61 research outputs found
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 with a spontaneous local velocity field
in the surrounding fluid. Such identification allows us to measure the
intruder's fluctuating entropy production as a function of and ,
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
Fourier's Law in a Generalized Piston Model
A simplified, but non trivial, mechanical model -- gas of particles of
mass in a box partitioned by mobile adiabatic walls of mass --
interacting with two thermal baths at different temperatures, is discussed in
the framework of kinetic theory. Following an approach due to Smoluchowski,
from an analysis of the collisions particles/walls, we derive the values of the
main thermodynamic quantities for the stationary non-equilibrium states. The
results are compared with extensive numerical simulations; in the limit of
large , and , we find a good approximation of
Fourier's law.Comment: 14 pages, 5 figure
Fluctuations of two-time quantities and non-linear response functions
We study the fluctuations of the autocorrelation and autoresponse functions
and, in particular, their variances and co-variance. In a first general part of
the Article, we show the equivalence of the variance of the response function
with the second-order susceptibility of a composite operator, and we derive an
equilibrium fluctuation-dissipation theorem beyond-linear order relating it to
the other variances. In a second part of the paper we apply the formalism to
the study to non-disordered ferromagnets, in equilibrium or in the coarsening
kinetics following a critical or sub-critical quench. We show numerically that
the variances and the non-linear susceptibility obey scaling with respect to
the coherence length in equilibrium, and with respect to the growing
length after a quench, similarly to what is known for the
autocorrelation and the autoresponse functions.Comment: 21 pages, 5 figures. To appear on Jsta
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" and with the internal granular one, ,
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 ,
growing with density, that characterizes order in the velocity field.Comment: 5 pages, 4 figure
Fluctuation-dissipation relations and field-free algorithms for the computation of response functions
We discuss the relation between the fluctuation-dissipation relation derived
by Chatelain and Ricci-Tersenghi [C.Chatelain, J.Phys. A {\bf 36}, 10739
(2003); F. Ricci-Tersenghi, Phys.Rev.E 68, 065104(R) (2003)] and that by
Lippiello-Corberi-Zannetti [E. Lippiello, F. Corberi and M. Zannetti Phys. Rev.
E {\bf 72}, 056103 (2005)]. In order to do that, we re-derive the
fluctuation-dissipation relation for systems of discrete variables evolving in
discrete time via a stochastic non-equilibrium Markov process. The calculation
is carried out in a general formalism comprising the Chatelain, Ricci-Tersenghi
result and that by Lippiello-Corberi-Zannetti as special cases. The
applicability, generality, and experimental feasibility of the two approaches
is thoroughly discussed. Extending the analytical calculation to the variance
of the response function we show the vantage of field-free numerical methods
with respect to the standard method where the perturbation is applied. We also
show that the signal to noise ratio is better (by a factor ) in the
algorithm of Lippiello-Corberi-Zannetti with respect to that of Chatelain-Ricci
Tersenghi.Comment: 17 pages, 5 figures. To appear in Phys. Rev.
Nonequilibrium fluctuations and enhanced diffusion of a driven particle in a dense environment
We study the diffusion of a tracer particle driven out-of-equilibrium by an
external force and traveling in a dense environment of arbitrary density. The
system evolves on a discrete lattice and its stochastic dynamics is described
by a master equation. Relying on a decoupling approximation that goes beyond
the naive mean-field treatment of the problem, we calculate the fluctuations of
the position of the tracer around its mean value on a lattice of arbitrary
dimension, and with different boundary conditions. We reveal intrinsically
nonequilibrium effects, such as enhanced diffusivity of the tracer induced both
by the crowding interactions and the external driving. We finally consider the
high-density and low-density limits of the model and show that our
approximation scheme becomes exact in these limits
Stochastic Thermodynamics of an Electromagnetic Energy Harvester
We study the power extracted by an electromagnetic energy harvester driven by broadband vibrations. We describe the system with a linear model, featuring an underdamped stochastic differential equation for an effective mass in a harmonic potential, coupled electromechanically with the current in the circuit. We compare the characteristic curve (power vs. load resistance) obtained in experiments for several values of the vibration amplitude with the analytical results computed from the model. Then, we focus on a more refined analysis, taking into account the temporal correlations of the current signal and the fluctuations of the extracted power over finite times. We find a very good agreement between the analytical predictions and the experimental data, showing that the linear model with effective parameters can describe the real system, even at the fine level of fluctuations. Our results could be useful in the framework of stochastic thermodynamics applied to energy harvesting systems
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