Anomalous force-velocity relation of driven inertial tracers in steady laminar flows

Absolute Negative Mobility of an Active Tracer in a Crowded Environment

Absolute negative mobility (ANM) refers to the situation where the average velocity of a driven tracer is opposite to the direction of the driving force. This effect was evidenced in different models of nonequilibrium transport in complex environments, whose description remains effective. Here, we provide a microscopic theory for this phenomenon. We show that it emerges in the model of an active tracer particle submitted to an external force and which evolves on a discrete lattice populated with mobile passive crowders. Resorting to a decoupling approximation, we compute analytically the velocity of the tracer particle as a function of the different parameters of the system and confront our results to numerical simulations. We determine the range of parameters where ANM can be observed, characterize the response of the environment to the displacement of the tracer, and clarify the mechanism underlying ANM and its relationship with negative differential mobility (another hallmark of driven systems far from the linear response).

Absolute negative mobility of active polymer chains in steady laminar flows

We investigate the transport of active polymer chains in steady laminar flows in the presence of thermal noise and an external constant force. In the model, the polymer chain is worm-like and is propelled by active forces along its tangent vectors. Compared with inertial Brownian particles, active polymer chains in steady laminar flows exhibit richer movement patterns due to their specific spatial structures. The simulation results show that the velocity-force relation is strongly dependent on the system parameters such as the chain length, bending rigidity, active force and so on. The polymer chain may move in some preferential movement directions and exhibits absolute negative mobility within appropriate parameter regimes, i.e., the polymer chain can move in a direction opposite to the external constant force. In particular, we can observe giant negative mobility in a broad range of parameter regimes.

Diffusion properties of self-propelled particles in cellular flows

We study the dynamics of a self-propelled particle advected by a steady laminar flow. The persistent motion of the self-propelled particle is described by an active Ornstein-Uhlenbeck process. We focus on the diffusivity properties of the particle as a function of persistence time and free-diffusion coefficient, revealing non-monotonic behaviors, with the occurrence of a minimum and a steep growth in the regime of large persistence time. In the latter limit, we obtain an analytical prediction for the scaling of the diffusion coefficient with the parameters of the active force. Our study sheds light on the effect of a flow-field on the diffusion of active particles, such as living microorganisms and motile phytoplankton in fluids.

Spontaneous rectification and absolute negative mobility of inertial Brownian particles induced by Gaussian potentials in steady laminar flows

We study the transport of inertial Brownian particles in steady laminar flows in the presence of two-dimensional Gaussian potentials. Through extensive numerical simulations, it is found that the transport is sensitively dependent on the external constant force and the Gaussian potential. Within tailored parameter regimes, the system exhibits a rich variety of transport behaviors. There exists the phenomenon of spontaneous rectification (SR), where the directed transport of particles can occur in the absence of any external driving forces. It is found that SR of the particles can be manipulated by the spatial position of the Gaussian potential. Moreover, when the potential lies at the center of the cellular flow, the system exhibits absolute negative mobility (ANM), i.e., the particles can move in a direction opposite to the constant force. More importantly, the phenomenon of ANM induced by Gaussian potentials is robust in a wide range of system parameters and can be further strengthened with the optimized parameters, which may pave the way to the implementation of related experiments.

Tracer diffusion in crowded narrow channels

We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.

Anomalous mobility of a driven active particle in a steady laminar flow

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 [Formula: see text]. 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 ([Formula: see text]) advected by the same laminar flow. Our results show that the phenomena of NDM and ANM are quite robust with respect to the details of the considered noise: in particular for finite [Formula: see text] a more complex force-velocity relation can be observed.

Transport and diffusion of paramagnetic ellipsoidal particles in a rotating magnetic field

Transport and diffusion of paramagnetic ellipsoidal particles under the action of a rotating magnetic field are numerically investigated in a two-dimensional channel. It is found that paramagnetic ellipsoidal particles in a rotating magnetic field can be rectified in the upper-lower asymmetric channel. The transport and the effective diffusion coefficient are much more different and complicated for active particles, while they have similar behaviors and change a little when applying rotating magnetic fields of different frequencies for passive particles. For active particles, the back-and-forth rotational motion facilitates the effective diffusion coefficient and reduces the rectification, whereas the rotational motion synchronous with the magnetic field suppresses the effective diffusion coefficient and enhances the rectification. There exist optimized values of the parameters (the anisotropic degree, the amplitude and frequency of magnetic field, the self-propelled velocity, and the rotational diffusion rate) at which the average velocity and diffusion take their maximal values. Particles with different shapes, self-propelled speeds, or rotational diffusion rates will move to the opposite directions and can be separated by applying rotating magnetic fields of suitable strength and frequency. Our results can be used to separate particles, orient the particles along any direction at will during motion, and control the particle diffusion.

Finding efficient swimming strategies in a three-dimensional chaotic flow by reinforcement learning

We apply a reinforcement learning algorithm to show how smart particles can learn approximately optimal strategies to navigate in complex flows. In this paper we consider microswimmers in a paradigmatic three-dimensional case given by a stationary superposition of two Arnold-Beltrami-Childress flows with chaotic advection along streamlines. In such a flow, we study the evolution of point-like particles which can decide in which direction to swim, while keeping the velocity amplitude constant. We show that it is sufficient to endow the swimmers with a very restricted set of actions (six fixed swimming directions in our case) to have enough freedom to find efficient strategies to move upward and escape local fluid traps. The key ingredient is the learning-from-experience structure of the algorithm, which assigns positive or negative rewards depending on whether the taken action is, or is not, profitable for the predetermined goal in the long-term horizon. This is another example supporting the efficiency of the reinforcement learning approach to learn how to accomplish difficult tasks in complex fluid environments.