G. D'Anna

Observing brownian motion in vibration-fluidized granular matter

Observation of the rotational brownian motion of a very fine wire immersed in a gas led to one of the most important ideas of equilibrium statistical mechanics. Namely, the many-particle problem of a large number of molecules colliding with the wire can be represented by just two macroscopic parameters: viscosity and temperature. Interest has arisen in the question of whether this idea (mathematically developed in the Langevin model and the fluctuation-dissipation theorem) can also be used to describe systems that are far from equilibrium. Here we report an experimental investigation of an archetypal non-equilibrium system, involving a sensitive torsion oscillator immersed in a granular system of millimetre-size grains that are fluidized by strong external vibrations. The vibro-fluidized granular medium is a driven environment, with continuous injection and dissipation of energy, and the immersed oscillator can be seen as analogous to an elastically bound brownian particle. By measuring the noise and the susceptibility, we show that the experiment can be treated (to a first approximation) with the equilibrium formalism. This gives experimental access to a granular viscosity and an effective temperature; however, these quantities are anisotropic and inhomogeneous. Surprisingly, the vibro-fluidized granular matter behaves as a ‘thermal’ bath satisfying a fluctuation-dissipation relation.

The jamming route to the glass state in weakly perturbed granular media.

It has been suggested that a common conceptual framework known as ‘jamming’ (refs 1 and 2) may be used to classify a wide variety of physical systems; these include granular media, colloidal suspensions and glass-forming liquids, all of which display a critical slowdown in their dynamics before a sudden transition to an amorphous rigid state. Decreasing the relevant control parameter (such as temperature, drive or inverse density) may cause geometrical constraints to build up progressively and thus restrict the accessible part of the systems phase space. In glass-forming liquids (thermal molecular systems), jamming is provided by the classical vitrification process of supercooling, characterized by a rapidly increasing and apparently diverging viscosity at sufficiently low temperatures. In driven (athermal) macroscopic systems, a similar slowdown has been predicted to occur, notably in sheared foam or vibrated granular media. Here we report experimental evidence for dynamic behaviour, qualitatively analogous to supercooling, in a driven granular system of macroscopic millimetre-size particles. The granular medium is perturbed by isolated tapping or continuous vibration, with the perturbation intensity serving as a control parameter. We observe the random deflection of an immersed torsion oscillator that moves each time the grains rearrange, like a ‘thermometer’ sensing the granular noise. We caution that our granular analogy to supercooling is based on similarities in the dynamical behaviour, rather than quantitative theory.

Nonlinear AC susceptibility, surface and bulk shielding

Abstract We calculate the nonlinear AC response of a thin superconducting strip in perpendicular field, shielded by an edge current due to the geometrical barrier. A comparison with the results for infinite samples in parallel field, screened by a surface barrier, and with those for screening by a bulk current in the critical state, shows that the AC response due to a barrier has general features that are independent of geometry, and that are significantly different from those for screening by a bulk current in the critical state. By consequence, the nonlinear (global) AC susceptibility can be used to determine the origin of magnetic irreversibility. A comparison with experiments on a Bi 2 Sr 2 CaCu 2 O 8+δ crystal shows that in this material, the low-frequency AC screening at high temperature is mainly due to the screening by an edge current, and that this is the unique source of the nonlinear magnetic response at temperatures above 40 K.

Anisotropy of perpendicular field penetration into high-Tc superconductors induced by strong longitudinal field

Abstract The geometry of penetration of a magnetic field oriented perpendicular to the surface of a superconductor is changed by the presence of a longitudinal field. This is studied directly by means of the magneto-optical technique in different high-Tc materials. In YBa2Cu3O7 single crystals Brandts mode of magnetization is observed, namely, penetration of an AC field only along the longitudinal field even if the corresponding dimension of the sample is much longer than the other two. This anisotropy is the evidence that the force-free configuration of current and vortices cannot be destroyed by cutting and reconnection of the vortices in this 3D superconductor. On the contrary, the absence of the induced anisotropy in Bi2Sr2CaCu2O8 single crystals reveals the independence of pancake vortices in CuO layers from longitudinal field which makes a realization of the force-free configuration impossible in the layered 2D superconductor. An intermediate effect in thin films indicates that vortices are almost normal to the film surface even if the applied field is nearly parallel to it. The described experiment can be used as a new tool to study the internal vortex structure in superconductors.

