Power injected in a granular gas

A granular gas may be modeled as a set of hard-spheres undergoing inelastic collisions; its microscopic dynamics is thus strongly irreversible. As pointed out in several experimental works bearing on turbulent flows or granular materials, the power injected in a dissipative system to sustain a steady-state over an asymptotically large time window is a central observable. We describe an analytic approach allowing us to determine the full distribution of the power injected in a granular gas within a steady-state resulting from subjecting each particle independently either to a random force (stochastic thermostat) or to a deterministic force proportional to its velocity (Gaussian thermostat). We provide an analysis of our results in the light of the relevance, for other types of systems, of the injected power to fluctuation relations.Comment: 9 pages, 4 figures. Contribution to Proceedings of "Work, Dissipation, and Fluctuations in Nonequilibrium Physics", Brussels, 200

Injected power and entropy flow in a heated granular gas

Our interest goes to the power injected in a heated granular gas and to the possibility to interpret it in terms of entropy flow. We numerically determine the distribution of the injected power by means of Monte-Carlo simulations. Then, we provide a kinetic theory approach to the computation of such a distribution function. Finally, after showing why the injected power does not satisfy a Fluctuation Relation a la Gallavotti-Cohen, we put forward a new quantity which does fulfill such a relation, and is not only applicable in a variety of frameworks outside the granular world, but also experimentally accessible.Comment: accepted in Europhys. Let

Fluctuation relation for a L\'evy particle

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat'' power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian. These tails lead to a strong violation of existing fluctuation theorems, as the ratio of the probabilities of positive and negative work fluctuations of equal magnitude behaves in a non-monotonic way. Possible experiments that could probe these features are proposed.Comment: 5 pages, 2 figures, RevTeX4; v2: minor corrections and references added; v3: typos corrected, new conclusion, close to published versio

Fluctuations of power injection in randomly driven granular gases

We investigate the large deviation function pi(w) for the fluctuations of the power W(t)=w t, integrated over a time t, injected by a homogeneous random driving into a granular gas, in the infinite time limit. Starting from a generalized Liouville equation we obtain an equation for the generating function of the cumulants mu(lambda) which appears as a generalization of the inelastic Boltzmann equation and has a clear physical interpretation. Reasonable assumptions are used to obtain mu(lambda) in a closed analytical form. A Legendre transform is sufficient to get the large deviation function pi(w). Our main result, apart from an estimate of all the cumulants of W(t) at large times t, is that pi(w) has no negative branch. This immediately results in the failure of the Gallavotti-Cohen Fluctuation Relation (GCFR), that in previous studies had been suggested to be valid for injected power in driven granular gases. We also present numerical results, in order to discuss the finite time behavior of the fluctuations of W(t). We discover that their probability density function converges extremely slowly to its asymptotic scaling form: the third cumulant saturates after a characteristic time larger than 50 mean free times and the higher order cumulants evolve even slower. The asymptotic value is in good agreement with our theory. Remarkably, a numerical check of the GCFR is feasible only at small times, since negative events disappear at larger times. At such small times this check leads to the misleading conclusion that GCFR is satisfied for pi(w). We offer an explanation for this remarkable apparent verification. In the inelastic Maxwell model, where a better statistics can be achieved, we are able to numerically observe the failure of GCFR.Comment: 23 pages, 15 figure

Modeling the dynamics of a tracer particle in an elastic active gel

The internal dynamics of active gels, both in artificial (in-vitro) model systems and inside the cytoskeleton of living cells, has been extensively studied by experiments of recent years. These dynamics are probed using tracer particles embedded in the network of biopolymers together with molecular motors, and distinct non-thermal behavior is observed. We present a theoretical model of the dynamics of a trapped active particle, which allows us to quantify the deviations from equilibrium behavior, using both analytic and numerical calculations. We map the different regimes of dynamics in this system, and highlight the different manifestations of activity: breakdown of the virial theorem and equipartition, different elasticity-dependent "effective temperatures" and distinct non-Gaussian distributions. Our results shed light on puzzling observations in active gel experiments, and provide physical interpretation of existing observations, as well as predictions for future studies.Comment: 11 pages, 6 figure

