Biological systems exhibit large-scale self-organized dynamics and structures which enable organisms to perform the functions of life. The field of active matter strives to develop and understand microscopically-driven nonequilibrium materials, with emergent properties comparable to those of living systems. This review will describe two recently developed classes of active matter systems, in which simple building blocks --- self-propelled colloidal particles or extensile rod-like particles --- self-organize to form macroscopic structures with features not possible in equilibrium systems. We summarize the recent experimental and theoretical progress on each of these systems, and we present simple descriptions of the physics underlying their emergent behaviors.
We introduce and study a model of active Brownian motion with multiplicative noise describing fluctuations in the self-propulsion or activity. We find that the standard picture of density accumulation in slow regions is qualitatively modified by active fluctuations, as stationary density profiles are generally not determined only by the mean self-propulsion speed landscape. As a result, activity gradients generically correlate the particle self-propulsion speed and orientation, leading to emergent polarization at interfaces pointing either towards dense or dilute regions depending on the amoun…
Minimal models of active Brownian colloids consisting of self-propelled spherical particles with purely repulsive interactions have recently been identified as excellent quantitative testing grounds for theories of active matter and have been the subject of extensive numerical and analytical investigation. These systems do not exhibit aligned or flocking states, but do have a rich phase diagram, forming active gases, liquids and solids with novel mechanical properties. This article reviews recent advances in the understanding of such models, including the description of the active gas and its …
We consider a phenomenological continuum model for an active nematic fluid and show a universal, model independent, instability which renders the homogeneous nematic state unstable to order fluctuations. Using numerical and analytic tools we show that, for low energy excitations in the vicinity of a critical point, this instability leads to a phase separation in which the ordered regions form bands with the direction of nematic order being perpendicular to the direction of density gradient. We argue that this mechanism of phase separation, which we term self-regulation, is a universal feature …
We propose a simple system of optically driven colloids that convert light into heat and move in response to self- and collectively- generated thermal gradients. We show that the system exhibits self-organization into a moving comet-like swarm and characterize the structure and response of the swarm to a light intensity dependent external tuning parameter. We observe many interesting features in this nonequilibrium system including circulation and evaporation, intensity-dependent shape, density and temperature fluctuations, and ejection of hot colloids from the swarm tip.
We study the dynamics of an entangled, isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for constant motor concentration taking into account excluded volume and entanglement. At low filament density the system develops a density instability, while at high filament density entanglement effects drive the instability of orientational fluctuations.
Using Brownian dynamics (BD) simulations we investigate the self-organization of a monolayer of chiral active particles with dipolar interactions. Each particle is driven by both, translational and rotational self-propulsion, and carries a permanent point dipole moment at its center. The direction of the translational propulsion for each particle is chosen to be parallel to its dipole moment. Simulations are performed at high dipolar coupling strength and a density below that related to motility-induced phase separation in simple active Brownian particles. Despite this restriction, we observe …
When the motion of a motile cell is observed closely, it appears erratic, and yet the combination of nonequilibrium forces and surfaces can produce striking examples of organization in microbial systems. While most of our current understanding is based on bulk systems or idealized geometries, it remains elusive how and at which length scale self-organization emerges in complex geometries. Here, using experiments, analytical and numerical calculations we study the motion of motile cells under controlled microfluidic conditions, and demonstrate that probability flux loops organize active motion …
Much recent progress has been made in the study of nematic solids, both glassy and elastomeric, particularly in the realm of stress-free, defect-driven deformation in thin sheets of material. In this paper we consider a subset of texture domains in nematic glasses that are simple to synthesize, and explore the ways that these simple domains may be compatibly combined to yield analogs of the traditional smooth disclination defect textures seen in standard liquid crystals. We calculate the deformation properties of these constructed textures, and show that, subject to the compatibility constrain…
We study a model of self-propelled particles interacting with their $k$ nearest neighbors through polar alignment. By exploring its phase space as a function of two nondimensional parameters (alignment strength $g$ and Peclet number $\mathrm{Pe}$), we identify two distinct order-disorder transitions. One is continuous, occurs at a low critical $g$ value independent of Pe, and resembles a mean-field transition with no density-order coupling. The other is discontinuous, depends on a combined control parameter involving $g$ and Pe, and results from the formation of small, dense, highly persistent…