Extreme events-driven glassy behaviour in granular media

Motivated by recent experiments on the approach to jamming of a weakly forced granular medium using an immersed torsion oscillator (Nature, 413 (2001) 407), we propose a simple model which relates the microscopic dynamics to macroscopic rearrangements and accounts for the following experimental facts: 1) the control parameter is the spatial amplitude of the perturbation and not its reduced peak acceleration; 2) a Vogel-Fulcher-Tammann–like form for the relaxation time. The model draws a parallel between macroscopic rearrangements in the system and extreme events whose probability of occurrence (and thus the typical relaxation time) is estimated using extreme-value statistics. The range of validity of this description in terms of the control parameter is discussed as well as the existence of other regimes.

Observing Brownian motion and measuring temperatures in vibration-fluidized granular matter

Understanding the behaviour of granular media, either at rest or moving under external driving, is a difficult task, although it is important and of very practical interest. Describing the motion of each individual grain is complicated, not only because of the large number of grains, but also because the mechanisms of interaction at the grain level involve complex contact forces. One would like to have, in fact, a description in terms of a few macroscopic quantities. Since a granular medium resembles a liquid or a gas when strongly vibrated or when flowing out of a container, a natural approach is to adopt usual equilibrium statistical mechanics tools in order to test if such a macroscopic description is possible. In other words, an interesting question is to investigate whether one can model granular media, when close to a liquid-like state for example, using viscosity, temperature, and so on, as one does for normal liquids. With this aim in view, we have developed a non-equilibrium version of the classical Brownian motion experiment. In particular, we have observed the motion of a torsion oscillator immersed in an externally vibrated granular medium of glass spheres, and have collected evidence that the motion is Brownian-like. An approximate fluctuation–dissipation relation holds, and we can define temperature-like and viscosity-like parameters.

Hall Anomaly and Vortex-Lattice Melting in Superconducting Single Crystal YBa 2 Cu 3 O 7 − δ

Subnanovolt resolution longitudinal and Hall voltages are measured in an ultrapure YBa2Cu3O7−δ single crystal. The Hall anomaly and the first-order vortex-lattice melting transition are observed simultaneously. Changes in the dynamic behavior of the vortex solid and liquid are correlated with features of the Hall conductivity σxy. With the magnetic field oriented at an angle from the twin boundaries, the Hall conductivity sharply decreases toward large negative values at the vortex-lattice melting transition.

Vibration-induced jamming transition in granular media.

The quasistatic frequency response of a granular medium is measured by a forced torsion oscillator method, with forcing frequency f(p) in the range 10(-4) Hz to 5 Hz, while weak vibrations at high-frequency f(s), in the range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of vibration Gamma is below the fluidization limit. A loss factor peak is observed in the oscillator response as a function of Gamma or f(p). In a plot of ln f(p) against 1/Gamma, the position of the peak follows an Arrhenius-like behavior over four orders of magnitude in f(p). The data can be described as a stochastic hopping process involving a probability factor exp(-Gamma(j)/Gamma) with Gamma(j) a f(s)-dependent characteristic vibration intensity. An f(s)-independent description is given by exp(-tau(j)/tau), with tau(j) an intrinsic characteristic time, and tau=Gamma(n)/2pif(s), n=0.5-0.6, an empirical control parameter with unit of time. tau is seen as the effective average time during which the perturbed grains can undergo structural rearrangement. The loss factor peak appears as a crossover in the dynamic behavior of the vibrated granular system, which, at the time scale 1/f(p), is solid-like at low Gamma, and the oscillator is jammed into the granular material, and is fluid-like at high Gamma, where the oscillator can slide viscously.

Pinning in the flux-line-cutting regime of Bi2Sr2Ca1Cu2O8 single crystals at high field

Abstract Using a low-frequency torsion pendulum we show that in a Bi2Sr2Ca1Cu2O8 single crystal the irreversibility line Birr(T) is frequency dependent down to 10-5 Hz in the high-field regime. The activation energy has a logarithmic field dependence, U0(B)=U∗ 1n(B∗/B). A microscopic model for flux-line-cutting and pancake collision yields quantitative expressions for U0 and for Birr(T)=B∗ exp(−T/T∗), which reproduce the experimental data very well.

Edge-shape barrier irreversibility and decomposition of vortices in Bi2Sr2CaCu2O8

Abstract Magnetic flux dynamics is studied in Bi 2 Sr 2 CaCu 2 O 8 single crystals by means of magneto-optical technique. It is clearly demonstrated that the magnetic irreversibility of these crystals in a magnetic field perpendicular to the basal plane at temperatures higher than approximately 35 K is governed by an edge-shape barrier and its disappearance determines the high temperature part of the magnetic irreversibility line which is commonly associated in the literature with vortex lattice melting. We argue that this barrier exists because of the non ellipsoidal shape of the samples and can disappear only when the flux lines lose their rigidity decomposing into pancakes, which is the only true magnetic phase transition on the B-T diagram for Bi 2 Sr 2 CaCu 2 O 8 .