The design of artificial microswimmers has generated significant research interest in recent years, for promise in applications such as nanomotors and targeted drug-delivery. However, many current designs suffer from a common problem, namely the swimmers remain in the fluid indefinitely, posing risks of clogging and damage. Inspired by recently proposed experimental designs, we investigate mathematically the dynamics of degradable active particles. We develop and compare two distinct chemical models for the decay of a swimmer, taking into account the material composition and nature of the chemical or enzymatic reaction at its surface. These include a model for dissolution without a reaction, as well as models for a reacting swimmer studied in the limit of large and small Damköhler number. A new dimensionless parameter emerges that allows the classification of colloids into ballistic and diffusive type. Using this parameter, we perform an asymptotic analysis to derive expressions for colloid lifetimes and their total mean-squared displacement from release and validate these by numerical Monte Carlo simulations of the associated Langevin dynamics. Supported by general scaling relationships, our theoretical results provide new insight into the experimental applicability of a wide range of designs for degradable active colloids.
Concentration gradients play a critical role in embryogenesis, bacterial locomotion, as well as the motility of active particles. Particles develop concentration profiles around them by dissolution, adsorption, or the reactivity of surface species. These gradients change the surface energy of the particles, driving both their self-propulsion and governing their interactions. Here we uncover a regime in which solute-gradients mediate interactions between slowly dissolving droplets without causing autophoresis. This decoupling allows us to directly measure the steady-state, repulsive force, whic…
We study collective dynamical behavior of active particles with topological interactions and directional reversals. Surprising phenomena are shown to emerge as the interaction relaxation time is varied relative to the reversal rate, such as spontaneous formation of collective chiral states due to phase synchronization, and collective directional reversals in the presence of confinement. The results have a direct relevance to modelling and understanding collective reversals and synchronization phenomena in active matter.
Grasping, in both biological and engineered mechanisms, can be highly sensitive to the gripper and object morphology, as well as perception, and motion planning. Here we circumvent the need for feedback or precise planning by using an array of fluidically-actuated slender hollow elastomeric filaments to actively entangle with objects that vary in geometric and topological complexity. The resulting stochastic interactions enable a unique soft and conformable grasping strategy across a range of target objects that vary in size, weight, and shape. We experimentally evaluate the grasping performan…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochasti…
Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the hydrodynamic or kinetic equations. By incorporating stochastic fluxes into the mean field kinetic equation, we quantify the dynamics of a suspension of microswimmers in the parameter regime where the deterministic equation is stable. We can thereby compute nontrivial collective phenomena concerning spatial correlations of orientation and stress as well as th…
We study the stochastic force dynamics of a model microswimmer (Chlamydomonas reinhardtii), using a combined experimental, theoretical, and numerical approach. While swimming dynamics have been extensively studied using hydrodynamic approaches, which infer forces from the viscous flow field, we directly measure the stochastic forces generated by the microswimmer using an optical trap via the photon momentum method. We analyze the force dynamics by modeling the microswimmer as a self-propelled particle, a la active matter, and analyze it's energetics using methods from stochastic thermodynamics…
We propose a new overarching model for self-propelled particles that flexibly generates a full family of "descendants". The general dynamics introduced in this paper, which we denote as "parental" active model (PAM), unifies two special cases commonly used to describe active matter, namely active Brownian particles (ABPs) and active Ornstein-Uhlenbeck particles (AOUPs). We thereby document the existence of a deep and close stochastic relationship between them, resulting in the subtle balance between fluctuations in the magnitude and direction of the self-propulsion velocity. Besides illustrati…
The equilibrium properties of a system of passive diffusing particles in an external magnetic field are unaffected by the Lorentz force. In contrast, active Brownian particles exhibit steady-state phenomena that depend on both the strength and the polarity of the applied magnetic field. The intriguing effects of the Lorentz force, however, can only be observed when out-of-equilibrium density gradients are maintained in the system. To this end, we use the method of stochastic resetting on active Brownian particles in two dimensions by resetting them to the line $x=0$ at a constant rate and peri…