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 colloids are microscopic particles, which self-propel through viscous fluids by converting energy extracted from their environment into directed motion. We first explain how articial microswimmers move forward by generating near-surface flow fields via self-phoresis or the self-induced Marangoni effect. We then discuss generic features of the dynamics of single active colloids in bulk and in confinement, as well as in the presence of gravity, field gradients, and fluid flow. In the third part, we review the emergent collective behavior of active colloidal suspensions focussing on their …
Spatially localised defect structures emerge spontaneously in a hydrodynamic description of an active polar fluid comprising polar 'actin' filaments and 'myosin' motor proteins that (un)bind to filaments and exert active contractile stresses. These emergent defect structures are characterized by distinct textures and can be either static or mobile - we derive effective equations of motion for these 'extended particles' and analyse their shape, kinetics, interactions and scattering. Depending on the impact parameter and propulsion speed, these active defects undergo elastic scattering or merger…
Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore the generic diagram of emerging states over a large range of rod densities and aspect ratios. The dynamics is studied using a simple numerical scheme for the overdamped noiseless frictional dynamics of a many-body system in which steric forces are dominant over hydrodynamic ones. The different emergent states are identified by various characteristic correlatio…
A living cell is an active environment where the organization and dynamics of chromatin are affected by different forms of activity. Optical experiments report that loci show subdiffusive dynamics and the chromatin fiber is seen to be coherent over micrometer-scale regions. Using a bead-spring polymer chain with dipolar active forces, we study how the subdiffusive motion of the loci generate large-scale coherent motion of the chromatin. We show that in the presence of extensile (contractile) activity, the dynamics of loci grows faster (slower) and the spatial correlation length increases (decr…
Active forces occurring within cells can drive crucial biological processes that involve spontaneous organization and shape change, such as cell division. Motivated by recent in vitro experiments of nematic droplets of cytoskeletal filaments and motors that self-organize and divide, we present a minimal hydrodynamic model that combines the nonequilibrium kinetics of motor-filament interactions with equilibrium nematic phase separation. The motors organize within droplets and structure filaments into polarized aster defects. At large motor activity, they can even deform or divide the droplet, o…
Coherent vortical motion has been reported in a wide variety of populations including living organisms (bacteria, fishes, human crowds) and synthetic active matter (shaken grains, mixtures of biopolymers), yet a unified description of the formation and structure of this pattern remains lacking. Here we report the self-organization of motile colloids into a macroscopic steadily rotating vortex. Combining physical experiments and numerical simulations, we elucidate this collective behavior. We demonstrate that the emergent-vortex structure lives on the verge of a phase separation, and single out…
Density and shape govern the dynamical self-organization of active matter on a closed surface
Sorbonne Université（索邦大学）；CNRS, Institut de Biologie Paris-Seine (IBPS), Laboratoire Jean Perrin (LJP)（法国国家科学研究中心，巴黎塞纳生物研究所，让·佩兰实验室）；Laboratoire Matière et Systèmes Complexes, Université Paris Cité/CNRS (UMR 7057)（物质与复杂系统实验室，巴黎西岱大学/法国国家科学研究中心）；Université de Lille（里尔大学）；CY Cergy Paris Université（塞吉-蓬图瓦兹巴黎大学）
The cytoskeleton is a model active matter system that controls diverse cellular processes from division to motility. While both active actomyosin dynamics and actin-microtubule interactions are key to the cytoskeleton's versatility and adaptability, an understanding of their interplay is lacking. Here, we couple microscale experiments with mechanistic modeling to elucidate how connectivity, rigidity, and force-generation affect emergent material properties in in vitro composites of actin, tubulin, and myosin. We use time-resolved differential dynamic microscopy and spatial image autocorrelatio…
Self-organization phenomena in ensembles of self-propelled particles open pathways to the synthesis of new dynamic states not accessible by traditional equilibrium processes. The challenge is to develop a set of principles that facilitate the control and manipulation of emergent active states. Here, we report that dielectric rolling colloids energized by a pulsating electric field self-organize into alternating square lattices with a lattice constant controlled by the parameters of the field. We combine experiments and simulations to examine spatiotemporal properties of the emergent collective…
We consider a system of independent point-like particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom that is subjected to a nonequilibrium source of noise, which affects their coupling with the background field. We explore the phase diagram of the system and pinpoint the role of the nonequilibrium drive in producing a nontrivial patterned spatial organization. We are able, by means of a weakly nonlinear analysis, to account for the parameter-dependence of the …
It is still challenging to control dynamic self-organization patterns of self-propelled particles. Although varieties of patterns associated with chirality have been observed, essential control factors determining patterns remain unclear. Here, we explore numerically how torque upon particle collision affects dynamic self-organization. Based on the particle-based model with both collision-induced torque and torque in self-propulsion, we find that introducing collision-induced torque turns homogeneous bi-polar orientation templated by bi-directional alignment into rotating mono-polar flocks.
