Active particles (i.e., self-propelled particles or called microswimmers), different from passive Brownian particles, possess more complicated translational and angular dynamics, which can generate a series of anomalous transport phenomena. In this letter, we study the two-dimensional dynamics of a self-propelled pointlike particle with self-aligning property moving in Poiseuille flow. The results show the effective anomalous diffusion coefficient changes sharply with the change of temperature and speed of background Poiseuille flow. The relaxation property of moving speed and the position probability distribution function of particles is also obtained. The observation of several types of anomalous diffusion and normal diffusion regime indicates the self-aligning property may be universal and can be used as a reference for future experiments analysis and modeling.
Using a simple model, we study the fluctuating dynamics of inextensible, semiflexible polar filaments interacting with active and directed force generating centres such as molecular motors. Taking into account the fact that the activity occurs on time-scales comparable to the filament relaxation time, we obtain some unexpected differences between both the steady-state and dynamical behaviour of active as compared to passive filaments. For the statics, the filaments have a {novel} length-scale dependent rigidity. Dynamically, we find strongly enhanced anomalous diffusion.
Chiral active fluids are known to have anomalous transport properties such as the so-called odd viscosity. In this paper, we provide a microscopic mechanism for how such anomalous transport coefficients can emerge. We construct an Irving-Kirkwood-type stress tensor for chiral liquids and express the transport coefficients in terms of orientation-averaged intermolecular forces and distortions of the pair correlation function induced by a flow field. We then show how anomalous transport properties can be expected naturally due to the presence of a transverse component in the orientation-averaged…
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…
Anomalous diffusion, manifest as a nonlinear temporal evolution of the position mean square displacement, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective behavior is often observed to emerge spontaneously from the mutual interactions between constituent motile units in biological systems. Examples where these phenomena can be observed simultaneously have been identified in recent experiments on bird flocks, fish schools and bacterial swarms. These results pose an intriguing question, which cannot be resolved by exist…
Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multi-folded states, whereas stiff membranes oscillates between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mecha…
The phenomenon that a system at a hot temperature cools faster than at a warm temperature, referred to as the Mpemba effect, has been recently realized for trapped colloids. Here, we investigate the cooling and heating process of a self-propelling active colloid using numerical simulations and theoretical calculations with a model that can directly be tested in experiments. Upon cooling the particles' active motion induces a Mpemba effect. Transiently the system can even exhibit smaller temperatures than its final temperature, a surprising phenomenon which we refer to as activity-induced overc…
With the use of the "two-fluid model", we discuss anomalous diffusion induced by active force dipoles in viscoelastic media. Active force dipoles, such as proteins and bacteria, generate non-thermal fluctuating flows that lead to a substantial increment of the diffusion. Using the partial Green's function of the two-fluid model, we first obtain passive (thermal) two-point correlation functions such as the displacement cross-correlation function between the two point particles separated by a finite distance. We then calculate active (non-thermal) one-point and two-point correlation functions du…
We simulate an experiment in which a colloidal probe is pulled through an active nematic fluid. We find that the drag on the particle is non-Stokesian (not proportional to its radius). Strikingly, a large enough particle in contractile fluid (such as an actomyosin gel) can show negative viscous drag in steady state: the particle moves in the opposite direction to the externally applied force. We explain this, and the qualitative trends seen in our simulations, in terms of the disruption of orientational order around the probe particle and the resulting modifications to the active stress.
We investigate the swim pressure exerted by non-chiral and chiral active particles on convex or concave circular boundaries. Active particles are modeled as non-interacting and non-aligning self-propelled Brownian particles. The convex and concave circular boundaries are used as models representing a fixed inclusion immersed in an active bath and a cavity (or container) enclosing the active particles, respectively. We first present a detailed analysis of the role of convex versus concave boundary curvature and of the chirality of active particles on their spatial distribution, chirality-induce…
Active systems exhibit spontaneous flows induced by self-propulsion of microscopic constituents and can reach a nonequilibrium steady state without an external drive. Constructing the analogy between the quantum anomalous Hall insulators and active matter with spontaneous flows, we show that topologically protected sound modes can arise in a steady-state active system in continuum space. We point out that the net vorticity of the steady-state flow, which acts as a counterpart of the gauge field in condensed-matter settings, must vanish under realistic conditions for active systems. The quantum…
The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects, solute redistribution, and rotational diffusion are identified and shown to lead to a plethora of different regimes involving inertial, propulsive, anomalous, and diffusive behaviors. For symmetric active colloids, a regime is found where the mean-squared displacement has a super-diffusive $t^{3/2}$ behavior. At the longest time scales, an effective diffusion…
We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a cluster distribution inconsistent with RP. Our model not only can account for these experiments, but also exhibits an unusual type of mixed phase transition: We find that the transition is characterized by signatures of criticality, but with a discontinuity in the order parameter.
