Giacomo Gradenigo

Brownian ratchet in a thermal bath driven by Coulomb friction.

The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical nonequilibrium 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 submicrometer Brownian motors in an equilibrium fluid, based purely upon nanofriction.

Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids

There is a certain consensus that the very fast growth of the relaxation time tau occurring in glass-forming liquids on lowering the temperature must be due to the thermally activated rearrangement of correlated regions of growing size. Even though measuring the size of these regions has defied scientists for a while, there is indeed recent evidence of a growing correlation length xi in glass formers. If we use Arrhenius law and make the mild assumption that the free-energy barrier to rearrangement scales as some power psi of the size of the correlated regions, we obtain a relationship between time and length, T log tau approximately xi(psi). According to both the Adam-Gibbs and the random first order theory the correlation length grows as xi approximately (T-T(k))(-1/(d-theta)), even though the two theories disagree on the value of theta. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents psi and theta through the relationship T log tau approximately (T-T(k))(-psi/(d-theta)). Despite a few theoretical speculations, up to now there has been no experimental determination of these two exponents. Here we measure them numerically in a model glass former, finding psi=1 and theta=2. Surprisingly, even though the values we found disagree with most previous theoretical suggestions, they give back the well-known VFT law for the relaxation time, T log tau approximately (T-T(k))(-1).

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: fluctuations of this field introduce a new time scale with its associated length scale. Such identification allows us to measure the intruders fluctuating entropy production as a function of V and U, obtaining a neat verification of the fluctuation relation.

Fluctuating hydrodynamics and correlation lengths in a driven granular fluid

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%. The hydrodynamic noise is the sum of the external noise due to the bath and the internal one due to collisions. Only the latter is assumed to satisfy the fluctuation-dissipation relation with the average granular temperature. The static velocity structure factors and display a general non-constant behavior with two plateaux at large and small k, representing the granular temperature Tg and the bath temperature Tb > Tg 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 behavior of dynamical structure factors, the decay of which becomes slower and slower at increasing density.

Phase-Separation Perspective on Dynamic Heterogeneities in Glass-Forming Liquids

We study dynamic heterogeneities in a model glass former whose overlap with a reference configuration is constrained to a fixed value. We find that the system phase separates into regions of small and large overlap, indicating that a nonzero surface tension plays an important role in the formation of dynamical heterogeneities. We calculate an appropriate thermodynamic potential and find evidence of a Maxwell construction consistent with a spinodal decomposition of two phases. Our results suggest that even in standard, unconstrained systems dynamic heterogeneities are the expression of an ephemeral phase-separating regime ruled by a finite surface tension.

Confinement as a tool to probe amorphous order.

We study the effect of confinement on glassy liquids using random first order transition theory as a framework. We show that the characteristic length scale above which confinement effects become negligible is related to the point-to-set length scale introduced to measure the spatial extent of amorphous order in supercooled liquids. By confining below this characteristic size, the system becomes a glass. Eventually, for very small sizes, the effect of the boundary is so strong that any collective glassy behavior is wiped out. We clarify similarities and differences between the physical behaviors induced by confinement and by pinning particles outside a spherical cavity (the protocol introduced to measure the point-to-set length). Finally, we discuss possible numerical and experimental tests of our predictions.

Evidence for a spinodal limit of amorphous excitations in glassy systems

What is the origin of the sharp slowdown displayed by glassy systems? Physical common sense suggests there must be a concomitant growing correlation length, but finding this length has been nontrivial. In random first-order theory, it is given by the size of amorphous excitations, which depends on a balance between their mutual interfacial energy and their configurational entropy. But how these excitations disappear when crossing over to the normal high temperature phase is unclear, chiefly due to lack of data about the surface tension. We measure the energy cost for creating amorphous excitations in a model glass-former, and discover that the surface tension vanishes at a well-defined spinodal energy, above which amorphous excitations cannot be sustained. This spinodal therefore marks the true onset of glassiness.C. Cammarota, 2 A. Cavagna, 3 G. Gradenigo, 5 T. S. Grigera, 7, 8 and P. Verrocchio 5, 9 Dipartimento di Fisica, Università di Roma “La Sapienza”. Centre for Statistical Mechanics and Complexity (SMC), CNR-INFM. Istituto Sistemi Complessi (ISC), CNR, Via dei Taurini 19, 00185 Roma, Italy. Dipartimento di Fisica, Università di Trento, via Sommarive 14, 38050 Povo, Trento, Italy. INFM CRS-SOFT, c/o Università di Roma “La Sapienza”, 00185, Roma, Italy. Instituto de Investigaciones Fisicoqúımicas Teóricas y Aplicadas (INIFTA). Departamento de F́ısica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, 1900 La Plata, Argentina. CCT La Plata, Consejo Nacional de Investigaciones Cient́ıficas y Técnicas, Argentina. Instituto de Biocomputación y F́ısica de Sistemas Complejos (BIFI), Spain.

Einstein relation in superdiffusive systems

We study the Einstein relation between diffusion and response to an external field in systems showing superdiffusion. In particular, we investigate a continuous time Levy walk where the velocity remains constant for a time τ with distribution Pτ(τ) ~ τ−g. At varying g the diffusion can be standard or anomalous; in spite of this, if in the unperturbed system a current is absent, the Einstein relation holds. In the case where a current is present the scenario is more complicated and the usual Einstein relation fails. This suggests that the main ingredient for the breaking of the Einstein relation is not the anomalous diffusion but the presence of a mean drift (current).

Entropy production in non-equilibrium fluctuating hydrodynamics

Fluctuating entropy production is studied for a set of linearly coupled complex fields. The general result is applied to non-equilibrium fluctuating hydrodynamic equations for coarse-grained fields (density, temperature, and velocity), in the framework of model granular fluids. We find that the average entropy production, obtained from the microscopic stochastic description, can be expressed in terms of macroscopic quantities, in analogy with linear non-equilibrium thermodynamics. We consider the specific cases of driven granular fluids with two different kinds of thermostat and the homogeneous cooling regime. In all cases, the average entropy production turns out to be the product of a thermodynamic force and a current: the former depends on the specific energy injection mechanism, the latter takes always the form of a static correlation between fluctuations of density and temperature time-derivative. Both vanish in the elastic limit. The behavior of the entropy production is studied at different length scales and the qualitative differences arising for the different granular models are discussed.

The ratchet effect in an ageing glass

We study the dynamics of an asymmetric intruder in a glass-former model. At equilibrium, the intruder diffuses with average zero velocity. After an abrupt quench to T deeply under the mode-coupling temperature, a net average drift is observed, steady on a logarithmic time scale. The phenomenon is well reproduced in an asymmetric version of the Sinai model. The sub-velocity of the intruder grows with Teff /T ,w hereTeff is defined by the response-correlation ratio, corresponding to a general behavior of thermal ratchets when in contact with two thermal reservoirs.