Non-equilibrium collective behavior of self-propelled colloidal rods in a confining channel is studied using Brownian dynamics simulations and dynamical density functional theory. We observe an aggregation process in which rods self-organize into transiently jammed clusters at the channel walls. In the early stage of the process, fast-growing hedgehog-like clusters are formed which are largely immobile. At later stages, most of these clusters dissolve and mobilize into nematized aggregates sliding past the walls.
We study, in two space dimensions, the large-scale properties of collections of constant-speed polar point particles interacting locally by nematic alignment in the presence of noise. This minimal approach to self-propelled rods allows one to deal with large numbers of particles, revealing a phenomenology previously unseen in more complicated models, and moreover distinctively different from both that of the purely polar case (e.g. the Vicsek model) and of active nematics.
We derive a set of minimal yet complete nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for the fronts forming density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.
Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via excluded volume and their dynamics is overdamped by the interaction with the substrate. Starting from a microscopic model with non-thermal noise sources, a continuum description of the system is derived. The hydrodynamic equations are then used to characterize the possible steady states of the systems and their stability as a function of the particles packing fract…
Motivated by aggregation phenomena in gliding bacteria, we study collective motion in a twodimensional model of active, self-propelled rods interacting through volume exclusion. In simulations with individual particles, we find that particle clustering is facilitated by a sufficiently large packing fraction (eta) or length-to-width ratio (kappa). The transition to clustering in simulations is well captured by a mean-field model for the cluster size distribution, which predicts that the transition values kappa_c of the aspect ratio for a fixed packing fraction is given by kappa_c = C/eta - 1 wh…
Using overdamped Brownian dynamics simulations we investigate the isotropic-nematic (IN) transition of self-propelled rods in three spatial dimensions. For two well-known model systems (Gay-Berne potential and hard spherocylinders) we find that turning on activity moves to higher densities the phase boundary separating an isotropic phase from a (nonpolar) nematic phase. This active IN phase boundary is distinct from the boundary between isotropic and polar-cluster states previously reported in two-dimensional simulation studies and, unlike the latter, is not sensitive to the system size. We th…
A wide range of experimental systems including gliding, swarming and swimming bacteria, in-vitro motility assays as well as shaken granular media are commonly described as self-propelled rods. Large ensembles of those entities display a large variety of self-organized, collective phenomena, including formation of moving polar clusters, polar and nematic dynamic bands, mobility-induced phase separation, topological defects and mesoscale turbulence, among others. Here, we give a brief survey of experimental observations and review the theoretical description of self-propelled rods. Our focus is …
Considering systems of self-propelled polar particles with nematic interactions ("rods"), we compare the continuum equations describing the evolution of polar and nematic order parameters, derived either from Smoluchowski or Boltzmann equations. Our main goal is to understand the discrepancies between the continuum equations obtained so far in both frameworks. We first show that in the simple case of point-like particles with only alignment interactions, the continuum equations obtained have the same structure in both cases. We further study, in the Smoluchowski framework, the case where an in…
Starting from a minimal physical model of self propelled hard rods on a substrate in two dimensions, we derive a modified Smoluchowski equation for the system. Self -propulsion enhances longitudinal diffusion and modifies the mean field excluded volume interaction. From the Smoluchowski equation we obtain hydrodynamic equations for rod concentration, polarization and nematic order parameter. New results at large scales are a lowering of the density of the isotropic-nematic transition and a strong enhancement of boundary effects in confined self-propelled systems.
We study a robust model of self-propelled rods interacting via volume exclusion and show that its collective dynamics encompasses both that of the corresponding Vicsek-style model (where local alignment is the sole interaction), and motility-induced phase separation (which occurs when repulsion is dominant). These results unify these heretofore largely disconnected bodies of knowledge on dry active matter and clarify the nature of the various phases involved.
Collective behavior of self-propelled particles is observed on a microscale for swimmers such as sperm and bacteria as well as for protein filaments in motility assays. The properties of such systems depend both on their dimensionality and the interactions between their particles. We introduce a model for self-propelled rods in two dimensions that interact via a separation-shifted Lennard-Jones potential. Due to the finite potential barrier, the rods are able to cross. This model allows us to efficiently simulate systems of self-propelled rods that effectively move in two dimensions but can oc…
Using experiments with anisotropic vibrated rods and quasi-2D numerical simulations, we show that shape plays an important role in the collective dynamics of self-propelled (SP) particles. We demonstrate that SP rods exhibit local ordering, aggregation at the side walls, and clustering absent in round SP particles. Furthermore, we find that at sufficiently strong excitation SP rods engage in a persistent swirling motion in which the velocity is strongly correlated with particle orientation.