Technische Universität Dresden（德累斯顿工业大学）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI（可扩展数据分析与人工智能中心 ScaDS.AI）；Cluster of Excellence Physics of Life, TU Dresden（德累斯顿工业大学生命物理卓越集群）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；University of Geneva（日内瓦大学）
We present a principled data-driven strategy for learning deterministic hydrodynamic models directly from stochastic non-equilibrium active particle trajectories. We apply our method to learning a hydrodynamic model for the propagating density lanes observed in self-propelled particle systems and to learning a continuum description of cell dynamics in epithelial tissues. We also infer from stochastic particle trajectories the latent phoretic fields driving chemotaxis. This demonstrates that statistical learning theory combined with physical priors can enable discovery of multi-scale models of …
Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most cells or synthetic swimmers are immersed in external flows, we consider theoretically in this paper the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. The stochasticity arises both from translational diffusion in physical space, and from a combination of rotary diffusion and run-and-tumble dynamics in …
Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained individual motion. It can lead to collective effects without any equilibrium equivalent, such as a phase separation for purely repulsive particles, or a collective motion (flocking) for aligning particles. Some of these effects can be rationalized by using equilibrium tools to recapitulate nonequilibrium transitions. An important challenge is then to delineate …
We report on the experimental observation of stochastic resonance (SR) in a nonGaussian active bath without any periodic modulation. A Brownian particle hopping in a nanoscale double-well potential under the influence of nonGaussian correlated noise, with mean interval ${{τ}_{P}}$ and correlation time ${{τ}_{c}}$, shows a series of equally-spaced peaks in the residence time distribution at integral multiples of ${{τ}_{P}}$. The strength of the first peak is found to be maximum when the mean residence time ${\bar{τ}_{d}}$ matches the double condition, $4{{τ}_{c}}\approx {{τ}_{P}}\approx {\bar{τ…
Thermodynamics of nanoscale devices is an active area of research. Despite their noisy surrounding they often produce mechanical work (e.g. micro-heat engines), display rectified Brownian motion (e.g. molecular motors). This invokes research in terms of experimentally quantifiable thermodynamic efficiencies. Here, a Brownian particle is driven by a harmonic confinement with time-periodic contraction and expansion. The system produces work by being alternately (time-periodically) connected to baths with different dissipations. We analyze the system theoretically using stochastic thermodynamics.…
From Action Principle to Stochastic Thermodynamics of Elastic and Viscous Active Matter
European Molecular Biology Laboratory（欧洲分子生物学实验室）；University of Turin（都灵大学）；Heidelberg University（海德堡大学）；University of Cambridge（剑桥大学）；Politecnico di Torino（都灵理工大学）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）
The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and product in the surrounding solution. Because of thermal and molecular fluctuations in the solution, the motion of micrometric or submicrometric active particles is stochastic. Coupled Langevin equations describing the translation, rotation, and reaction of such active particles are deduced from fluctuating chemohydrodynamics and fluctuating boundary conditions …
Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such non-equilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and…
Chemotaxis is the response of a particle to a gradient in the chemical composition of the environment. While it was originally observed for biological organisms, it is of great interest in the context of synthetic active particles such as nanomotors. Experimental demonstration of chemotaxis for chemically-powered colloidal nanomotor was reported in the literature in the context of chemo-attraction in a still fluid or in a microfluidic channel where the gradient is sustained by a specific inlet geometry. In this work, we use mesoscopic particle-based simulations of the colloid and solvent to de…
From synthetic active devices such as self-propelling Janus colloids to micro-organisms like bacteria, micro-algae, living cells in tissues, active fluctuations are ubiquitous. Thermodynamics of small systems involving thermal as well as active fluctuations are of immense importance. They can be employed to extract thermodynamic work. Here we propose a simple model system that can produce thermodynamic work exploiting active fluctuations. We consider a Brownian particle, trapped by an externally controlled harmonic confinement which time-periodically contracts and expands by modulating its spr…
Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a gene…
