ABSTRACT: The rectification of unbiased fluctuations, also known as the ratchet effect,
is normally obtained under statistical non-equilibrium conditions. Here we
propose a new ratchet mechanism where a thermal bath solicits the random
rotation of an asymmetric wheel, which is also subject to Coulomb friction due
to solid-on-solid contacts. Numerical simulations and analytical calculations
demonstrate a net drift induced by friction. If the thermal bath is replaced by
a granular gas, the well known granular ratchet effect also intervenes,
becoming dominant at high collision rates. For our chosen wheel shape the
granular effect acts in the opposite direction with respect to the
friction-induced torque, resulting in the inversion of the ratchet direction as
the collision rate increases. We have realized a new granular ratchet
experiment where both these ratchet effects are observed, as well as the
predicted inversion at their crossover. Our discovery paves the way to the
realization of micro and sub-micrometer Brownian motors in an equilibrium
fluid, based purely upon nano-friction.
Physical Review Letters 03/2013; 110:120601. · 7.37 Impact Factor
ABSTRACT: The effect of Coulomb friction is studied in the framework of collisional
ratchets. It turns out that the average drift of these devices can be expressed
as the combination of a term related to the lack of equipartition between the
probe and the surrounding bath, and a term featuring the average frictional
force. We illustrate this general result in the asymmetric Rayleigh piston,
showing how Coulomb friction can induce a ratchet effect in a Brownian particle
in contact with an equilibrium bath. An explicit analytical expression for the
average velocity of the piston is obtained in the rare collision limit.
Numerical simulations support the analytical findings.
ABSTRACT: We prove that, in particular regimes of a broad class of continuous time
random walks, a small external field can turn diffusion from standard into
anomalous. We illustrate our findings in the trap model, a prototype of
subdiffusion in disordered and glassy materials, and in the L\'evy walk
process, which describes superdiffusion within inhomogeneous media. For both
models, in the presence of an external field, rare events induce a singular
behavior in the originally Gaussian displacements distribution, giving rise to
power-law tails. Remarkably, in the subdiffusive trap model, the combined
effect of highly fluctuating waiting times and of a drift yields a non-Gaussian
distribution characterized by long spatial tails and strong anomalous
ABSTRACT: We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field E and collides, elastically or inelastically, with a bath of particles at temperature T. We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production Δs(tot). One is the entropy production of the medium Δs(m), which is equal to the energy exchanged with the scatterers, divided by a parameter θ, coinciding with the particle temperature at E=0. The other is the work W done by the external field, again rescaled by θ. At small E, a good collapse of the two distributions is found: in this case, the two quantities also verify the fluctuation relation (FR), indicating that both are good approximations of Δs(tot). Differently, for large values of E, the fluctuations of W violate the FR, while Δs(m) still verifies it.
Physical Review E 03/2012; 85(3 Pt 1):031112. · 2.26 Impact Factor
ABSTRACT: A massive intruder in a homogeneously driven granular fluid, in dilute
configurations, performs a memory-less Brownian motion with drag and
temperature simply related to the average density and temperature of the fluid.
At volume fraction $\sim 10-50%$ the intruder's velocity correlates with the
local fluid velocity field: such situation is approximately described by a
system of coupled linear Langevin equations equivalent to a generalized
Brownian motion with memory. Here one may verify the breakdown of the
Fluctuation-Dissipation relation and the presence of a net entropy flux - from
the fluid to the intruder - whose fluctuations satisfy the Fluctuation
ABSTRACT: Velocity and density structure factors are measured over a hydrodynamic range
of scales in a horizontal quasi-2d fluidized granular experiment, with packing
fractions $\phi\in[10%,40%]$. The fluidization is realized by vertically
vibrating a rough plate, on top of which particles perform a Brownian-like
horizontal motion in addition to inelastic collisions. On one hand, the density
structure factor is equal to that of elastic hard spheres, except in the limit
of large length-scales, as it occurs in the presence of an effective
interaction. On the other hand, the velocity field shows a more complex
structure which is a genuine expression of a non-equilibrium steady state and
which can be compared to a recent fluctuating hydrodynamic theory with
non-equilibrium noise. The temporal decay of velocity modes autocorrelations is
compatible with linear hydrodynamic equations with rates dictated by viscous
momentum diffusion, corrected by a typical interaction time with the
thermostat. Equal-time velocity structure factors display a peculiar shape with
a plateau at large length-scales and another one at small scales, marking two
different temperatures: the "bath" temperature $T_b$, depending on shaking
parameters, and the "granular" temperature $T_g<T_b$, which is affected by
collisions. The two ranges of scales are separated by a correlation length
which grows with $\phi$, after proper rescaling with the mean free path.