In many active matter systems, particle trajectories have a well-defined handedness or chirality. Whether such chiral activity can introduce stereoselective interactions between particles is not known. Here we developed a strategy to tune the nature of chiral activity of 3D-printed granular ellipsoids without altering their shape or size. In vertically agitated monolayers of these particles, we observed two types of dimers form depending on the chirality of the pairing monomers. Heterochiral dimers moved collectively as a single achiral active unit, while homochiral ones formed a translational…
Emergent universal long-range structure in random-organizing systems
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；Center for Soft Matter Research, Department of Physics, New York University（纽约大学物理系软物质研究中心）；Simons Center for Computational Physical Chemistry, Department of Chemistry, New York University（纽约大学化学系西蒙斯计算物理化学中心）；Center for Neural Science, New York University（纽约大学神经科学中心）
Cells in tissues can organize into a broad spectrum of structures according to their function. Drastic changes of organization, such as epithelial-mesenchymal transitions or the formation of spheroidal aggregates, are often associated either to tissue morphogenesis or to cancer progression. Here, we study the organization of cell colonies by means of simulations of self-propelled particles with generic cell-like interactions. The interplay between cell softness, cell-cell adhesion, and contact inhibition of locomotion (CIL) yields structures and collective dynamics observed in several existing…
Collections of interacting, self-propelled particles have been extensively studied as minimal models of many living and synthetic systems from bird flocks to active colloids. However, the influence of active rotations in the absence of self-propulsion i.e. spinning without walking) remains less explored. Here, we numerically and theoretically investigate the behaviour of ensembles of self-spinning dimers. We find that geometric frustration of dimer rotation by interactions yields spatiotemporal order and active melting with no equilibrium counterparts. At low density, the spinning dimers self-…
Novel "smectic-P" behavior, in which self-propelled particles form rows and move on average along them, occurs generically within the orientationally-ordered phase of simple models that we simulate. Both apolar (head-tail symmetric) and polar (head-tail asymmetric) models with aligning and repulsive interactions exhibit slow algebraic decay of smectic order with system size up to some finite length scale, after which faster decay occurs. In the apolar case, this scale is that of an undulation instability of the rows. In the polar case, this instability is absent, but traveling fluctuations dis…
The shear-induced self-organization of active rotors into stripy aggregates is studied by carrying out computational simulations. The rotors, modeled by monolayers of frictional spheres, develop to stripy microstructures only when they counterrotate with respect to the vorticity of the imposed shear flow. The average width of the stripes is demonstrated to be linearly dependent on the relative intensity of active torque to the shear rate. By giving insight into three collective particle behaviors, i.e., shear-induced diffusion, rotation-induced rearrangement, and edge flows, we explain the mec…
Recent attempts towards a theory of active matter utilize concepts and methods from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, such approaches typically do not seem to recognize the critical feature of some kinds of active matter (particularly the biological ones), namely, the role of purpose, and the naturally attendant concept of the pursuit of maximum utility, which we believe is the crucial difference between active and passive matter. Here we introduce a novel game-theoretic framework, statistical teleodynamics, that accounts for this feature explicit…
Active nematics are microscopically driven liquid crystals that exhibit dynamical steady states characterized by the creation and annihilation of topological defects. Motivated by experimental realizations of such systems made of biopolymer filaments and motor proteins, we describe a large-scale simulation study of a particle-based computational model that explicitly incorporates the semiflexibility of the biopolymers. We find that energy injected into the system at the particle scale preferentially excites bend deformations, renormalizing the filament bend modulus to smaller values. The emerg…