We study self-propelled particles with velocity reversal interacting by uniaxial (nematic) alignment within a coarse-grained hydrodynamic theory. Combining analytical and numerical continuation techniques, we show that the physics of this active system is essentially controlled by the reversal frequency. In particular, we find that elongated, high-density, ordered patterns, called bands, emerge via subcritical bifurcations from spatially homogeneous states. Our analysis reveals further that the interaction of bands is weakly attractive and, consequently, bands fuse upon collision in analogy wi…
Systems of self-propelled particles are known for their tendency to aggregate and to display swarm behavior. We investigate two model systems, self-propelled rods interacting via volume exclusion, and sinusoidally-beating flagella embedded in a fluid with hydrodynamic interactions. In the flagella system, beating frequencies are Gaussian distributed with a non-zero average. These systems are studied by Brownian-dynamics simulations and by mesoscale hydrodynamics simulations, respectively. The clustering behavior is analyzed as the particle density and the environmental or internal noise are va…
We study the collective dynamics of self-propelled rods in an inhomogeneous motility field. At the interface between two regions of constant but different motility, a smectic rod layer is spontaneously created through aligning interactions between the active rods, reminiscent of an artificial, semi-permeable membrane. This "active membrane" engulfes rods which are locally trapped in low-motility regions and thereby further enhances the trapping efficiency by self-organization, an effect which we call "self-encapsulation". Our results are gained by computer simulations of self-propelled rod mod…
We study collections of self-propelled rods (SPR) moving in two dimensions for packing fractions less than or equal to 0.3. We find that in the thermodynamical limit the SPR undergo a phase transition between a disordered gas and a novel phase-separated system state. Interestingly, (global) orientational order patterns -- contrary to what has been suggested -- vanish in this limit. In the found novel state, the SPR self-organize into a highly dynamical, high-density, compact region - which we call aggregate - which is surrounded by a disordered gas. Active stresses build inside aggregates as r…
We study mixtures of self-propelled and passive rod-like particles in two dimensions using Brownian dynamics simulations. The simulations demonstrate that the two species spontaneously segregate to generate a rich array of dynamical domain structures whose properties depend on the propulsion velocity, density, and composition. In addition to presenting phase diagrams as a function of the system parameters, we investigate the mechanisms driving segregation. We show that the difference in collision frequencies between self-propelled and passive rods provides a driving force for segregation, whic…
Non-equilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions. We studied high-aspect-ratio self-propelled rods over a wide range of packing fraction and driving to determine the nonequilibrium state diagram and dynamic properties. Flocking and nematic-laning states occupy much of the parameter space. In the flocking state the average internal pressure is high and structural and mechanical relaxation times are long, su…
Active matter research focuses on the emergent behavior among interacting self-propelled particles. Unification of seemingly disconnected paradigms -- active phase-separation of repulsive discs and collective motion of self-propelled rods -- is a major challenge in contemporary active matter. Inspired by the quanto-mechanical wave-particle duality, we develop an approach based on the representation of active particles by smoothed continuum fields. On the basis of the collision kinetics, we demonstrate analytically and numerically how nonequilibrium stresses acting among self-driven, anisotropi…
Active agents - like phoretic particles, bacteria, sperm, and cytoskeletal filaments in motility assays - show a large variety of motility-induced collective behaviors, such as aggregation, clustering and phase separation. The behavior of dense suspensions of phoretic particles and of bacteria during biofilm formation is determined by two principle physical mechanisms: (i) volume exclusion (short-range steric repulsion) and (ii) quorum sensing (longer-range reduced propulsion due to alteration of the local chemical environment). To systematically characterize such systems, we study semi-penetr…
Active screws: Emergent active chiral nematics of spinning self-propelled rods
Institute for Theoretical Physics, Georg-August-Universität Göttingen（哥廷根大学理论物理研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Cluster of Excellence Physics of Life, TU Dresden（德累斯顿工业大学生命物理卓越集群）；Departament de Física de la Matèria Condensada, Universitat de Barcelona（巴塞罗那大学凝聚态物理系）；Universitat de Barcelona Institute of Complex Systems (UBICS)（巴塞罗那大学复杂系统研究所）；Institució Catalana de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚高级研究学院）
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…
We use coarse-grained molecular dynamics simulations to study the motility of a 2D vesicle containing self-propelled rods, as a function of the vesicle bending rigidity and the number density, length, and activity of the enclosed rods. Above a threshold value of the rod length, distinct dynamical regimes emerge, including a dramatic enhancement of vesicle motility characterized by a highly persistent random walk. These regimes are determined by clustering of the rods within the vesicle; the maximum motility state arises when there is one long-lived polar cluster. We develop a scaling theory th…
