Rare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state theory. In particular, the dynamic framework developed by Kramers marks an outstanding milestone for the field. Its predictions, however, do not apply to systems driven by non-conservative forces or correlated noise histories. An important class of such systems are active particles, prominent in both biology and nanotechnology. Here, we trap a silica nanoparticle in a bistable potential. To emulate an active particle, we subject the particle to an engineered external force that mimics self-propulsion. We investigate the active particle's transition rate between metastable states as a function of friction and correlation time of the active force. Our experiments reveal the existence of an optimal correlation time where the transition rate is maximized. This novel \emph{active turnover} is reminiscent of the much celebrated Kramers turnover despite its fundamentally different origin. Our observations are quantitatively supported by a theoretical analysis of a one-dimensional model. Besides providing a deeper understanding of the escape dynamics of active particles in multistable potentials, our work establishes a new, versatile experimental platform to study particle dynamics in non-equilibrium settings.
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.
We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and far-from-equilibrium regimes by varying the persistence time of the active force and the swim velocity. A non-monotonic behavior of the mean escape time is observed with the persistence time of the activity, revealing the existence of an optimal choice of the parameters favoring the escape process. For small persistence times, a Kramers-like formula with an e…
It is now well established that microswimmers can be sorted or segregated fabricating suitable microfluidic devices or using external fields. A natural question is how these techniques can be employed for dividing swimmers of different motility. In this paper, using numerical simulations in the dilute limit, we investigate how motility parameters (time of persistence and velocity) impacts the narrow-escape time of active particles from circular domains. We show that the escape time undergoes a crossover between two asymptotic regimes. The control parameters of the crossover is the ratio betwee…
We evaluate the steady-state distribution and escape rate for an Active Ornstein-Uhlenbeck Particle (AOUP) using methods from the theory of large deviations. The calculation is carried out both for small and large memory times of the active force in one-dimension. We compare our results to those obtained in the literature about colored noise processes, and we emphasize their relevance for the field of active matter. In particular, we stress that contrary to equilibrium particles, the invariant measure of such an active particle is a non-local function of the potential. This fact has many inter…
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…
The dynamics of active particles is of interest at many levels and is the focus of theoretical and experimental research. There have been many attempts to describe the dynamics of particles affected by random active forces in terms of an effective temperature. This kind of description is tempting due to the similarities (or lack thereof) with systems in or near thermal equilibrium. However, the generality and validity of the effective temperature is not yet fully understood. Here, we studied the dynamics of trapped particles subjected to both thermal and active forces. The particles were not o…
Active matter broadly covers the dynamics of self-propelled particles. While the onset of collective behavior in homogenous active systems is relatively well understood, the effect of inhomogeneities such as obstacles and traps lacks overall clarity. Here, we study how interacting self-propelled particles become trapped and released from a trap. We have found that captured particles aggregate into an orbiting condensate with a crystalline structure. As more particles are added, the trapped condensate escape as a whole. Our results shed light on the effects of confinement and quenched disorder …
Spontaneous persistent motions driven by active processes play a central role to maintain the living cells far from equilibrium. In the majority of the research works, the steady state dynamics of an active system has been described in terms of an effective temperature. In the majority of the research works, the steady state dynamics of an active system has been described in terms of an effective temperature. By contrast, we have examined a prototype model for diffusion in an activity-induced rugged energy landscape to describe the slow dynamics of a tagged particle in a dense active environme…
The escape rate of a Brownian particle over a potential barrier is accurately described by the Kramers theory. A quantitative theory explicitly taking the activity of Brownian particles into account has been lacking due to the inherently out-of-equilibrium nature of these particles. Using an effective equilibrium approach [Farage et al., Phys. Rev. E 91, 042310 (2015)] we study the escape rate of active particles over a potential barrier and compare our analytical results with data from direct numerical simulation of the colored noise Langevin equation. The effective equilibrium approach gener…