Non Poissonian statistics in a low density fluid

Our interest goes to the collisional statistics in an arbitrary interacting fluid. We show that even in the low density limit and contrary to naive expectation, the number of collisions experienced by a tagged particle in a given time does not obey Poisson law, and that conversely, the free flight time distribution is not a simple exponential. As an illustration, the hard sphere fluid case is worked out in detail. For this model, we quantify analytically those deviations and successfully compare our predictions against molecular dynamics simulations.Comment: 4 pages, 2 figure

Collisional statistics of the hard-sphere gas

We investigate the probability distribution function of the free flight time and of the number of collisions in a hard sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writing an equation for the generating function of the cumulants of the number of collisions, we came across a perfect mapping between our problem and a previously introduced model: the probabilistic ballistic annihilation process [Coppex et al., Phys. Rev. E 69 11303 (2004)]. We exploit this analogy to construct a Monte-Carlo like algorithm able to investigate the asymptotically large time behavior of the collisional statistics within a reasonable computational time. In addition, our predictions are confronted against the results of Molecular Dynamics simulations and Direct Simulation Monte Carlo technique. An excellent agreement is reported.Comment: 13 pages, 12 figure

Dark Matter searches using gravitational wave bar detectors: quark nuggets and newtorites

Many experiments have searched for supersymmetric WIMP dark matter, with null results. This may suggest to look for more exotic possibilities, for example compact ultra-dense quark nuggets, widely discussed in literature with several different names. Nuclearites are an example of candidate compact objects with atomic size cross section. After a short discussion on nuclearites, the result of a nuclearite search with the gravitational wave bar detectors Nautilus and Explorer is reported. The geometrical acceptance of the bar detectors is 19.5 $\rm m^2$ sr, that is smaller than that of other detectors used for similar searches. However, the detection mechanism is completely different and is more straightforward than in other detectors. The experimental limits we obtain are of interest because, for nuclearites of mass less than $10^{-5}$ g, we find a flux smaller than that one predicted considering nuclearites as dark matter candidates. Particles with gravitational only interactions (newtorites) are another example. In this case the sensitivity is quite poor and a short discussion is reported on possible improvements.Comment: published on Astroparticle Physics Sept 25th 2016 replaced fig 1

The effect of a temporary absence of target velocity information on visual tracking

Experiments with the Rashbass ‘step-ramp’ paradigm have revealed that the initial catchup saccade that occurs near pursuit onset uses target velocity as well as position information in its programming. Information about both position and motion also influences smooth pursuit. To investigate the timing of velocity sampling near the initiation of saccades and smooth pursuit, we analyzed the eye movements made in nine ‘step-ramp’ conditions, produced by combining –2, 0 and +2 deg steps with –8, 0 and +8 deg/s ramps. Each trial had either no temporal gap or a 50-ms gap during which the laser target was extinguished, beginning 25, 50, 75 or 100 ms after the step. Six subjects repeated each of the resulting 45 conditions 25 times. With no temporal gap, saccades were larger in the step-ramp-away’ than the ‘step-only’ condition, confirming that saccade programming incorporates ramp velocity information. A temporal gap had no effect on the accuracy of saccades on ‘step-only’ trials, but often caused undershoots in ‘step-ramp’ trials. A 50-ms gap within the first 100 ms also increased the latency of the initial saccade. Although initial pursuit velocity was unaffected by a temporal gap, a gap that started at 25 ms reliably delayed pursuit onset for ramp motion of the target toward the fovea. Later gaps had a minimal effect on initial pursuit latency. The similar timing of the temporal gaps in target motion information that affect the initiation of saccades and pursuit provides further behavioral evidence that the two types of eye movements share pre-motor neural mechanisms

How Far from Equilibrium Is Active Matter?

Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturbatively their steady-state measure and show that, for short persistent times, the entropy production rate vanishes. This endows such systems with an effective fluctuation-dissipation theorem akin to that of thermal equilibrium systems. Last, we show how interacting particle systems with viscous drags and correlated noises can be seen as in equilibrium with a viscoelastic bath but driven out of equilibrium by nonconservative forces, hence providing energetic insight into the departure of active systems from equilibrium.JT was supported by ANR project Bactterns. CN was supported by EPSRC grant Nr. EP/J007404.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the American Physical Society