Anderson transition for elastic waves in three dimensions

We use two different fully vectorial microscopic models featuring nonresonant and resonant scattering, respectively, to demonstrate the Anderson localization transition for elastic waves in three-dimensional (3D) disordered solids. Critical parameters of the transition determined by finite-time and finite-size scaling analyses suggest that the transition belongs to the 3D orthogonal universality class. Similarities and differences between the elastic-wave and light scattering in strongly disordered media are discussed.Comment: A misprint in Eq. (21) was corrected. No other change

First-Order Transition in the Breakdown of Disordered Media

We study the approach to global breakdown in disordered media driven by increasing external forces. We first analyze the problem by mean-field theory, showing that the failure process can be described as a first-order phase transition, similarly to the case of thermally activated fracture in homogeneous media. Then we quantitatively confirm the predictions of the mean-field theory using numerical simulations of discrete models. Widely distributed avalanches and the corresponding mean-field scaling are explained by the long-range nature of elastic interactions. We discuss the analogy of our results to driven disordered first-order transitions and spinodal nucleation in magnetic systems.Comment: 4 RevTeX pages, 3 postscript figure

Bi-functional nonlinearities in monodisperse ZnO nano-grains - Self-consistent transport and random lasing

We report a quantum field theoretical description of light transport and random lasing. The Bethe-Salpeter equation is solved including maximally crossed diagrams and non-elastic scattering. This is the first theoretical framework that combines so called off-shell scattering and lasing in random media. We present results for the self-consistent scattering mean free path that varies over the width of the sample. Further we discuss the density dependent correlation length of self-consistent transport in disordered media composed of semi-conductor Mie scatterers.Comment: AIP (accepted

Static and Dynamic Properties of Inhomogeneous Elastic Media on Disordered Substrate

The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of a $D$-dimensional random manifold embedded in $(D+D)$-dimensions. The analogy is found to be very robust, applicable to a wide range of elastic media, including those which are amorphous or nearly-periodic, with local or nonlocal elasticity. Also demonstrated explicitly is the equivalence between the dynamic depinning transition obtained at a constant driving force, and the self-organized, near-critical behavior obtained by a (small) constant velocity drive.Comment: 20 pages, RevTeX. Related (p)reprints also available at http://matisse.ucsd.edu/~hwa/pub.htm

From depinning transition to plastic yielding of amorphous media: A soft modes perspective

A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a d + 1 dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic deformation of amorphous media can be regarded as the motion of an elastic manifold in a disordered landscape. While the associated depinning transition leads to scaling properties, the quadrupolar Eshelby interactions at play in amorphous plasticity induce specific additional features like shear-banding and weak ergodicity breakdown. The latters are shown to be controlled by the existence of soft modes of the elastic interaction, the consequence of which is discussed in the context of depinning

Effect of Poisson ratio on cellular structure formation

Mechanically active cells in soft media act as force dipoles. The resulting elastic interactions are long-ranged and favor the formation of strings. We show analytically that due to screening, the effective interaction between strings decays exponentially, with a decay length determined only by geometry. Both for disordered and ordered arrangements of cells, we predict novel phase transitions from paraelastic to ferroelastic and anti-ferroelastic phases as a function of Poisson ratio.Comment: 4 pages, Revtex, 4 Postscript figures include

Variant Monte Carlo algorithm for driven elastic strings in random media

We discuss the non-local Variant Monte Carlo algorithm which has been successfully employed in the study of driven elastic strings in disordered media at the depinning threshold. Here we prove two theorems, which establish that the algorithm satisfies the crucial no-passing rule and that, after some initial time, the string exclusively moves forward. The Variant Monte Carlo algorithm overcomes the shortcomings of local methods, as we show by analyzing the depinning threshold of a single-pin problem.Comment: 6 pages, 2 figures, proceedings of Conference on Computational Physics, CCP2004 (Genova, Italy