One standard approach to describe the collective behaviour of self-propelled particles is the Vicsek model: point-like self-propelled particles tend to align their migration directions to the ones of their nearer neighbours at each time-step. Here we use a variant of the Vicsek model that includes pairwise repulsive interactions. Confining the system between parallel walls can qualitatively change its appearance: a laning state can emerge that is different from the ones previously reported. All lanes show on average the same migration direction of the contained particles with a finite separati…
The colonisation of a soft passive material by motile cells such as bacteria is common in biology. The resulting colonies of the invading cells are often observed to exhibit intricate patterns whose morphology and dynamics can depend on a number of factors, particularly the mechanical properties of the substrate and the motility of the individual cells. We use simulations of a minimal 2D model of self-propelled rods moving through with a passive compliant medium consisting of particles that offer elastic resistance before being plastically displaced from their equilibrium positions. It is obse…
Catching fish with a fishing net is typically done either by dragging a fishing net through quiescent water or by placing a stationary basket trap into a stream. We transfer these general concepts to micron-sized self-motile particles moving in a solvent at low Reynolds number and study their collective trapping behaviour by means of computer simulations of a two-dimensional system of self-propelled rods. A chevron-shaped obstacle is dragged through the active suspension with a constant speed $v$ and acts as a trapping "net". Three trapping states can be identified corresponding to no trapping…
The study of active matter consisting of many self-propelled (active) swimmers in an imposed flow is important for many applications. Self-propelled swimmers may represent both living and artificial ones such as bacteria and chemically driven bi-metallic nano-particles. In this work we focus on a kinetic description of active matter represented by self-propelled rods swimming in a viscous fluid confined by a wall. It is well-known that walls may significantly affect the trajectories of active rods in contrast to unbounded or periodic containers. Among such effects are accumulation at walls and…
Using Brownian Dynamics simulations, we study effective interactions mediated between two identical and impermeable disks (inclusions) immersed in a bath of identical, active (self-propelled), Brownian rods in two spatial dimensions, by assuming that the self-propulsion axis of the rods may generally deviate from their longitudinal axis. When the self-propulsion is transverse (perpendicular to the rod axis), the accumulation of active rods around the inclusions is significantly enhanced, causing a more expansive steric layering (ring formation) of the rods around the inclusions, as compared wi…
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.
We study the noise-driven escape of active Brownian particles (ABPs) and run-and-tumble particles (RTPs) from confining potentials. In the small noise limit, we provide an exact expression for the escape rate in term of a variational problem in any dimension. For RTPs in one dimension, we obtain an explicit solution, including the first sub-leading correction. In two dimensions we solve the escape from a quadratic well for both RTPs and ABPs. In contrast to the equilibrium problem we find that the escape rate depends explicitly on the full shape of the potential barrier, and not only on its he…
We consider a Stokeslet applied to a viscous fluid next to an infinite, flat wall, or in-between two parallel walls. We calculate the forces exerted by the resulting flow on the confining boundaries, and use the results obtained to estimate the hydrodynamic contribution to the pressure exerted on boundaries by force-free self-propelled particles.
We numerically explore the behavior of repelling and aligning self-propelled polar particles (boids) in 2D enclosed by a damped flexible and elastic loop-shaped boundary. We observe disordered, polar ordered (or jammed) and circulating states. The latter produce a rich variety of boundary shapes including; circles, ovals, irregulars, ruffles, or sprockets, depending upon the bending moment of the boundary and the boundary to particle mass ratio. With the exception of the circulating states with non-round boundaries, states resemble those exhibited by attracting self-propelled particles, but he…
In many biological systems, the curvature of the surfaces cells live on influence their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) that curvature sign and magnitude can alter the system's collective behavior. Curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, whic…
The coupling of active, self-motile particles to topological constraints can give rise to novel non-equilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of tim…
Active swarms, consisting of individual agents which consume energy to move or produce work, are known to generate a diverse range of collective behaviors. Many examples of active swarms are biological in nature (e.g., fish shoals and bird flocks) and have been modeled extensively by numerical simulations. Such simulations of swarms usually assume that the swarm is homogeneous; that is, every agent has exactly the same dynamical properties. However, many biological swarms are highly heterogeneous, such as multispecies communities of micro-organisms in soil, and individual species may have a wi…
Many motile cells exhibit migratory behaviors, such as chemotaxis (motion up or down a chemical gradient) or chemokinesis (when speed depends on concentration), which enable them to carry out vital functions including immune response, egg fertilization, and predator evasion. These have inspired researchers to develop self-propelled colloidal analogues to biological microswimmers, known as active colloids, that perform similar feats. Here, we study the behavior of half-platinum half-gold (Pt/Au) self-propelled rods in antiparallel gradients of hydrogen peroxide fuel and salt (which tends to slo…
We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges.In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, w…
