arXiv subjects

Andrea Puglisi

Publications and source records attributed to Andrea Puglisi.

At least 55 records · Page 3Linked to original sources

arXiv2017

Heat, temperature and Clausius inequality in a model for active brownian particles

Methods of stochastic thermodynamics and hydrodynamics are applied to the a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system's Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.

cond-mat.stat-mech↗

arXiv2017

Dissipative lateral walls are sufficient to trigger convection in vibrated granular gases

Buoyancy-driven (thermal) convection in dilute granular media, fluidized by a vibrating base, is known to appear without the need of lateral boundaries in a restricted region of parameters (inelasticity, gravity, intensity of energy injection). We have recently discovered a second buoyancy-driven convection effect which occurs at any value of the parameters, provided that the impact of particles with the lateral walls is inelastic (Pontuale et al., Phys. Rev. Lett. 117, 098006 (2016)). It is understood that this novel convection effect is strictly correlated to the existence of perpendicular energy fluxes: a vertical one, induced by both bulk and wall inelasticity, and a horizontal one, induced only by dissipation at the walls. Here we first review those previous results, and then present new experimental and numerical data concerning the variations of box geometry, intensity of energy injection, number of particles and width of the box.

cond-mat.soft↗

arXiv2017

Clausius relation for active particles: what can we learn from fluctuations?

Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom - or arbitrariness - appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an "active heat" satisfies the original Clausius relation and can be experimentally verified.

cond-mat.stat-mech↗

arXiv2016

Unified rheology of vibro-fluidized dry granular media: From slow dense flows to fast gas-like regimes

Granular media take on great importance in industry and geophysics, posing a severe challenge to materials science. Their response properties elude known soft rheological models, even when the yield-stress discontinuity is blurred by vibro-fluidization. Here we propose a broad rheological scenario where average stress sums up a frictional contribution, generalizing conventional $μ(I)$-rheology, and a kinetic collisional term dominating at fast fluidization. Our conjecture fairly describes a wide series of experiments in a vibrofluidized vane setup, whose phenomenology includes velocity weakening, shear thinning, a discontinuous thinning transition, and gaseous shear thickening. The employed setup gives access to dynamic fluctuations, which exhibit a broad range of timescales. In the slow dense regime the frequency of cage-opening increases with stress and enhances, with respect to $μ(I)$-rheology, the decrease of viscosity. Diffusivity is exponential in the shear stress in both thinning and thickening regimes, with a huge growth near the transition.

cond-mat.soft↗

arXiv2016

Thermal convection in granular gases with dissipative lateral walls

We consider a granular gas under the action of gravity, fluidized by a vibrating base. We show that a horizontal temperature gradient, here induced by limiting dissipative lateral walls (DLW), leads always to a granular thermal convection (DLW-TC) that is essentially different from ordinary buoyancy-driven convection (BD-TC). In an experiment where BD-TC is inhibited, by reducing gravity with an inclined plane, we always observe a DLW-TC cell next to each lateral wall. Such a cell squeezes towards the nearest wall as the gravity and/or the number of grains increase. Molecular dynamics simulations reproduce the experimental results and indicate that at large gravity or number of grains the DLW-TC is barely detectable.

cond-mat.soft↗

arXiv2016

Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations

We investigate a kinetic heat engine model constituted by particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period $τ$ : their relative excursions, $δ$ and $ε$ respectively, constitute the thermodynamic forces dragging the system out-of-equilibrium. The analysis of the entropy production of the system allows to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small $δ$ and $ε$ the fluxes are linear in the forces through a $τ$-dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which - in the linear regime - yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e. outside of the linear regime. In all our analysis the adiabatic limit $τ\to \infty$ and the the small force limit $δ,ε\to 0$ are not directly related.

cond-mat.stat-mech↗

arXiv2016

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.

cond-mat.soft↗

arXiv2015

Consistent description of fluctuations requires negative temperatures

We review two definitions of temperature in statistical mechanics, $T_B$ and $T_G$, corresponding to two possible definitions of entropy, $S_B$ and $S_G$, known as surface and volume entropy respectively. We restrict our attention to a class of systems with bounded energy and such that the second derivative of $S_B$ with respect to energy is always negative: the second request is quite natural and holds in systems of obvious relevance, i.e. with a number $N$ of degrees of freedom sufficiently large (examples are shown where $N \sim 100$ is sufficient) and without long-range interactions. We first discuss the basic role of $T_B$, even when negative, as the parameter describing fluctuations of observables in a sub-system. Then, we focus on how $T_B$ can be measured dynamically, i.e. averaging over a single long experimental trajectory. On the contrary, the same approach cannot be used in a generic system for $T_G$, since the equipartition theorem may be spoiled by boundary effects due to the limited energy. These general results are substantiated by the numerical study of a Hamiltonian model of interacting rotators with bounded kinetic energy. The numerical results confirm that the kind of configurational order realized in the regions at small $S_B$, or equivalently at small $|T_B|$, depends on the sign of $T_B$.

cond-mat.stat-mech↗

arXiv2015

Entropy production for velocity-dependent macroscopic forces: the problem of dissipation without fluctuations

