ABSTRACT
Characterization of the microscopic fluctuations in systems that are far from equilibrium is crucial for understanding the macroscopic response. One approach is to use an 'effective temperature'--such a quantity has been invoked for chaotic fluids, spin glasses, glasses and colloids, as well as non-thermal systems such as flowing granular materials and foams. We therefore ask to what extent the concept of effective temperature is valid. Here we investigate this question experimentally in a simple system consisting of a sphere placed on a fine screen in an upward flow of gas; the sphere rolls because of the turbulence it generates in the gas stream. In contrast to many-particle systems, in which it is difficult to measure and predict fluctuations, our system has no particle-particle interactions and its dynamics can be captured fully by video imaging. Surprisingly, we find that the sphere behaves exactly like a harmonically bound brownian particle. The random driving force and frequency-dependent drag satisfy the fluctuation-dissipation relation, a cornerstone of statistical mechanics. The statistical mechanics of near-equilibrium systems is therefore unexpectedly useful for studying at least some classes of systems that are driven far from equilibrium.
ABSTRACT
Dynamic light-scattering techniques provide noninvasive probes of diverse media such as colloidal suspensions, granular materials, and foams. Traditional analysis relies on the Gaussian properties of the scattering process found in most experimental situations and uses second-order intensity-correlation functions. This approach fails in the presence of, among other things, the collective intermittent dynamics found in systems such as granular materials. By extending the existing formalism and introducing higher-order intensity-correlation functions, we show how to detect and quantify the intrinsic dynamics and switching statistics of intermittent processes. We then explore two systems: (1) an auger-driven granular column for which the granular dynamics are controlled and the formalism is tested and (2) a granular heap whose dynamics are a priori unknown but may, now, be characterized.
ABSTRACT
We present a boundary-element-method numerical procedure that can be used to solve for the diffusion equation of the field autocorrelation function in any arbitrary geometry with various boundary and source properties. We use this numerical method to study finite-sized effects in a circular slab and the influence of the angle in a cone-plate geometry. The latter is also compared with exact analytical solutions obtained for an equivalent bidimensional geometry. In most cases the deviation from well-known predictions of the correlation function remains small.