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

On the role of electron-nucleus contact and microwave saturation in Thermal Mixing DNP

We have explored the manifold physical scenario emerging from a model of Dynamic Nuclear Polarization (DNP) via thermal mixing under the hypothesis of highly effective electron-electron interaction. When the electron and nuclear reservoirs are also assumed to be in strong thermal contact and the microwave irradiation saturates the target electron transition, the enhancement of the nuclear polarization is expected to be considerably high even if the irradiation frequency is set far away from the centre of the ESR line (as already observed by Borghini) and the typical polarization time is reduced on moving towards the boundaries of said line. More reasonable behaviours are obtained by reducing the level of microwave saturation or the contact between electrons and nuclei in presence of nuclear leakage. In both cases the function describing the dependency of the steady state nuclear polarization on the frequency of irradiation becomes sharper at the edges and the build up rate decreases on moving off-resonance. If qualitatively similar in terms of the effects produced on nuclear polarization, the degree of microwave saturation and of electron-nucleus contact has a totally different impact on electron polarization, which is of course strongly correlated to the effectiveness of saturation and almost insensitive, at the steady state, to the magnitude of the interactions between the two spin reservoirs. The likelihood of the different scenario is discussed in the light of the experimental data currently available in literature, to point out which aspects are suitably accounted and which are not by the declinations of thermal mixing DNP considered here.Comment: 15 pages, 7 figure