Chemically active systems such as living cells are maintained out of thermal equilibrium due to chemical events which generate heat and lead to active fluctuations. A key question is to understand on which time and length scales active fluctuations dominate thermal fluctuations. Here, we formulate a stochastic field theory with Poisson white noise to describe the heat fluctuations which are generated by stochastic chemical events and lead to active temperature fluctuations. We find that on large length and time scales, active fluctuations always dominate thermal fluctuations. However, at inter…
A particle that is immersed in a uniform temperature bath performs Brownian diffusion, as discussed by Einstein. But Sinai has realized that in a "random environment" the diffusion is suppressed. Follow-up works have pointed out that in the presence of bias $f$ there are delocalization and sliding transitions, with threshold value $f_c$ that depends on the disorder strength. We discuss in a critical way the emergence of Sinai physics for both passive and active Brownian particles. Tight-binding and Fokker-Planck versions of the model are addressed on equal footing. We assume that the transitio…
An active network is a prototype model in non-equilibrium statistical mechanics. It can represent, for example, a system with particles that have a self-propulsion mechanism. Each node of the network specifies a possible location of a particle, and its orientation. The orientation (which is formally like a spin degree of freedom) determines the self-propulsion direction. The bonds represent the possibility to make transitions: to hop between locations; or to switch the orientation. In systems of experimental interest (Janus particles), the self-propulsion is induced by illumination. An emergen…
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…
Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained, until a large enough impulse by an additional stochastic force reverses it. Examples may be provided by self-propelled droplets, gliding bacteria stochastically reversing their propulsion direction, or nonpolar vibrated hoppers. The magnitude of active forcing is regarded as constant, and we include the effect of inertial contributions. Interestingly, this …
Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics
Nihon University（日本大学）；University of Chinese Academy of Sciences（中国科学院大学）；Kyoto University（京都大学）；Technion - Israel Institute of Technology（以色列理工学院）；Tel Aviv University（特拉维夫大学）
Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotrop…
Simplest extensions of single particle dynamics in momentum conserving active fluid - that of an active suspension of two colloidal particles or a single particle confined by a wall - exhibit strong departures from Boltzmann behavior, resulting in either a breakdown of an effective temperature description or a steady state with nonzero entropy production rate. This is a consequence of hydrodynamic interactions that introduce multiplicative noise in the stochastic description of the particle positions. This results in fluctuation induced interactions that depend on distance as a power law. We f…
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…
Biological assemblies such as chromosomes, membranes, and the cytoskeleton are driven out of equilibrium at the nanoscale by enzymatic activity and molecular motors. Similar non-equilibrium dynamics can be realized in synthetic systems, such as chemically fueled colloidal particles. Characterizing the stochastic non-equilibrium dynamics of such active soft assemblies still remains a challenge. Recently, new non-invasive approaches have been proposed to determine non-equilibrium behavior, which are based on detecting broken detailed balance in the stochastic trajectories of several coordinates …
The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations in a generic class of stochastic active processes consisting of distinct states of motion characterized by their persistence and switching probabilities between the states. For exponentially distributed sojourn times, the orientation autocorrelation is analytically derived and the characteristic times of its crossovers are obtained in terms of the persistence…
A recently developed theory of stochastic swimming is used to study the notion of coherence in active systems that couple via hydrodynamic interactions. It is shown that correlations between various modes of deformation in stochastic systems play the same role as the relative internal phase in deterministic systems. An example is presented where a simple swimmer can use these correlations to hunt a non-swimmer by forming a hydrodynamic bound state of tunable velocity and equilibrium separation. These results highlight the significance of coherence in the collective behavior of nano-scale stoch…
Current understanding of how contractility emerges in disordered actomyosin networks of non-muscle cells is still largely based on the intuition derived from earlier works on muscle contractility. This view, however, largely overlooks the free energy gain following passive cross-linker binding, which, even in the absence of active fluctuations, provides a thermodynamic drive towards highly overlapping filamentous states. In this work, we shed light on this phenomenon, showing that passive cross-linkers, when considered in the context of two anti-parallel filaments, generate noticeable contract…
