We discuss recent advances in developing a mode-coupling theory of the glass transition (MCT) of two-dimensional systems of active Brownian particles (ABP). We specifically discuss the case of a single ABP tracer in a glass-forming passive host suspension; a case that has recently been studied in experiments on colloidal Janus particles. We employ event-driven Brownian dynamics (ED-BD) computer simulations to test the ABP-MCT, and find good agreement between the two for the MSD. The ED-BD simulation results also compare well to experimental data, although a peculiar non-monotonic mapping of self-propulsion velocities is required. The ABP-MCT predicts a specific self-propulsion dependence of the Stokes-Einstein relation between the long-time diffusion coefficient and the host-system viscosity that matches well the results from simulation. An application of ABP-MCT within the integration-through transients (ITT) framework to calculate the density-renormalized effective swim velocity of the interacting ABP agrees qualitatively with the ED-BD simulation data at densities close to the glass transition, and quantitatively for the full density range only after the mapping of packing fractions employed for the passive system.
We develop an exact Green-Kubo formula relating nonequilibrium averages in systems of interacting active Brownian particles to equilibrium time-correlation functions. The method is applied to calculate the density-dependent average swim speed, which is a key quantity entering coarse grained theories of active matter. The average swim speed is determined by integrating the equilibrium autocorrelation function of the interaction force acting on a tagged particle. Analytical results are validated using Brownian dynamics simulations.
In this paper we provide high precision estimates of the phase diagram of active Brownian particles. We extract coexisting densities from simulations of phase separated states in an elongated box (slab geometry) which minimizes finite-size effects and allows for precise determination of points on the binodal lines. Using this method, we study the influence of both shape and dimensionality on the two-phase region. Active spheres and dumbbells of active particles are compared to the known phase diagram of active Brownian disks. In the case of dimers, both correlated and uncorrelated propulsion o…
Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends explicitly on the particle orientation. In this case, the active particle moves faster when oriented along one direction and slower when oriented along another, leading to an anisotropic translational dynamics which is coupled to the particle's rotational diffusion. We propose a basic model of active Brownian motion for orientation-dependent motility. Based on this m…
The transport properties of a spherical active Brownian particle in a periodic potential under heavy damping are considered. The self-propelled particle is subjected to the asymmetric potential, detailed balance is lost and the particles generate a non-zero drift speed. The average current is calculated and the diffusivity of the particle is analyzed from the effective diffusion coefficient. For chiral active particles, the diffusivity decreases with increasing the angular velocity, confining the particle near the initial position, and reducing the average current.
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 derive equations of motion for the mean-squared displacement (MSD) of an active Brownian particle (ABP) in a crowded environment modeled by a dense system of passive Brownian particles, and of a passive tracer particle in a dense active-Brownian particle system, using a projection-operator scheme. The interaction of the tracer particle with the dense host environment gives rise to strong memory effects. Evaluating these approximately in the framework of a recently developed mode-coupling theory for the glass transition in active Brownian particles (ABP-MCT), we discuss the various regimes o…
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…
Active gels perform key mechanical roles inside the cell, such as cell division, motion and force sensing. The unique mechanical properties required to perform such functions arise from the interactions between molecular motors and semi-flexible polymeric filaments. Molecular motors can convert the energy released in the hydrolysis of ATP into forces of up to pico-Newton magnitudes. Moreover, the polymeric filaments that form active gels are flexible enough to respond to Brownian forces, but also stiff enough to support the large tensions induced by the motor-generated forces. Brownian forces …
We propose a unifying rheological framework for dense suspensions of non-Brownian spheres, predicting the onsets of particle friction and particle inertia as distinct shear thickening mechanisms, while capturing quasistatic and soft particle rheology at high volume fractions and shear rates respectively. Discrete element method simulations that take suitable account of hydrodynamic and particle-contact interactions corroborate the model predictions, demonstrating both mechanisms of shear thickening, and showing that they can occur concurrently with carefully selected particle surface propertie…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape rate of the particle. In this paper we study the escape problem for a Brownian particle that is transiently active; the activity decreases rapidly during the escape process. Using the effective equilibrium approach we analytically calculate the escape rate, under the assumption that the particle is either completely passive or fully active when crossing the b…
We study dynamical properties of confined, self-propelled Brownian particles in an inhomogeneous activity profile. Using Brownian dynamics simulations, we calculate the probability to reach a fixed target and the mean first passage time to the target of an active particle. We show that both these quantities are strongly influenced by the inhomogeneous activity. When the activity is distributed such that high-activity zone is located between the target and the starting location, the target finding probability is increased and the passage time is decreased in comparison to a uniformly active sys…
The traction on the surface of a spherical active colloid in a thermally fluctuating Stokesian fluid contains passive, active, and Brownian contributions. Here we derive these three parts systematically, by "projecting out" the fluid using the boundary-domain integral representation of slow viscous flow. We find an exact relation between the statistics of the Brownian traction and the thermal forces in the fluid and derive, thereby, fluctuation-dissipation relations for every irreducible tensorial harmonic traction mode. The first two modes give the Brownian force and torque, from which we con…