ABSTRACT: We study the stationary state of a one-dimensional kinetic model where a
probe particle is driven by an external field E and collides, elastically or
inelastically, with a bath of particles at temperature T. We focus on the
stationary distribution of the velocity of the particle, and of two estimates
of the total entropy production \Delta s_tot. One is the entropy production of
the medium \Delta s_m, which is equal to the energy exchanged with the
scatterers, divided by a parameter \theta, coinciding with the particle
temperature at E=0. The other is the work W done by the external field, again
rescaled by \theta. At small E, a good collapse of the two distributions is
found: in this case the two quantities also verify the Fluctuation Relation
(FR), indicating that both are good approximations of \Delta s_tot.
Differently, for large values of E, the fluctuations of W violate the FR, while
\Delta s_m still verifies it.
ABSTRACT: Velocity correlations in a quasi-2D driven granular fluid are studied in experiments and numerical simulations. The transverse velocity structure factor reveals two well-defined energy scales, associated with the external "bath temperature"Tb and with the internal granular one, Tg<Tb, 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.
EPL (Europhysics Letters) 09/2011; 96(1):14004. · 2.17 Impact Factor
ABSTRACT: Static and dynamical structure factors for shear and longitudinal modes of the velocity and density fields are computed for a granular system fluidized by a stochastic bath with friction. Analytical expressions are obtained through fluctuating hydrodynamics and are successfully compared with numerical simulations up to a volume fraction ∼ 50%. Hydrodynamic noise is the sum of external noise due to the bath and internal one due to collisions. Only the latter is assumed to satisfy the fluctuation-dissipation relation with the average granular temperature. Static velocity structure factors S ⊥ (k) and S (k) display a general non-constant behavior with two plateaux at large and small k, representing the granular temperature T g and the bath temperature T b > T g respectively. From this behavior, two different velocity correlation lengths are measured, both increasing as the packing fraction is raised. This growth of spatial order is in agreement with the behaviour of dynamical structure factors, the decay of which becomes slower and slower at increasing density.
ABSTRACT: The energy of a finite system thermally connected to a thermal reservoir may
fluctuate, while the temperature is a constant representing a thermodynamic
property of the reservoir. The finite system can also be used as a thermometer
for the reservoir. From such a perspective the temperature has an uncertainty,
which can be treated within the framework of estimation theory. We review the
main results of this theory, and clarify some controversial issues regarding
temperature fluctuations. We also offer a simple example of a thermometer with
a small number of particles. We discuss the relevance of the total observation
time, which must be much longer than the decorrelation time.
ABSTRACT: We study how the Einstein relation between spontaneous fluctuations and the
response to an external perturbation holds in the absence of currents, for the
comb model and the elastic single-file, which are examples of systems with
subdiffusive transport properties. The relevance of non-equilibrium conditions
is investigated: when a stationary current (in the form of a drift or an energy
flux) is present, the Einstein relation breaks down, as is known to happen in
systems with standard diffusion. In the case of the comb model, a general
relation, which has appeared in the recent literature, between the response
function and an unperturbed suitable correlation function, allows us to explain
the observed results. This suggests that a relevant ingredient in breaking the
Einstein formula, for stationary regimes, is not the anomalous diffusion but
the presence of currents driving the system out of equilibrium.
ABSTRACT: 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: fluctuations of this field introduce a new time scale with its associated length scale. 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.
EPL (Europhysics Letters) 11/2010; 92(3):34001. · 2.17 Impact Factor
ABSTRACT: We study the stochastic motion of an intruder in a dilute driven granular gas. All particles are coupled to a thermostat, representing the external energy source, which is the sum of random forces and a viscous drag. The dynamics of the intruder, in the large mass limit, is well described by a linear Langevin equation, combining the effects of the external bath and of the 'granular bath'. The drag and diffusion coefficients are calculated under a few assumptions, whose validity is well verified in numerical simulations. We also discuss the non-equilibrium properties of the intruder dynamics, as well as the corrections due to finite packing fraction or finite intruder mass.
Journal of Statistical Mechanics Theory and Experiment 04/2010; 2010(04):P04013. · 1.73 Impact Factor
ABSTRACT: We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and covariance. In a first general part of the paper, we show the equivalence of the variance of the response function to 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 in the study of 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 ξ in equilibrium, and with respect to the growing length L(t) after a quench, similar to what is known for the autocorrelation and the autoresponse functions.
Journal of Statistical Mechanics Theory and Experiment 03/2010; 2010(04):P04003. · 1.73 Impact Factor
ABSTRACT: We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which takes a similar form for systems governed by a master equation or by a Langevin equation, can be derived to every order, in large generality with respect to the considered model, in equilibrium and out of equilibrium as well. On the basis of the fluctuation dissipation relation we propose a particular response function, namely the second order susceptibility of the two-particle correlation function, as an effective quantity to detect and quantify cooperative effects in glasses and disordered systems. We test this idea by numerical simulations of the Edwards-Anderson model in one and two dimensions.