The dynamics and pair trajectory of two self-propelled colloids are reported. The autonomous motions of the colloids are due to a catalytic chemical reaction taking place asymmetrically on their surfaces that generates a concentration gradient of interactive solutes around the particles and actuate particle propulsion. We consider two spherical particles with symmetric catalytic caps extending over the local polar angles $θ^1_{cap}$ and $θ^2_{cap}$ from the centers of active sectors in an otherwise quiescent fluid. A combined analytical-numerical technique was developed to solve the coupled ma…
Nonreciprocal buckling makes active filaments polyfunctional
School of Physics, UNSW（新南威尔士大学物理学院）；ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems - UNSW Node（澳大利亚研究委员会细胞系统数学分析卓越中心-新南威尔士大学节点）；Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo（奥斯陆大学数学与自然科学院数学系）；Institute of Physics, Universiteit van Amsterdam（阿姆斯特丹大学物理研究所）；TCM Group, Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室理论凝聚态物理组）
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 investigate the escape rate of an overdamped, self-propelled spherical Brownian particle on a surface from a metastable potential well. Within a modeling in terms of a 1D constant speed of the particle's active dynamics we consider the associated rate using both numerical and analytical approaches. Regarding the properties of the stationary state in the potential well, two major timescales exist, each governing the translational and the rotational dynamics of the particle, respectively. The particle radius is identified to present the essential quantity in charge of regulating the ratio bet…
Transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers could be passive, such as colloids or active (self-propelled), such as synthetic nanomotors or bacteria. Computer simulations in principle should be extremely useful in exploring the mechanism of active (self-propelled) transport of tracer particles through the mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside…
The persistent character of the motion of active particles gives rise to accumulation at boundaries. I investigate the problem of run-and-tumble swimmers confined in a 1D box with hard walls, reporting expressions for the particles probability distribution and wall pressure. A crossover box length value is found below which the initial value of the pressure turns out to be higher than the asymptotic one, indicating a bounce effect of the active "wave" of swimmers. The case of attracting and repelling boundaries are also investigated using two different tumble rates for particles in the bulk an…
We consider the thermal and athermal overdamped motion of particles in 1D geometries where discrete internal degrees of freedom (spin) are coupled with the translational motion. Adding a driving velocity that depends on the time-dependent spin constitutes the simplest model of active particles (run-and-tumble processes) where the violation of the equipartition principle and of the Sutherland-Einstein relation can be studied in detail even when there is generalized reversibility. We give an example (with four spin values) where the irreversibility of the translational motion manifests itself on…
Active particles in a tube: a generalized entropy potential approach
Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University（苏州大学物理科学与技术学院、软凝聚态物质与交叉研究卓越中心）；School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学物理与天文学院、自然科学研究院）
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…
Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active network materials. We construct a general microscopic network model that incorporates nonlinear elasticity of individual filaments and steric constraints due to crowding. Based on constructive analogies between structural glass forming liquids and random field Ising magnets implemented using a heterogeneous self-consistent phonon method, our scheme provides …
How fast must an oriented collection of extensile swimmers swim to escape the instability of viscous active suspensions? We show that the answer lies in the dimensionless combination $R=ρv_0^2/2σ_a$, where $ρ$ is the suspension mass density, $v_0$ the swim speed and $σ_a$ the active stress. Linear stability analysis shows that for small $R$ disturbances grow at a rate linear in their wavenumber $q$, and that the dominant instability mode involves twist. The resulting steady state in our numerical studies is isotropic hedgehog-defect turbulence. Past a first threshold $R$ of order unity we find…
We present an experimental realization of the collective trapping phase transition [Kaiser et al., PRL 108, 268307 (2012)], using motile polar granular rods in the presence of a V-shaped obstacle. We offer a theory of this transition based on the interplay of motility-induced condensation and liquid-crystalline ordering and show that trapping occurs when persistent influx overcomes the collective expulsion of smectic defect structures. In agreement with the theory, our experiments find that a trap fills to the brim when the trap angle $θ$ is below a threshold $θ_c$, while all particles escape …