We study active Brownian particles as a paradigm for genuine non-equilibrium phase transitions. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a modification of sampling finite-size fluctuations and successfully test this method for the 2D Ising model. Using this model allows us to determine accurately the critical point of two dimensional active Brownian particles at $\text{Pe}_{\text{cr}}=40(2)$, $ϕ_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $β$, $γ/ν$, and $ν$. Our res…
The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both rela…
We investigate exploration patterns of a microswimmer, modeled as an active Brownian particle, searching for a target region located in a well of an energy landscape and separated from the initial position of the particle by high barriers. We find that the microswimmer can enhance its success rate in finding the target by tuning its activity and its persistence in response to features of the environment. The target-search patterns of active Brownian particles are counterintuitive and display characteristics robust to changes of the energy landscape. On the contrary, the transition rates and tr…
We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently-observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev and P. Chaikin, Nature Physics, 2016, doi:10.1038/nphys3970]. We present a stochastic Adams-Bashforth integrator for the equations of Brownian dynamics, which has the same cost as but is more accurate than the widely-used Euler-Maruyama scheme, and uses a random finite difference to capture the stochastic drift proportional to the…
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 a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of the particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to ve…
We derive a mode-coupling theory (MCT) to describe the dynamics of tracer particles in dense systems of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian dynamics, and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a passive colloidal particle in a suspension of ABP, that of a single active…
A simple theoretical approach is used to investigate active colloids at the free interface and near repulsive substrates. We employ dynamical density functional theory to determine the steady-state density profiles in an effective equilibrium system [Farage et al., Phys. Rev. E, 91 (2015) 042310]. In addition to the known accumulation at surfaces, we predict wetting and drying transitions at a flat repulsive wall and capillary condensation and evaporation in a slit pore. These new phenomena are closely related to the motility-induced phase separation (MIPS) in the bulk.
Computer simulations are used to test whether a recently introduced generalization of Rosenfeld's excess-entropy scaling method for estimating transport coefficients in systems obeying molecular dynamics can be extended to predict long-time diffusivities in fluids of particles undergoing Brownian dynamics in the absence of interparticle hydrodynamic forces. Model fluids with inverse-power-law, Gaussian-core, and Hertzian pair interactions are considered. Within the generalized Rosenfeld scaling method, long-time diffusivities of ultrasoft Gaussian-core and Hertzian particle fluids, which displ…
A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the jamming point of frictional particles; here the thickened state is completely jammed and (unless particles deform) cannot flow without inhomogeneity or fracture. The second regime shows strain- rate hyste…
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…
The non-thermal nature of self-propelling colloids offers new insights into non-equilibrium physics. The central mathematical model to describe their trajectories is active Brownian motion, where a particle moves with a constant speed, while randomly changing direction due to rotational diffusion. While several feedback strategies exist to achieve position-dependent velocity, the possibility of spatial and temporal control over rotational diffusion, which is inherently dictated by thermal fluctuations, remains untapped. Here, we decouple rotational diffusion from thermal noise. Using external …
A harmonically trapped active Brownian particle exhibits two types of positional distributions -- one has a single peak, the other has a single well -- that signify steady-state dynamics with low and high activity, respectively. Adding inertia to the translational motion preserves this strict single peak/well classification of the densities but shifts the dividing boundary between the states in the parameter space. We characterize this shift for the dynamics in one spatial dimension using the static Fokker--Planck equation for the full joint distribution of the state space. We derive local res…
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…
Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals persistent anti-correlations manifested by a negative algebraic power-law tail $t^{-5/2}$ at all densities. At small packing fractions, the simulations fully agree with the analytic low-density prediction, yet the amplitude of the tail becomes dramatically suppressed as the packing fraction is increased. The mod…
Unlike equilibrium systems, active matter is not governed by the conventional laws of thermodynamics. Through a series of analytic calculations and Langevin dynamics simulations, we explore how systems cross over from equilibrium to active behavior as the activity is increased. In particular, we calculate the profiles of density and orientational order near straight or circular walls, and show the characteristic width of the boundary layers. We find a simple relationship between the enhancements of density and pressure near a wall. Based on these results, we determine how the pressure depends …
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 consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behaviour adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher order powers in time for the MSD. …
We computationally study the behavior of underdamped active Brownian particles in a sheared channel geometry. Due to their underdamped dynamics, the particles carry momentum a characteristic distance away from the boundary before it is dissipated into the substrate. We correlate this distance with the persistence of particle trajectories, determined jointly by their friction and self-propulsion. Within this characteristic length, we observe new and counterintuitive phenomena stemming from the interplay of activity, interparticle interactions, and the boundary driving. Depending on values of fr…
Here, I review the large-scale properties of collections of active Brownian elongated objects, in particular rods, moving in a dissipative medium/substrate. I address the problem by presenting three different models of decreasing complexity, which I refer to as model I, II, and III, respectively.
