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-dimensionnal 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.
Using Brownian vibrators, where single particles can undergo Brownian motion under vibration, we experimentally investigated self-organized structures and dynamics of quasi-two-dimensional (quasi-2d) granular materials with volume fractions $0.111\leϕ\le0.832$. We show rich structures and dynamics in hard-disk systems of inelastic particle collisions, with four phases corresponding to cluster fluid, collective fluid, poly-crystal, and crystal. While poly-crystal and crystal are strikingly similar to the equilibrium hard disks, the first two phases differ substantially from the equilibrium ones…
Single-orientation Crystalline Domains of Active Brownian Particles Lead to Collective Motions
School of Physics and Electronic Information, Mianyang Teachers’ College（绵阳师范学院物理与电子信息学院）；Computer Network Information Center, Chinese Academy of Sciences（中国科学院计算机网络信息中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
In the simplest realization of Brownian motion, a colloidal sphere moves randomly in an isotropic fluid; its mean squared displacement (MSD) grows linearly with time $\textitτ$. Brownian motion in an orientationally ordered fluid, a nematic, is anisotropic, with the MSD being larger along the axis of molecular orientation, called the director. We show that at short time scales, the anisotropic diffusion in a nematic becomes also anomalous, with the MSD growing slower (subdiffusion) and faster (superdiffusion) than $\textitτ$. The anomalous diffusion occurs at time scales that correspond to the…
The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the microscopic local density of colloids, in terms of a space and rotation state, also evolves according to a Langevin equation. The latter can then be used as the starting point of a variety of approaches, ranging from dynamical density functional theory to mode-coupling approximations.
In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing diffusivity model where the equation of motion of the active particle involves a time-dependent motility and diffusivities. Within our model, those fluctuations are coupled to each other. Using analytical methods, we obtain the probability distribution function of particle displacement and its moments for a single particle. We then investigate the impact of the envi…
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…
Suspensions of motile active particles with space dependent activity form characteristic polarization and density patterns. Recent single-particle studies for planar activity landscapes identified several quantities associated with emergent density-polarization patterns, including swim pressure, that are solely determined by bulk variables and thus constitute state functions. We show that for radially symmetric activity steps these variables depend on the curvature of the active-passive interface. In the specific case of total polarization and swim pressure, we generalize this result for arbit…
We investigate the nonequilibrium dynamics of spherical active Brownian particles in three spatial dimensions that interact via a pair potential. The investigation is based on a predictive local field theory that is derived by a rigorous coarse-graining starting from the overdamped Langevin dynamics of the particles. This field theory is highly accurate and applicable even for the highest activities. It includes configurational order parameters and derivatives up to infinite orders. We present also three finite reduced models that result from the general field theory by suitable approximations…
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…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochasti…
We describe simulations of active Brownian particles carried out to explore how dynamics and clustering are influenced by particle shape. Our particles are composed of four disks, held together by springs, whose relative size can be varied. These compound objects can be tuned smoothly from having a concave to a convex surface. We show that even two of these composite particles can exhibit collective motion modifying the effective Peclet number. We then investigate how particle geometry can be used to explain the phase behaviour of many such particles.
We experimentally study a monolayer of vibrated disks with a built-in polar asymmetry which enables them to move quasi-balistically on a large persistence length. Alignment occurs during collisions as a result of self-propulsion and hard core repulsion. Varying the amplitude of the vibration, we observe the onset of large-scale collective motion and the existence of giant number fluctuations with a scaling exponent in agreement with the predicted theoretical value.