In macroscopic systems, velocity-dependent phenomenological forces $F(v)$ are used to model friction, feedback devices or self-propulsion. Such forces usually include a dissipative component which conceals the fast energy exchanges with a thermostat at the environment temperature $T$, ruled by a microscopic Hamiltonian $H$. The mapping $(H,T) \to F(v)$ - even if effective for many purposes - may lead to applications of stochastic thermodynamics where an $incomplete$ fluctuating entropy production (FEP) is derived. An enlightening example is offered by recent macroscopic experiments where dissipation is dominated by solid-on-solid friction, typically modelled through a deterministic Coulomb force $F(v)$. Through an adaptation of the microscopic Prandtl-Tomlinson model for friction, we show how the FEP is dominated by the heat released to the $T$-thermostat, ignored by the macroscopic Coulomb model. This problem, which haunts several studies in the literature, cannot be cured by weighing the time-reversed trajectories with a different auxiliary dynamics: it is only solved by a more accurate stochastic modelling of the thermostat underlying dissipation.

cond-mat.stat-mech↗

arXiv2015

Individual Biases, Cultural Evolution, and the Statistical Nature of Language Universals: The Case of Colour Naming Systems

Language universals have long been attributed to an innate Universal Grammar. An alternative explanation states that linguistic universals emerged independently in every language in response to shared cognitive or perceptual biases. A computational model has recently shown how this could be the case, focusing on the paradigmatic example of the universal properties of colour naming patterns, and producing results in quantitative agreement with the experimental data. Here we investigate the role of an individual perceptual bias in the framework of the model. We study how, and to what extent, the structure of the bias influences the corresponding linguistic universal patterns. We show that the cultural history of a group of speakers introduces population-specific constraints that act against the pressure for uniformity arising from the individual bias, and we clarify the interplay between these two forces.

physics.soc-ph↗

arXiv2015

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.

cond-mat.stat-mech↗

arXiv2015

Cages and anomalous diffusion in vibrated dense granular media

A vertically shaken granular medium hosts a blade rotating around a fixed vertical axis, which acts as a mesorheological probe. At high densities, independently from the shaking intensity, the blade's dynamics show strong caging effects, marked by transient sub-diffusion and a maximum in the velocity power density spectrum (vpds), at a resonant frequency $\sim 10$ Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic constant of the granular medium and its collective diffusion coefficient. For high frequencies $f$, a tail $\sim 1/f$ in the vpds reveals non-trivial correlations in the intra-cage micro-dynamics. At very long times (larger than $10$ s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times $τ$ displays a power-law decay, likely due to persistent collective fluctuations of the host medium.

cond-mat.soft↗

arXiv2015

A kinetic model for the finite-time thermodynamics of small heat engines

We study a molecular engine constituted by a gas of $N \sim 10^2$ molecules enclosed between a massive piston and a thermostat. The force acting on the piston and the temperature of the thermostat are cyclically changed with a finite period $τ$. In the adiabatic limit $τ\to \infty$, even for finite size $N$, the average work and heats reproduce the thermodynamic values, recovering the Carnot result for the efficiency. The system exhibits a stall time $τ^*$ where net work is zero: for $τ<τ^*$ it consumes work instead of producing it, acting as a refrigerator or as a heat sink. At $τ>τ^*$ the efficiency at maximum power is close to the Curzorn-Ahlborn limit. The fluctuations of work and heat display approximatively a Gaussian behavior. Based upon kinetic theory, we develop a three-variables Langevin model where the piston's position and velocity are linearly coupled together with the internal energy of the gas. The model reproduces many of the system's features, such as the inversion of the work's sign, the efficiency at maximum power and the approximate shape of fluctuations. A further simplification in the model allows to compute analytically the average work, explaining its non-trivial dependence on $τ$.

cond-mat.stat-mech↗

arXiv2014

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.

cond-mat.stat-mech↗

arXiv2014

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.

cond-mat.stat-mech↗

arXiv2013

Time-resolved dynamics of granular matter by random laser emission

Because of the huge commercial importance of granular systems, the second-most used material in industry after water, intersecting the industry in multiple trades, like pharmacy and agriculture, fundamental research on grain-like materials has received an increasing amount of attention in the last decades. In photonics, the applications of granular materials have been only marginally investigated. We report the first phase-diagram of a granular as obtained by laser emission. The dynamics of vertically-oscillated granular in a liquid solution in a three-dimensional container is investigated by employing its random laser emission. The granular motion is function of the frequency and amplitude of the mechanical solicitation, we show how the laser emission allows to distinguish two phases in the granular and analyze its spectral distribution. This constitutes a fundamental step in the field of granulars and gives a clear evidence of the possible control on light-matter interaction achievable in grain-like system.

physics.optics↗

arXiv2013

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.

cond-mat.stat-mech↗

arXiv2013

About an H-theorem for systems with non-conservative interactions

We exhibit some arguments in favour of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term. Such a non-linear equation describing the evolution of the single particle probability $P_i(t)$ of being in state $i$ at time $t$, is a suitable model for granular gases and is indicated here as Boltzmann-Fokker-Planck (BFP) equation. The conjectured H-functional, which appears to be non-increasing, is $H_C(t)=\sum_i P_i(t) \ln P_i(t)/Π_i$ with $Π_i = \lim_{t \to \infty} P_i(t)$, in analogy with the H-functional of Markov processes. The extension to continuous states is straightforward. A simple proof can be given for the elastic BFP equation. A semi-analytical proof is also offered for the BFP equation for so-called inelastic Maxwell molecules. Other evidence is obtained by solving particular BFP cases through numerical integration or through "particle schemes" such as the Direct Simulation Monte Carlo.

cond-mat.stat-mech↗