Nonlinear Response of Inertial Tracers in Steady Laminar Flows: Differential and Absolute Negative Mobility

We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence ofthermal noise and under the actionof an external force. We show, with extensive numerical simulations, that the force-velocity rela-tion for the tracer, in the nonlinear regime, displays complex and rich behaviors, including negativedifferential and absolute mobility. These effects rely upon asubtle coupling between inertia andapplied force which induce the tracer to persist in particular regions of phase space with a velocityopposite to the force. The relevance of this coupling is revisited in the framework of non-equilibriumresponse theory, applying a generalized Einstein relationto our system. The possibility of experi-mental observation of these results is also discussed

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 $\tau_A$. 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 ($\tau_A=0$) 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 $\tau_A$ a more complex force-velocity relation can be observed.Comment: 12 pages, 9 figures, paper submitted for the Special Issue of Journal of Physics: Condensed Matter, "Transport in Narrow Channels", Guest Editors P. Malgaretti, G. Oshanin, J. Talbo

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

We study the nonlinear response to an external force of an inertial tracer advected by a two-dimensional incompressible laminar flow and subject to thermal noise. In addition to the driving external field $F$, the main parameters in the system are the noise amplitude $D_0$ and the characteristic Stokes time $\tau$ of the tracer. The relation velocity vs force shows interesting effects, such as negative differential mobility (NDM), namely a non-monotonic behavior of the tracer velocity as a function of the applied force, and absolute negative mobility (ANM), i.e. a net motion against the bias. By extensive numerical simulations, we investigate the phase chart in the parameter space of the model, $(\tau,D_0)$, identifying the regions where NDM, ANM and more common monotonic behaviors of the force-velocity curve are observed.Comment: 5 pages, 13 figures. Contribution to the Topical Issue "Fluids and Structures: Multi-scale coupling and modeling", edited by Luca Biferale, Stefano Guido, Andrea Scagliarini, Federico Toschi. The final publication is available at Springer via http://dx.doi.org/10.1140/epje/i2017-11571-

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

Infinite impulse response modal filtering in visible adaptive optics

Diffraction limited resolution adaptive optics (AO) correction in visible wavelengths requires a high performance control. In this paper we investigate infinite impulse response filters that optimize the wavefront correction: we tested these algorithms through full numerical simulations of a single-conjugate AO system comprising an adaptive secondary mirror with 1127 actuators and a pyramid wavefront sensor (WFS). The actual practicability of the algorithms depends on both robustness and knowledge of the real system: errors in the system model may even worsen the performance. In particular we checked the robustness of the algorithms in different conditions, proving that the proposed method can reject both disturbance and calibration errors

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

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