P.-A. Lemieux

Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions

Dynamic light-scattering techniques provide noninvasive probes of diverse media, such as colloidal suspensions, granular materials, or foams. In homodyne photon correlation spectroscopy, the dynamical properties of the medium are extracted from the intensity autocorrelation g(2)(τ) of the scattered light by means of the Siegert relation g(2)(τ)=1+|〈E(0)E*(τ)〉|2/〈EE*〉2. This approach is unfortunately limited to systems where the electric field is a Gaussian random variable and thus breaks down when the scattering sites are few or correlated. We propose to extend the traditional analysis by introducing intensity correlation functions g(n) of higher order, which allow us both to detect non-Gaussian scattering processes and to extract information not available in g(2) alone. The g(n) are experimentally measured by a combination of a commercial correlator and a custom digital delay line. Experimental results for g(3) and g(4) are presented for both Gaussian and non-Gaussian light-scattering processes and compared with theoretical predictions.

From avalanches to fluid flow: A continuous picture of grain dynamics down a heap

Surface flows are excited by steadily adding spherical glass beads to the top of a heap. To simultaneously characterize the fast single-grain dynamics and the much slower collective intermittency of the flow, we extend photon-correlation spectroscopy via fourth-order temporal correlations in the scattered light intensity. We find that microscopic grain dynamics during an avalanche are similar to those in the continuous flow just above the transition. We also find that there is a minimum jamming time, even arbitrarily close to the transition.

Statistical mechanics of a gas-fluidized particle.

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.

Quasi-elastic light scattering for intermittent dynamics

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.

Angular distribution of diffusely backscattered light

We demonstrate that the angular distribution of light diffusely backscattered from an opaque slab depends not only on sample boundary reflectivity but also, in contrast to previous results for diffusely transmitted light, on the anisotropy of the scattering events. This influence of scattering anisotropy is modeled within diffusion theory by a discontinuity in the photon concentration at the source point that is proportional to the average cosine of the scattering angle. The resulting predictions are compared with random walk simulations and with measurements of transmitted and backscattered intensity versus angle for glass frits and aqueous suspensions of polystyrene spheres held in air or immersed in a water bath. Predicted distributions capture the features of experimental and simulation data to within 1% for the best case of high reflectivity and weak anisotropy and to within 10% for the worst case of low reflectivity and strong anisotropy.

Diffusing-wave spectroscopy for arbitrary geometries: numerical analysis by a boundary-element method

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.

Light scattering from superfluid fog

Abstract The dynamics of the droplets of superfluid 4 He fog created by an ultrasonic transducer are investigated using a laser scattering technique. Diffusing-wave spectroscopy probes the motion of the droplets, which is found to be ballistic for times shorter than a characteristic viscous time τ v =10 −5 s . The average relative velocity between the droplets is small compared to the velocity that the droplets are ejected from the surface into the fog, but increases proportionally to it.