Roger Maynard

Imaging of dynamic heterogeneities in multiple-scattering media

A new method of visualizing objects with distinct internal dynamics of the constituent scattering particles embedded in a liquid multiple-scattering medium is presented. We report dynamic multiple-light-scattering experiments and a theoretical model, based on diffusing photon-density waves for concentrated colloidal suspensions in Brownian motion, as a background medium into which is inserted a capillary containing (i) the same suspension under flow, or (ii) suspensions of different particle sizes in Brownian motion. These model objects, with purely dynamic but no static scattering contrast, can be visualized by space-resolved measurements of the time autocorrelation function g2(t) of the scattered light intensity at the sample surface. Maximum contrast occurs at a parameter-dependent finite correlation time t. The physical origin of this effect is outlined. Our data are in excellent quantitative agreement with the model, with no adjustable parameter.

Diffusing wave spectroscopy in inhomogeneous flows

A theoretical study of the time-dependent correlation function of the multiply scattered light in laminar and stationary flow is presented. We study an inhomogeneous system of flow, i.e. when the strain tensor σij(r) depends on the space variables. Since in such flows the dephasing of light is space dependent, we introduce the useful function of the local density distribution of diffusion paths. We show that the time-dependent correlation function C1(t) of the scattered field is sensitive to the root mean square of velocity gradients weighted by the cloud of diffusive light paths. We establish a general formulation of C1(t) for laminar and stationary flow in the weak scattering limit kl ⪢ 1. The effects of the dimension of the inhomogeneous system and of the boundary conditions are also discussed. These results are applied to the cases of an infinitely thin and continuous sheet of vorticity, of a Rankine vortex, and of a Gaussian shaped velocity gradient.

Derivation of Lévy-type anomalous superdiffusion from generalized statistical mechanics

The robustness and ubiquity of the macroscopic normal diffusion is well known to be derivable within Boltzmann-Gibbs statistical mechanics. It is essentially founded on (i) a variational principle applied to S = − fdxp(x)ln[p(x)] with simple a priori constraints, and (ii) the central limit theorem. Its basic characterization consists in the time evolution ∝t. A recently generalized statistical mechanics enables the extension of the same program in order to also cover the long-tail Levy-like anomalous superdiffusion, a phenomenon frequently encountered in Nature. By so doing, this formalism succeeds where standard statistical mechanics and thermodynamics are known to fail.

Polarization Statistics in Multiple Scattering of Light: A Monte Carlo Approach

The statistics of the depolarization of light by multiple scattering is a complex problem in the regime of Mie scattering. Nevertheless, the correlation functions (Stokes intensities) can be entirely determined by studying the loss of memory of both initial linear and circular polarizations as a function of the thickness of a slab (L) in units of the transport mean free path (l*).

Superconductivity pairing induced by two level systems in amorphous metals

Abstract From the standard interaction between electrons and two level systems a superconductive pairing is envisaged. The solutions of the Eliashberg equations for the critical temperature as well as the zero temperature gap lead to expressions as exp (−1/√ λ 0 ) instead of exp (−1/ λ 0 ) in the BCS case, which enhances considerably the superconducting properties in the weak coupling case.

Elastic and thermal properties of hierarchical structures: Application to silica aerogels

Scaling laws of the elastic constant as a function of density are obtained for a hierarchical structure built up with micro-rods of various size. Spectral density and dimension as well as thermal conductivity are deduced from the structural and elastic parameters. The related properties of silica aerogels are well described within this model.

ANHARMONIC VIBRATIONS IN ORDERED AND DISORDERED ONE- AND TWO-DIMENSIONAL SYSTEMS

We present extensive results of computer simulations on vibrations in one- and two-dimensional lattices with quartic anharmonicity. The existence of localized mode in ordered lattice is confirmed but the long term stability is questionable. Rather our results indicate an ergodic behavior at large times when several modes are present. Concerning disordered systems we have found that anharmonicity leads to a surprising new phenomenon of anomalous diffusion and thus to the possibility of anharmonically induced transport.

On the geometrical interpretation of fraction and fractal dimensionality

Abstract We suggest that vibrations in generic fractals, when discussed in terms of Fourier-transformed components, present a third regime in addition to the well-known phonon and fracton ones.

Diffuse Waves in Nonlinear Disordered Media

The field of multiple scattering of classical waves (electromagnetic, acoustic and elastic waves, etc.) in disordered media has revived in the eighties [1]– [6], when the far-reaching analogies between the diffuse transport of waves and electrons in mesoscopic systems have been realized (see Ref. [7] for a comprehensive review of the latter issue). Using classical waves to study such phenomena as weak and strong localization, mesoscopic correlations and universal conductance fluctuations (see Refs. [8]–[10] for reviews) appears to be advantageous in many aspects: no need for low temperatures and small samples, better control of the experimental apparatus, possibility of more sensitive measurements, etc. In addition, experiments with classical waves can be readily performed in the linear regime, excluding interaction between scattered waves and hence simplifying the interpretation of experimental data, whereas the electron-electron interaction is always present in the realm of mesoscopic electronics and cannot simply be ‘turned off’, introducing significant difficulties in the theoretical model [11].

The role of the step length distribution in wave-diffusion

Abstract We discuss the relation between two standard approaches applied to diffusion in the presence of anisotropic scattering. The diffusion constant obtained from the Boltzmann equation is different from that obtained by a random walk model with fixed step length. By varying the step length according to a Lambert-Beer law we recover the Boltzmann result.