Using molecular dynamics simulations we investigate the translational dynamics of particles with dipolar interactions in homogenous external fields. For a broad range of concentrations, we find that the anisotropic, yet normal diffusive behavior characterizing weakly coupled systems becomes anomalous both parallel and perpendicular to the field at sufficiently high dipolar coupling and field strength. After the ballistic regime, chain formation first yields cage-like motion in all directions, followed by transient, mixed diffusive-superdiffusive behavior resulting from cooperative motion of th…
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…
Bacterial swarms display intriguing dynamical states like active turbulence. Using a hydrodynamic model we now show that such dense active suspensions manifest super-diffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared-displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behaviour of microorganisms, our study underlines the essential differences between active and inertial tu…
The interaction between polymer brush and colloidal particles has been intensively studied in the last two decades. Here we consider a flat chain-grafted substrate immersed in a bath of active particles. Simulations show that an increase in the self-propelling force causes an increase in the number of particles that penetrate into the brush. Anomalously, the particle density inside the main body of the brush eventually becomes higher than that outside the brush at very large self-propelling force. The grafted chains are further stretched due to the steric repulsion from the intruded particles.…
We derive the long-time dynamics of a tracer immersed in a one-dimensional active bath. In contrast to previous studies, we find that the damping and noise correlations possess long-time tails with exponents that depend on the tracer symmetry. For generic tracers, shape asymmetry induces ratchet effects that alter fluctuations and lead to superdiffusion and friction that grows with time when the tracer is dragged at a constant speed. In the singular limit of a completely symmetric tracer, we recover normal diffusion and finite friction. Furthermore, for small symmetric tracers, the active cont…
We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations at zero wavenumber. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature ${\bf 503}$, 95 (2013), b…
We study the structural and dynamical behaviors of a diblock copolymer chain in a bath of active Brownian particles (ABPs) by extensive Brownian dynamics simulation in a two-dimensional model system. Specifically, the A block of chain is self-attractive, while the B block is self-repulsive. We find, beyond a threshold, the A block unfolds with a pattern like extracting a woolen string from a ball. The critical force decreases with the increase of the B block length,NB, for short cases, then keeps a constant with further increase of NB. In addition, we find a power law exists between the unfold…
We study, via extensive numerical simulations, the force-velocity curve of an active particle advected by a steady laminar flow, in the nonlinear response regime. Our model for an active particle relies on a colored noise term that mimics its persistent motion over a time scale $τ_A$. We find that the active particle dynamics shows non-trivial effects, such as negative differential and absolute mobility (NDM and ANM, respectively). We explore the space of the model parameters and compare the observed behaviors with those obtained for a passive particle ($τ_A=0$) advected by the same laminar fl…
In their recent work Sheinman et al. [Phys. Rev. Lett. 114, 098104 (2015)] introduce a variation of percolation which they call no-enclaves percolation (NEP). The main claims are 1) the salient physics captured in NEP is closer to what happens experimentally; 2) The Fisher exponent of NEP, is $τ=1.82(1)$; 3) Due to the different Fisher exponent, NEP constitutes a universality class distinct from random percolation (RP). While we fully agree with 1) and found NEP to be a very interesting variation of random percolation, we disagree with 2) and 3). We will demonstrate that $τ$ is exactly $2$, di…
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…
Anomalous Mean-Squared Displacement in Quantum Active Matter from a Wigner Phase-Space Framework
Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学）；Heinrich-Heine-Universität Düsseldorf（海因里希·海涅杜塞尔多夫大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；Universität des Saarlandes（萨尔兰州立大学）；Saarland University（萨尔兰大学）
We show that Lagrangian measurements in active turbulence bear imprints of turbulent and anomalous streaky hydrodynamics leading to a self-selection of persistent trajectories - Levy walks - over diffusive ones. This emergent dynamical heterogeneity results in a super-diffusive first passage distribution which could lead to biologically advantageous motility. We then go beyond single-particle statistics to show that for the pair-dispersion problem as well, active flows are at odds with inertial turbulence. Our study, we believe, will readily inform experiments in establishing the extent of uni…
The unique pressure exerted by active particles -- the "swim" pressure -- has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an \textit{extremely negative} surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure \textit{is not a true pressure}. At a boundary or interface, the reduction in particle swimming generates a net active force density -- an entirely \textit{self-gen…
The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton, leading to anomalous diffusive behavior. Experiments tracking the behavior of cell-attached objects have observed anomalous diffusion with a distribution of displacements that is non-Gaussian, with heavy tails. This has been attributed to "cytoquakes" or other spatially extended collective effects. We show, using simulations and analytical theory, that a simple continuum active gel model driven by fluctuating force dipoles nat…
We study the collective dynamics of elongated swimmers in a very thin fluid layer by devising long, filamentous, non-tumbling bacteria. The strong confinement induces weak nematic alignment upon collision, which, for large enough density of cells, gives rise to global nematic order. This homogeneous but fluctuating phase, observed on the largest experimentally-accessible scale of millimeters, exhibits the properties predicted by standard models for flocking such as the Vicsek-style model of polar particles with nematic alignment: true long-range nematic order and non-trivial giant number fluct…
We introduce a novel model for active particles with short-range aligning interactions and study their behaviour in crowded environments using numerical simulations. When only active particles are present, we observe a transition from a gaseous state to the emergence of metastable clusters as the level of orientational noise is reduced. When also passive particle are present, we observe the emergence of a network of metastable channels.
