Coulomb friction driving Brownian motors

We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation (linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a ``collisional noise'', that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein-Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.Comment: 19 pages, 10 figures, Proceedings of the Conference "Small system nonequilibrium fluctuations, dynamics and stochastics, and anomalous behavior", KITPC, Beijing, Chin

Coarsening in granular systems

We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular media. Thereafter, dilute systems, the so-called "granular gases" are discussed: idealized kinetic models, such as the gas of inelastic hard spheres in the cooling regime, are the optimal playground to study the slow growth of correlated structures, e.g. shear patterns, vortices and clusters. In fluidized experiments, liquid-gas or solid-gas separations have been observed. In the case of monolayers of particles, phase coexistence and coarsening appear in several different setups, with mechanical or electrostatic energy input. Phenomenological models describe, even quantitatively, several experimental measures, both for the coarsening dynamics and for the dynamic transition between different granular phases. The origin of the underlying bistability is in general related to negative compressibility from granular hydrodynamics computations, even if the understanding of the mechanism is far from complete. A relevant problem, with important industrial applications, is related to the demixing or segregation of mixtures, for instance in rotating tumblers or on horizontally vibrated plates. Finally, the problem of compaction of highly dense granular materials, which has many important applications, is usually described in terms of coarsening dynamics: there, bubbles of mis-aligned grains evaporate, allowing the coalescence of optimally arranged islands and a progressive reduction of total occupied volume.Comment: 12 pages, 10 figures, to appear in "Dynamics of coarsening" Comptes Rendus Physique special issue, https://sites.google.com/site/ppoliti/crp-special-issu

Irreversible dynamics of a massive intruder in dense granular fluids

A Generalized Langevin Equation with exponential memory is proposed for the dynamics of a massive intruder in a dense granular fluid. The model reproduces numerical correlation and response functions, violating the equilibrium Fluctuation Dissipation relations. The source of memory is identified in the coupling of the tracer velocity $V$ with a spontaneous local velocity field $U$ in the surrounding fluid. Such identification allows us to measure the intruder's fluctuating entropy production as a function of $V$ and $U$, obtaining a neat verification of the Fluctuation Relation.Comment: 5 pages, 3 figures accepted for publication in EP

Nonequilibrium Brownian motion beyond the effective temperature

The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own "effective" temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein's relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.Comment: 10 pages, 5 figure

Growing non-equilibrium length in granular fluids: from experiment to fluctuating hydrodynamics

Velocity correlations in a 2D granular fluid are studied in experiments and numerical simulations. The transverse component of the velocity structure factor reveals two well defined energy scales, associated with the external "bath temperature" $T_b$ and with the internal granular one, $T_g<T_b$, relevant at large and small wavelengths respectively. Experimental and numerical data are discussed within a fluctuating hydrodynamics model, which allows one to define and measure a non-equilibrium coherence length $\xi$, growing with density, that characterizes order in the velocity field.Comment: 5 pages, 4 figure

Lattice models for granular-like velocity fields: Hydrodynamic limit

A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but dissipate energy. The dynamics can be described by a stochastic equation in full phase space, or through the corresponding Master Equation for the time evolution of the probability distribution. In the hydrodynamic limit, equations for the average velocity and temperature fields with fluctuating currents are derived, which are analogous to those of granular fluids when restricted to the shear modes. Therefore, the homogeneous cooling state, with its linear instability, and other relevant regimes such as the uniform shear flow and the Couette flow states are described. The evolution in time and space of the single particle probability distribution, in all those regimes, is also discussed, showing that the local equilibrium is not valid in general. The noise for the momentum and energy currents, which are correlated, are white and Gaussian. The same is true for the noise of the energy sink, which is usually negligible

Ricerca-azione e analisi delle reti sociali in contesti di apprendimento linguistico online: una proposta metodologica

