X-ray diffraction of a disordered charge density wave

We study the X-ray diffraction spectrum produced by a collectively pinned charge density wave (CDW), for which one can expect a Bragg glass phase. The spectrum consists of two asymmetric divergent peaks. We compute the shape of the peaks, and discuss the experimental consequences.Comment: 5 pages, 2 figure

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

Universal width distributions in non-Markovian Gaussian processes

We study the influence of boundary conditions on self-affine random functions u(t) in the interval t/L \in [0,1], with independent Gaussian Fourier modes of variance ~ 1/q^{\alpha}. We consider the probability distribution of the mean square width of u(t) taken over the whole interval or in a window t/L \in [x, x+\delta]. Its characteristic function can be expressed in terms of the spectrum of an infinite matrix. This distribution strongly depends on the boundary conditions of u(t) for finite \delta, but we show that it is universal (independent of boundary conditions) in the small-window limit. We compute it directly for all values of \alpha, using, for \alpha<3, an asymptotic expansion formula that we derive. For \alpha > 3, the limiting width distribution is independent of \alpha. It corresponds to an infinite matrix with a single non-zero eigenvalue. We give the exact expression for the width distribution in this case. Our analysis facilitates the estimation of the roughness exponent from experimental data, in cases where the standard extrapolation method cannot be usedComment: 15 page

From microstructural features to effective toughness in disordered brittle solids

The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on planar crack propagation and describe the front evolution as the propagation of a long-range elastic line within a plane with random distribution of toughness. Our study reveals two regimes: in the collective pinning regime, the macroscopic toughness can be expressed as a function of a few parameters only, namely the average and the standard deviation of the local toughness distribution and the correlation lengths of the heterogeneous toughness field; in the individual pinning regime, the passage from micro to macroscale is more subtle and the full distribution of local toughness is required to be predictive. Beyond the failure of brittle solids, our findings illustrate the complex filtering process of microscale quantities towards the larger scales into play in a broad range of systems governed by the propagation of an elastic interface in a disordered medium.Comment: 7 pages, 4 figure

Effect of disorder geometry on the critical force in disordered elastic systems

We address the effect of disorder geometry on the critical force in disordered elastic systems. We focus on the model system of a long-range elastic line driven in a random landscape. In the collective pinning regime, we compute the critical force perturbatively. Not only our expression for the critical force confirms previous results on its scaling with respect to the microscopic disorder parameters, it also provides its precise dependence on the disorder geometry (represented by the disorder two-point correlation function). Our results are successfully compared to the results of numerical simulations for random field and random bond disorders.Comment: 18 pages, 7 figure