Large-scale collective behavior in suspensions of many particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the application of collective forces in synthetic active matter, as well as their role in living active matter.
We study collective dynamical behavior of active particles with topological interactions and directional reversals. Surprising phenomena are shown to emerge as the interaction relaxation time is varied relative to the reversal rate, such as spontaneous formation of collective chiral states due to phase synchronization, and collective directional reversals in the presence of confinement. The results have a direct relevance to modelling and understanding collective reversals and synchronization phenomena in active matter.
Active work measures how far the local self-forcing of active particles translates into real motion. Using Population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes.
We propose a simple deterministic dynamic equation and reveal the mechanism of large-scale endless evolvement of spatial density inhomogeneity in active nematic. We determine the phase regions analytically. The interplay of density, magnitude of nematic order, and nematic director is crucial for the long-wave-length instability and the emergence of seemingly fluctuated collective motions. Ordered nematic domains can absorb particles, grow and divide endlessly. The present finding extends our understanding of the large-scale and seemingly fluctuated organization in active fluids.
Collective order reorganizes dissipation and powers an active engine
TU Dresden（德累斯顿工业大学）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology（里尔大学、法国国家科学研究中心、法国航空航天实验室、巴黎国立高等工艺学院）；University of Luxembourg（卢森堡大学）
We present a comprehensive analysis of effective temperatures based on fluctuation-dissipation relations in a model of an active fluid composed of self-propelled hard disks. We first investigate the relevance of effective temperatures in the dilute and moderately dense fluids. We find that a unique effective temperature does not in general characterize the non-equilibrium dynamics of the active fluid over this broad range of densities, because fluctuation-dissipation relations yield a lengthscale-dependent effective temperature. By contrast, we find that the approach to a non-equilibrium glass…
We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition from a disordered and stuck state to an ordered state of global collective motion where the particles rotate persistently clockwise or anticlockwise. We describe this behavior by introducing a suitable order parameter, the velocity polarization, measuring the global alignment of the particles' velocities along the tangential direction of the ring. We also m…
Using computer simulations, we study a two-dimensional system of sterically interacting self-mobile run-and-tumble disk-shaped particles with an underlying periodic quasi-one-dimensional asymmetric substrate, and show that a rich variety of collective active ratchet behaviors arise as a function of particle density, activity, substrate strength, and substrate period. The ratchet efficiency is nonmonotonic since the ratcheting is enhanced by increased activity but diminished by the onset of self-clustering of the active particles. Increasing the particle density decreases the ratchet efficiency…
We derive a general lower bound on distributions of entropy production in interacting active matter systems. The bound is tight in the limit that interparticle correlations are small and short-ranged, which we explore in four canonical active matter models. In all models studied, the bound is weak where collective fluctuations result in long-ranged correlations, which subsequently links the locations of phase transitions to enhanced entropy production fluctuations. We develop a theory for the onset of enhanced fluctuations and relate it to specific phase transitions in active Brownian particle…
We explore the emergence of nonequilibrium collective motion in disordered non-thermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled particles. In stark contrast with monodisperse systems, we find that polydispersity stabilizes a homogeneous active liquid at arbitrary large persistence times, characterized by remarkable velocity correlations and irregular turbulent flows. For all persistence values, the active fluid undergoes a nonequilibrium glass transition at large density. This is accompan…
We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with internal energy depot and interactions inspired by the dissipative particle dynamics method, imposing pairwise friction force on the nearest neighbours. We study orientational ordering in a 2D system as a function of energy influx rate and particle density. The model demonstrates a transition into the ordered state on increasing the particle density and increasing the input power. Although both the alignment mechanism and the cha…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyse the symmetry breaking by an optimal-control rep…
We numerically examine 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 where 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 can occur as a function of the substrate speed, maximum …