We study the dynamics of non-aligning, non-interacting self-propelled particles confined to a box in two dimensions. In the strong confinement limit, when the persistence length of the active particles is much larger than the size of the box, particles stay on the boundary and align with the local boundary normal. It is then possible to derive the steady-state density on the boundary for arbitrary box shapes. In non-convex boxes, the non-uniqueness of the boundary normal results in hysteretic dynamics and the density is non-local, i.e. it depends on the global geometry of the box. These findin…
We study the dynamics of neutral and charged rods embedded in varying-section channels. By means of systematic approximations, we derive the dependence of the local diffusion coefficient on both the geometry and charge of the rods. This microscopic insight allows us to provide predictions for the permeability of varying-section channels to rods with diverse lengths, aspect ratios and charge. Our analysis shows that the dynamics of charged rods is sensitive to the geometry of the channel and that their transport can be controlled by tuning both the shape of the confining walls and the charge of…
We study a strongly interacting crowded system of self-propelled stiff filaments by event-driven Brownian dynamics simulations and an analytical theory to elucidate the intricate interplay of crowding and self-propulsion. We find a remarkable increase of the effective diffusivity upon increasing the filament number density by more than one order of magnitude. This counter-intuitive 'crowded is faster' behavior can be rationalized by extending the concept of a confining tube pioneered by Doi and Edwards for highly entangled crowded, passive to active systems. We predict a scaling theory for the…
For many applications, it is important to catch collections of autonomously navigating microbes and man-made microswimmers in a controlled way. Here we propose an efficient trap to collectively capture self-propelled colloidal rods. By means of computer simulation in two dimensions, we show that a static chevron-shaped wall represents an optimal boundary for a trapping device. Its catching efficiency can be tuned by varying the opening angle of the trap. For increasing angles, there is a sequence of three emergent states corresponding to partial, complete, and no trapping. A trapping `phase di…
Self-propelled particles can exhibit surprising non-equilibrium behaviors, and how they interact with obstacles or boundaries remains an important open problem. Here we show that chemically propelled micro-rods can be captured, with little change in their speed, into close orbits around solid spheres resting on or near a horizontal plane. We show that this interaction between sphere and particle is short-range, occurring even for spheres smaller than the particle length, and for a variety of sphere materials. We consider a simple model, based on lubrication theory, of a force- and torque-free …
Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic, nematic background. Whilst the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is super-diffusive, with an anomalous scaling $\propto t \ln t$ of the mean squared displacement with time $t$. This behavior is predicted by an analytical theory that we present here, and is corroborated by numerical simulation of active particle diff…
We examine the ordering properties of rectangular hard rods with length L and diameter D at a single planar wall and between two parallel hard walls using the second-virial density functional theory. The theory is implemented in the three-state Zwanzig approximation, where only three mutually perpendicular directions are allowed for the orientations of hard rods. The effect of varying shape anisotropy is examined at L/D=10, 15 and 20. In contact with a single hard wall, the density profiles show planar ordering, damped oscillatory behavior, and wall induced surface ordering transition below th…
The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction $\barϕ$, motility force $F_D$, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of $F_D$. This exclusion zo…
Self-propelled particles move along circles rather than along a straight line when their driving force does not coincide with their propagation direction. Examples include confined bacteria and spermatozoa, catalytically driven nanorods, active, anisotropic colloidal particles and vibrated granulates. Using a non-Hamiltonian rate theory and computer simulations, we study the motion of a Brownian "circle swimmer" in a confining channel. A sliding mode close to the wall leads to a huge acceleration as compared to the bulk motion, which can further be enhanced by an optimal effective torque-to-fo…
A plethora of active matter models exist that describe the behavior of self-propelled particles (or swimmers), both with and without hydrodynamics. However, there are few studies that consider shape-anisotropic swimmers and include hydrodynamic interactions. Here, we introduce a simple method to simulate self-propelled colloids interacting hydrodynamically in a viscous medium using the lattice-Boltzmann technique. Our model is based on raspberry-type viscous coupling and a force/counter-force formalism which ensures that the system is force free. We consider several anisotropic shapes and char…
A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs es…
We characterize cell motion in experiments and show that the transition to collective motion in colonies of gliding bacterial cells confined to a monolayer appears through the organization of cells into larger moving clusters. Collective motion by non-equilibrium cluster formation is detected for a critical cell packing fraction around 17%. This transition is characterized by a scale-free power-law cluster size distribution, with an exponent $0.88\pm0.07$, and the appearance of giant number fluctuations. Our findings are in quantitative agreement with simulations of self-propelled rods. This s…
