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 height. This leads to a host of unusual behaviors. For example, when a particle is trapped between two barriers it may preferentially escape over the higher one. Moreover, as the self-propulsion speed is varied, the escape route may discontinuously switch from one barrier to the other, leading to a dynamical phase transition. arXiv:1904.00599v2 [cond-mat.soft]

Motivated by the dynamics of particles embedded in active gels, both in-vitro and inside the cytoskeleton of living cells, we study an active generalization of the classical trap model. We demonstrate that activity leads to dramatic modifications in the diffusion compared to the thermal case: the mean square displacement becomes sub-diffusive, spreading as a power-law in time, when the trap depth distribution is a Gaussian and is slower than any power-law when it is drawn from an exponential distribution. The results are derived for a simple, exactly solvable, case of harmonic traps. We then argue that the results are robust for more realistic trap shapes when the activity is strong. PACS numbers:Introduction. In-vitro experiments have probed the non-thermal (active) fluctuations in an "active gel", which is most often realized as a network composed of cross-linked actin filaments and myosin-II molecular motors [1][2][3][4]. The fluctuations inside the active gel are measured using the tracking of tracer particles, and was used to demonstrate the non-equilibrium nature of these systems through the breaking of the Fluctuation-Dissipation theorem (FDT) [4]. In these active gels, myosin-II molecular motors generate relative motion between the actin filaments, through consumption of ATP, and thus drive the athermal random motion of the probe particles dispersed throughout the network. Similar motion of tracer particles was observed in living cells [5,6].In both the in-vitro gels, and in cells, over short times, the tracer particle seems to perform caged random motion, while trapped in the elastic network. On longer times it is observed that the actin network allows the tracer to perform "hopping" diffusion, as it makes large amplitude motions [2,[5][6][7][8], driven by the same active forces. This large scale motion was treated on a coarsegrained scale in [6] [37].Here we explore in more detail the process by which active forces can drive hopping diffusion in a heterogeneous medium. We use a trap model [9] where the particle is assumed to be trapped in a potential well of variable depth, representing the structural inhomogeneity present in the system. The particle is affected by random active forces, which eventually "kick" the particle from the well. This event can correspond to the release of the tracer particle from the confining network, or more generally to the triggering of some unspecified rearrangement of the constituents of the system. After each such event, the particle (system) is locked in a new confining organization, and a new activated escape process begins.The distribution of potential well depths determines the type of hopping diffusion performed by the particle. Indeed, it is well known that for a thermal system, a Gaussian distribution of potential depths gives rise to normal hopping diffusion, while an exponential distribution of potential depths can give rise to anomalous diffu-sion: x 2 ∝ t α , 0 < α < 1. (for a review see [10]). This result is a direct consequence of the Kramers escape rate whi...

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 interesting consequences, which we illustrate through two phenomena. First, active particles in the presence of an asymmetric barrier tend to accumulate on one side of the potential—a ratchet effect that was missing is previous treatments. Second, an active particle can escape over a deep metastable state without spending any time at its bottom.

It is extremely uncommon to be able to predict the velocity profile of a turbulent flow. In twodimensional flows, atmosphere dynamics, and plasma physics, large scale coherent jets are created through inverse energy transfers from small scales to the largest scales of the flow. We prove that in the limits of vanishing energy injection, vanishing friction, and small scale forcing, the velocity profile of a jet obeys an equation independent of the details of the forcing. We find another general relation for the maximal curvature of a jet and we give strong arguments to support the existence of an hydrodynamic instability at the point with minimal jet velocity. Those results are the first computations of Reynolds stresses and self consistent velocity profiles from the turbulent dynamics, and the first consistent analytic theory of zonal jets in barotropic turbulence.Theoretical prediction of velocity profiles of inhomogeneous turbulent flows is a long standing challenge, since the nineteenth century. It involves closing hierarchy for the velocity moments, and for instance obtaining a relation between the Reynolds stress and the velocity profile. Since Boussinesq in the nineteenth century, most of the approaches so far have been either empirical or phenomenological. Even for the simple case of a three dimensional turbulent boundary layer, plausible but so far unjustified similarity arguments may be used to derive von Kármán logarithmic law for the turbulent boundary layer (see for instance [1]), but the related von Kármán constant [2] has never been computed theoretically. Still this problem is a crucial one and has some implications in most of scientific fields, in physics, astrophysics, climate dynamics, and engineering. Equations (6-7), (9), and (11) are probably the first prediction of the velocity profile for turbulent flows, and relevant for barotropic flows.In this paper we find a way to close the hierarchy of the velocity moments, for the equation of barotropic flows with or without effect of the Coriolis force. This two dimensional model is relevant for laboratory experiments of fluid turbulence [3], liquid metals [4], plasma [5], and is a key toy model for understanding planetary jet formation [6] and basics aspects of plasma dynamics on Tokamaks in relation with drift waves and zonal flow formation [7]. It is also a relevant model for Jupiter troposphere organization [8]. Moreover, our approach should have future implications for more complex turbulent boundary layers, which are crucial in climate dynamics in order to quantify momentum and energy transfers between the atmosphere and the ocean.It has been realized since the sixties and seventies in the atmosphere dynamics and plasma communities that in some regimes two dimensional turbulent flows are * Eric.Woillez@ens-lyon.fr † Freddy.Bouchet@ens-lyon.fr strongly dominated by large scale coherent structures. Jets and large vortices are often observed in numerical simulations or in experiments, but the general mechanism leading to such an organization of t...

The effects of quenched disorder on a single and many active run-and-tumble particles are studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in three parameters: a bounded external potential, the particle's speed, and its tumbling rate. We show that in the case of a disordered potential, the behavior is like an equilibrium particle diffusing on a random force landscape, implying a dynamics that is logarithmically slow in time. In the situations of disorder in the speed or tumbling rate, we find that the particle generically exhibits diffusive motion, although particular choices of the disorder may lead to anomalous diffusion. Based on the single-particle results, we find that in a system with many interacting particles, disorder in the potential leads to strong clustering. We characterize the clustering in two different regimes depending on the system size and show that the mean cluster size scales with the system size, in contrast to nondisordered systems.