The cage effect is generally invoked when discussing the delay in the decay of time correlation functions of dense fluids. In an attempt to examine the role of caging more closely we consider the spread of the displacement distributions of Brownian particles. These distributions are necessarily biased by the presence of neighbouring particles. Accommodation of this bias by those neighbours conserves the displacement distribution locally and presents a collective mechanism for exploring configuration space that is more efficient than the intrinsic Brownian motion. Caging of some particles incur…
The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in th…
We study the spontaneous motion, binary collisions, and collective dynamics of "polar disks", i.e. purpose-built particles which, when vibrated between two horizontal plates, move coherently along a direction strongly correlated to their intrinsic polarity. The motion of our particles, although nominally three-dimensional and complicated, is well accounted for by a two-dimensional persistent random walk. Their binary collisions are spatiotemporally extended events during which multiple actual collisions happen, yielding a weak average effective alignment. We show that this well-controlled, "dr…
Estimation of spatial and time scales of collective behaviors of active matters through learning hydrodynamic equations from particle dynamics
Future University Hakodate（函馆未来大学）；AIST（产业技术综合研究所）；Mathematics for Advanced Materials-OIL (MathAM-OIL), AIST（产业技术综合研究所 先进材料数学-OIL）；WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学 WPI-材料研究高级研究所）
We numerically study active Brownian particles that can respond to environmental cues through a small set of actions (switching their motility and turning left or right with respect to some direction) which are motivated by recent experiments with colloidal self-propelled Janus particles. We employ reinforcement learning to find optimal mappings between the state of particles and these actions. Specifically, we first consider a predator-prey situation in which prey particles try to avoid a predator. Using as reward the squared distance from the predator, we discuss the merits of three state-ac…
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance equations. We obtain expressions for the heat flux and the pressure tensor which enable one to describe the kinetic and potential energy interchange of the particles with the heat bath. Through the momentum balance we analyze in particular the diffusion regime to obtain the collective diffusion coefficient in terms of the hydrodynamic and the effective forces …
Active particles which are self-propelled by converting energy into mechanical motion represent an expanding research realm in physics and chemistry. For micron-sized particles moving in a liquid ("microswimmers"), most of the basic features have been described by using the model of overdamped active Brownian motion. However, for macroscopic particles or microparticles moving in a gas, inertial effects become relevant such that the dynamics is underdamped. Therefore, recently, active particles with inertia have been described by extending the active Brownian motion model to active Langevin dyn…
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 p…
Hypothesis: The collective dynamics and self-assembly of colloids floating at a fluid/fluid interface is a balance between deterministic lateral interaction forces, viscous resistance to colloid motion along the surface and thermal (Brownian) fluctuations. As the colloid size decreases, thermal forces become important and can affect the self assembly into ordered patterns and crystal structures that are the starting point for various materials applications. Numerics: Langevin dynamic simulations involving two particles straddling a liquid/liquid interface with a high viscosity contrast are pre…
Slender bodies capable of spontaneous motion in the absence of external actuation in an otherwise quiescent fluid are common in biological, physical and technological contexts. The interplay between the spontaneous fluid flow, Brownian motion, and the elasticity of the body presents a challenging fluid-structure interaction problem. Here, we model this problem by approximating the slender body as an elastic filament that can impose non-equilibrium velocities or stresses at the fluid-structure interface. We derive equations of motion for such an active filament by enforcing momentum conservatio…
We investigate the stochastic dynamics of one sedimenting active Brownian particle in three dimensions under the influence of gravity and passive fluctuations in the translational and rotational motion. We present an analytical solution of the Fokker--Planck equation for the stochastic process which allows us to describe the dynamics of the active Brownian particle in three dimensions. We address the time evolution of the monopole, the polarization, and the steady-state solution. We also perform Brownian dynamics simulations and study the effect of the activity of the particles on their collec…
We study the Brownian motion of an assembly of mobile inclusions embedded in a fluid membrane. The motion includes the dispersal of the assembly, accompanied by the diffusion of its center of mass. Usually, the former process is much faster than the latter, since the diffusion coefficient of the center of mass is inversely proportional to the number of particles. However, in the case of membrane inclusions, we find that the two processes occur on the same time scale, thus prolonging significantly the lifetime of the assembly as a collectively moving object. This effect is caused by the quasi-t…
Collective dynamics of densely confined active polar disks with self- and mutual alignment
Beijing Normal University（北京师范大学）；Humboldt Universität zu Berlin（柏林洪堡大学）；Research Cluster of Excellence ‘Science of Intelligence’（智能科学卓越研究中心）；Northwestern University（西北大学）；Beijing Jiaotong University（北京交通大学）；CHuepe Labs（CHuepe实验室）
We consider chirality in active systems by exemplarily studying the phase behavior of planar systems of interacting Brownian circle swimmers with a spherical shape. Continuing previous work presented in [G.-J. Liao, S. H. L. Klapp, Soft Matter, 2018, 14, 7873-7882], we derive a predictive field theory that is able to describe the collective dynamics of circle swimmers. The theory yields a mapping between circle swimmers and noncircling active Brownian particles and predicts that the angular propulsion of the particles leads to a suppression of their motility-induced phase separation, being in …
We present a fundamental classification of forces relevant in nonequilibrium structure formation under collective flow in Brownian many-body systems. The internal one-body force field is systematically split into contributions relevant for the spatial structure and for the coupled motion. We demonstrate that both contributions can be obtained straightforwardly in computer simulations, and present a power functional theory that describes all types of forces quantitatively. Our conclusions and methods are relevant for flow in inertial systems, such as molecular liquids and granular media.
