to drive their motion, most commonly through fluids) constitutes a new frontier in science and achievable technology. This review surveys the current status of the research field, what kinds of new scientific problems can be tackled in the short term, and what long-term directions are envisioned. We focus on: (1) attempts to formulate design principles to tailor active particles; (2) attempts to design principles according to which active particles interact under circumstances where particle-particle interactions of traditional colloid science are augmented by a family of nonequilibrium effects discussed here; (3) attempts to design intended patterns of collective behavior and dynamic assembly; (4) speculative links to equilibrium thermodynamics. In each aspect, we assess achievements, limitations, and research opportunities.

Nonmonotonic Classical Magnetoconductivity of a Two-Dimensional Electron Gas in a Disordered Array of Obstacles

Magnetotransport measurements in combination with molecular dynamics simulations on two-dimensional disordered Lorentz gases in the classical regime are reported. In quantitative agreement between experiment and simulation, the magnetoconductivity displays a pronounced peak as a function of the perpendicular magnetic field B which cannot be explained by existing kinetic theories. This peak is linked to the onset of a directed motion of the electrons along the contour of the disordered obstacle matrix when the cyclotron radius becomes smaller than the size of the obstacles. This directed motion leads to transient superdiffusive motion and strong scaling corrections in the vicinity of the insulator-to-conductor transitions of the Lorentz gas.

Effective equilibrium states in mixtures of active particles driven by colored noise

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power-law potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.

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.