Self-propelled particle (SPP) systems are intrinsically out of equilibrium systems, where each individual particle converts energy into work to move in a dissipative medium. When interacting through a velocity alignment mechanism, and the medium acts as a momentum sink, even momentum is not conserved. In this scenario, a mapping into an equilibrium system seems unlikely. Here, we show that an entropy functional can be derived for SPPs with velocity alignment and density-dependent speed, at least in the (orientationally) disordered phase. This non-trivial result has important physical consequen…
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.
We study steady-state properties of a suspension of active, nonchiral and chiral, Brownian particles with polar alignment and steric interactions confined within a ring-shaped (annulus) confinement in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying …
Many active matter systems, especially on the microscopic scale, are well approximated as overdamped, meaning that any inertial momentum is immediately dissipated by the environment. On the other hand, especially for macroscopic active systems but also for many mesoscopic systems the time scale of inertial motion can become large enough to be relevant for the dynamics. This raises the question how collective dynamics and the resulting states in active matter are influenced by inertia. Therefore, we propose a coarsegrained continuum model for underdamped active matter based on a mean field desc…
Hardly any real self-propelling or actively driven object is perfect. Thus, undisturbed motion will generally not follow straight lines but rather circular trajectories. We here address self-propelled or actively driven objects that move in discrete steps and additionally tempt to migrate towards a certain direction by discrete angular adjustment. Overreaction in the angular alignment is possible. This competition implies pronounced nonlinear dynamics including period doubling and chaotic behavior in a broad parameter regime. Such behavior directly affects the appearance of the trajectories, a…
We use continuum simulations to study the impact of anisotropic hydrodynamic friction on the emergent flows of active nematics. We show that, depending on whether the active particles align with or tumble in their collectively self-induced flows, anisotropic friction can result in markedly different patterns of motion. In a flow-aligning regime and at high anisotropic friction, the otherwise chaotic flows are streamlined into flow lanes with alternating directions, reproducing the experimental laning state that has been obtained by interfacing microtubule-motor protein mixtures with smectic li…
We present a numerical study of the phase behavior of repulsively interacting active polar particles that align their active velocities nematically. The amplitude of the active velocity, and the noise in its orientational alignment control the active nature of the system. At high values of orientational noise, the structural fluid undergoes a continuous nematic-isotropic transition in active orientation. This transition is well separated from an active phase separation, characterized by the formation of high density hexatic clusters, observed at lower noise strengths. With increasing activity,…
The dynamics of self-locomotion of active particles in aligned or liquid crystalline fluids strongly deviates from that in simple isotropic media. We explore the long-time dynamics of a swimmer moving in a three-dimensional smectic liquid crystal and find that the mean-square displacement (MSD) transverse to the director exhibits a distinct logarithmic tail at long times. The scaling is distinctly different from that in an isotropic or nematic fluid and hints at the subtle but important role of the director fluctuation spectrum in governing the long-time motility of active particles. Our findi…
Switching on high activity in a relatively dense system of active Janus colloids, we observe fast clustering, followed by cluster aggregation towards full phase separation. The phase separation process is however interrupted when large enough clusters start breaking apart. Following the cluster size distribution as a function of time, we identify three successive dynamical regimes. Tracking both the particle positions and orientations, we characterize the structural ordering and alignment in the growing clusters and thereby unveil the mechanisms at play in these regimes. In particular, we iden…
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 sel…