We find that crystalline states of repulsive active Brownian particles at high activity melt into a hexatic state but this transition is not driven by an unbinding of bound dislocation pairs as suggested by the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. Upon reducing the density, the crystalline state melts into a high-density hexatic state devoid of any defects. Decreasing the density further, the dislocations proliferate and introduce plasticity in the system, nevertheless maintaining the hexatic state, but eventually melting into a fluid state. Remarkably, the elastic constan…
We study the motility-induced aggregation of active Brownian particles (ABPs) on a porous, circular wall. We observe that the morphology of aggregated dense-phase on a static wall depends on the wall porosity, particle motility, and the radius of the circular wall. Our analysis reveals two morphologically distinct, dense aggregates; a connected dense cluster that spreads uniformly on the circular wall and a localized cluster that breaks the rotational symmetry of the system. These distinct morphological states are similar to the macroscopic structures observed in aggregates on planar, porous w…
Motility-induced wall aggregation of active Brownian particles (ABPs) is a well-studied phenomenon. Here, we study the aggregation of ABPs on porous walls, which allows the particles to penetrate through at large motility. We show that the active aggregates undergo a morphological transition from a connected dense-phase to disconnected droplets with an increase in wall porosity and the particle self-motility, similar to wetting-dewetting transitions in equilibrium fluids. We show that both morphologically distinct states are stable, and independent of initial conditions at least in some parame…
Shear flow of dense, non-Brownian suspensions is simulated using the discrete element method, taking particle contact and hydrodynamic lubrication into account. The resulting flow regimes are mapped in the parametric space of solid volume fraction, shear rate, fluid viscosity and particle stiffness. Below a critical volume fraction $ϕ_c$, the rheology is governed by the Stokes number, which distinguishes between viscous and inertial flow regimes. Above $ϕ_c$, a quasistatic regime exists for low and moderate shear rates. At very high shear rates, the $ϕ$ dependence is lost and soft particle rhe…
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…
The diffusion behavior of an active Brownian particle (ABP) in polymer solutions is studied using Langevin dynamics simulations. We find that the long time diffusion coefficient $D$ can show a non-monotonic dependence on the particle size $R$ if the active force $F_{a}$ is large enough, wherein a bigger particle would diffuse faster than a smaller one which is quite counterintuitive. By analyzing the short time dynamics in comparison to the passive one, we find that such non-trivial dependence results from the competition between persistence motion of the ABP and the length-scale dependent eff…
We have performed a case study investigating a recently proposed scheme to obtain an effective pair potential for active Brownian particles [Farage et al., Phys. Rev. E 91, 042310 (2015)]. Applying this scheme to the Lennard-Jones potential, numerical simulations of active Brownian particles are compared to simulations of passive Brownian particles interacting by the effective pair potential. Analyzing the static pair correlations, our results indicate a limited range of activity parameters (speed and orientational correlation time) for which we obtain quantitative, or even qualitative, agreem…
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 investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modeled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate $r$ on the mean first passage time to a fixed target of a single free Active Brownian Particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal …
We present a microscopic theory for the nonequilibrium interfacial tension $γ_{\rm gl}$ of the free interface between gas and liquid phases of active Brownian particles. The underlying square gradient treatment and the splitting of the force balance in flow and structural contributions is general and applies to inhomogeneous nonequilibrium steady states. We find $γ_{\rm gl}\geq 0$, which opposes claims by Bialké et al. [Phys. Rev. Lett. $\bf{115}$, 098301 (2015)] and delivers the theoretical justification for the widely observed interfacial stability in active Brownian dynamics many-body simul…
We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is calculated exactly for active Brownian and run-and-tumble particles and the results are compared. Theoretical predictions are in excellent agreement with Langevin simulations. Our results shed further light onto how active particles with different dynamics may be equivalent in the bulk, yet behave differently near boundaries or obstacles.
We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a nonmonotonic dependence on the noise intensity. We relate this behavior to the fact that the active particle escapes from a limit cycle rather than from a fixed point and that a certain amount of noise can stabilize the sojourn of the particle on this limit cycle.
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…