Based on extensive Brownian dynamics simulations we study the thermally driven motion of a tracer bead in a cross-linked, dynamic gel network in the limit when the tracer bead's size is of the same size or even larger than the equilibrium mesh size of the gel. The analysis of long individual trajectories of the tracer bead demonstrates the existence of pronounced transient anomalous diffusion, accompanied by a drastic slow-down of the gel-bead relaxation dynamics. From the time averaged mean squared displacement and the van Hove cross-correlation function we elucidate the many-body origin of t…
Hydrodynamically interacting active particles in an external harmonic potential form a self-assembled fluid pump at large enough Péclet numbers. Here, we give a quantitative criterion for the formation of the pump and show that particle orientations align in the self-induced flow field in surprising analogy to ferromagnetic order where the active Péclet number plays the role of inverse temperature. The particle orientations follow a Boltzmann distribution $Φ(\mathbf{p}) \sim \exp(A p_z)$ where the ordering mean field $A$ scales with active Péclet number and polar order parameter. The mean flow…
Active particles may happen to be confined in channels so narrow that they cannot overtake each other (Single File conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong inter-particle correlations developed in collective rearrangements. We consider a minimal model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) Single File picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian partic…
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.
Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models, where hard spheres are driven by a constant drag force through a periodic potential. Here, we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically w…
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 de…
Magnetotactic swimmers tend to align along magnetic field lines against stochastic reorientations. We show that the swimming strategy, e.g. active Brownian motion versus run-and-tumble dynamics, strongly affects the orientation statistics. The latter can exhibit a velocity condensation whereby the alignment probability density diverges. As a consequence, we find that the swimming strategy affects the nature of the phase transition to collective motion, indicating that Lévy run-and-tumble walks can outperform active Brownian processes as strategies to trigger collective behavior.
We investigate the full pair-distribution function of a homogeneous suspension of spherical active Brownian particles interacting by a Weeks-Chandler-Andersen potential in two spatial dimensions. The full pair-distribution function depends on three coordinates describing the relative positions and orientations of two particles, the Péclet number specifying the activity of the particles, and their mean packing density. This five-dimensional function is obtained from Brownian dynamics simulations. We discuss its structure taking into account all of its degrees of freedom. In addition, we present…
We present the exact solution of a Brownian inchworm model of a self-propelled elastic dimer which has recently been proposed in [K. V. Kumar \textit{et al}, Phys. Rev. E \textbf{77}, 020102(R) (2008)] as a unifying model for the propulsion mechanisms of DNA helicase, polar rods on a vibrated surface, crawling keratocytes, and Myosin VI.
Giant number fluctuations (GNF) are an anomaly universally observed in active fluids with polar or nematic order. In this paper, we show that GNF arise in the fluid phase of active Brownian particles (ABP), where the polar order is absent. GNF in ABP extends over a large but finite length which characterizes the growing velocity correlations. To suppress unwanted phase separation and allow ones to explore the disordered fluid phase at large activities, we impart the inertia, or the mass, to the ABP. A linearized hydrodynamic theory captures our findings, but only qualitatively. We find numeric…
We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external …
Chiral active particles (or self-propelled circle swimmers) feature a rich collective behavior, comprising rotating macro-clusters and micro-flock patterns which consist of phase-synchronized rotating clusters with a characteristic self-limited size. These patterns emerge from the competition of alignment interactions and rotations suggesting that they might occur generically in many chiral active matter systems. However, although excluded volume interactions occur naturally among typical circle swimmers, it is not yet clear if macro-clusters and micro-flock patterns survive their presence. Th…