At the present time, talking about “distance” education means almost exclusively talking about education that takes place on the Web and through its use for educational purposes. More specifically, the last two years have shown a dramatic increase in the popularity of MOOCs (Massive Open Online Courses); this phenomenon, especially with reference to Language MOOCs, requires to be observed and studied adequately. Subsequently, it is necessary to shape and develop critical skills and tools to notice and confront issues in massive online learning contexts.This paper aims to present a methodology that encompasses action research and social network analysis to detect and address issues in LMOOCs. Relying on Moore’s transactional distance theory, the methodology involves a four-phases process in which two distinct analyses are conducted. On the one hand, a monitoring system gathers a large amount of data, regarding the social network in the LMOOC, to be examined; on the other hand, the LMOOC tutor makes use of different tools to reflect upon his/her teaching. All this leads, therefore, to the availability of a brand-new procedure (to be empirically validated) in studying learning interactions, in a broader sense, in massive online learning contexts

Single prazosin infusion in prelimbic cortex Fosters extinction of amphetamine-induced conditioned place preference

Exposure to drug-associated cues to induce extinction is a useful strategy to contrast cue-induced drug seeking. Norepinephrine (NE) transmission in medial prefrontal cortex has a role in the acquisition and extinction of conditioned place preference induced by amphetamine. We have reported recently that NE in prelimbic cortex delays extinction of amphetamine-induced conditioned place preference (CPP). A potential involvement of α1-adrenergic receptors in the extinction of appetitive conditioned response has been also suggested, although their role in prelimbic cortex has not been yet fully investigated. Here, we investigated the effects of the α1-adrenergic receptor antagonist prazosin infusion in the prelimbic cortex of C57BL/6J mice on expression and extinction of amphetamine-induced CPP. Acute prelimbic prazosin did not affect expression of amphetamine-induced CPP on the day of infusion, while in subsequent days it produced a clear-cut advance of extinction of preference for the compartment previously paired with amphetamine (Conditioned stimulus, CS). Moreover, prazosin-treated mice that had extinguished CS preference showed increased mRNA expression of brain-derived neurotrophic factor (BDNF) and post-synaptic density 95 (PSD-95) in the nucleus accumbens shell or core, respectively, thus suggesting that prelimbic α1-adrenergic receptor blockade triggers neural adaptations in subcortical areas that could contribute to the extinction of cue-induced drug-seeking behavior. These results show that the pharmacological blockade of α1-adrenergic receptors in prelimbic cortex by a single infusion is able to induce extinction of amphetamine-induced CPP long before control (vehicle) animals, an effect depending on contingent exposure to retrieval, since if infused far from or after reactivation it did not affect preference. Moreover, they suggest strongly that the behavioral effects depend on post-treatment neuroplasticity changes in corticolimbic network, triggered by a possible “priming” effect of prazosin, and point to a potential therapeutic power of the antagonist for maladaptive memories

Fluctuation relations without uniform large deviations

We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external field to determine the extent to which fluctuation relations are related to large deviations. Focusing on the total entropy production of this model in its steady state, we show that, although the probability density of this quantity globally satisfies (by definition) a fluctuation relation, its negative tail decays exponentially with time, whereas its positive tail decays slower than exponentially with time because of long collision-free trajectories. This provides an example of physical system for which the fluctuation relation does not derive, as commonly thought, from a probability density decaying everywhere exponentially with time or, in other words, from a probability density having a uniform large deviation form.Comment: 12 pages, 1 figure; v2: published versio

Non-equilibrium fluctuations in frictional granular motor: experiments and kinetic theory

We report the study of a new experimental granular Brownian motor, inspired to the one published in [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating pawl whose surfaces break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main novelty of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance $v_0^2$. We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe for the first time the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions (RC), with an average drift $\ \sim v_0^3$, and (ii) frequent collisions (FC), with $\ \sim v_0$. We also study the fluctuations of the angle spanned in a large time interval, $\Delta \theta$, which in the FC regime is proportional to the work done upon the motor. We observe that the Fluctuation Relation is satisfied with a slope which weakly depends on the relative collision frequency.Comment: 7 pages, 6 figure