Colloids with patchy metal coating under laser irradiation could act as local sources of heat due to the absorption of light. While for asymmetric colloids this could induce self-propulsion, it also leads to the generation of a slowly decaying temperature profile that other colloids could interact with. The collective behavior of a dilute solution of such thermally active particles is studied using a stochastic formulation. It is found that when the Soret coefficient is positive, the system could be described in stationary-state by the nonlinear Poisson-Boltzmann equation and could adopt densi…
We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with n…
We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force-free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing …
Microswimmers are active particles of microscopic size that self-propel by setting the surrounding fluid into motion. According to the kind of far-field fluid flow that they induce, they are classified into pushers and pullers. Many studies have explored similarities and differences between suspensions of either pushers or pullers, but the behavior of mixtures of the two is still to be investigated. Here, we rely on a minimal discrete microswimmer model, particle-resolved, including hydrodynamic interactions, to examine the orientational ordering in such binary pusher-puller mixtures. In agree…
The multicellular organization of diverse systems, such as embryos, intestines and tumours, relies on the coordinated migration of cells in 3D curved environments. In these settings, cells establish supracellular patterns of motion, including collective rotation and invasion. While such collective modes are increasingly well understood in 2D flat systems, the consequences of geometrical and topological constraints on collective cell migration in 3D curved tissues are largely unknown. Here, we study 3D collective migration in mammary cell spheroids, which represent a common and conceptually sim…
Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology, single-particle superdiffusion and fat-tailed displacement statistics are also widespread. The collective properties of interacting systems exhibiting such anomalous diffusive dynamics, which we call active Lévy matter, cannot be captured by current active fluid theories. Here, we formulate a hydrodynamic theory of active Lévy matter by coarse-graining a microscopic…
We study the stochastic force dynamics of a model microswimmer (Chlamydomonas reinhardtii), using a combined experimental, theoretical, and numerical approach. While swimming dynamics have been extensively studied using hydrodynamic approaches, which infer forces from the viscous flow field, we directly measure the stochastic forces generated by the microswimmer using an optical trap via the photon momentum method. We analyze the force dynamics by modeling the microswimmer as a self-propelled particle, a la active matter, and analyze it's energetics using methods from stochastic thermodynamics…
The perturbation of a medium field (a particle wake) determines the Stokes drag on the particle itself. Besides, it affects the motion of other particles, inducing non-equilibrium correlations between them. We study the induced non-equilibrium correlations and forces, acting on constituent particles of the bunch or cluster of impurities exposed to a gas stream. Such induced correlations exhibit many striking features that are determined by the properties of particle bunch collective scattering in a medium. The characteristics of collective scattering are determined by the structure of the bunc…
Lecture notes from the Les Houches summer school on Active Matter and Non-Equilibrium Statistical Physics 2018. The notes contain a pedagogical introduction to the statistics of forces in dry active matter. In particular, the physics behind the existence of an equation of state, or lack thereof, is discussed along with its implications.
The study of systems with sustained energy uptake and dissipation at the scale of the constituent particles is an area of central interest in nonequilibrium statistical physics. Identifying such systems as a distinct category -- Active Matter -- unifies our understanding of autonomous collective move- ment in the living world and in some surprising inanimate imitations. In this article I present the Active Matter framework, briefly recall some early work, review our recent results on single-particle and collective behaviour, including experiments on active granular monolayers, and discuss new …
We introduce a class of lattice gas models of active matter systems whose hydrodynamic description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviours in active matter: the motility-induced phase separation and the transition to collective motion. In both cases, we derive coupled partial differential equation describing the dynamics of the local density and polarization fields and show how they quantitatively predict the emerging properties of the macroscopic lattice gases.
We calculate the effect of the interaction between an optically active material and a Bose-Einstein condensate on the collective oscillations of the condensate. We provide explicit expressions for the frequency shift of the center of mass oscillation in terms of the potential generated by the substrate and of the density profile of the gas. The form of the potential is discussed in details and various regimes (van der Waals-London, Casimir-Polder and thermal regimes) are identified as a function of the distance of atoms from the surface. Numerical results for the frequency shifts are given for…
