Large-scale numerical simulations of ultrametric long-range depinning

Random systems in ultrametric spaces

We discuss percolation and random walks in a class of homogeneous ultrametric spaces together with similarities and differences in ultrametric and Euclidean spaces. We briefly outline the role of these models in the study of interacting systems. Several open problems are presented.

Kinetic roughening of a soft dewetting line under quenched disorder: A numerical study

An elegant simulation method, suitable for investigating the dewetting dynamics of thin and viscous liquid layers, is discussed. The efficiency of the method is exemplified by studying a two-parameter depinninglike model defined on inhomogeneous solid surfaces. The morphology and the statistical properties of the contact line are mapped in the relevant parameter space, and as a result critical behavior in the vicinity of the depinning transition is revealed. The model allows for the tearing of the layer, which leads to a new propagation regime resulting in nontrivial collective behavior. The large deformations observed for the interface are a result of the interplay between the substrate inhomogeneities and the capillary forces.

Crack propagation through phase-separated glasses: effect of the characteristic size of disorder

We perform fracture experiments on nanoscale phase-separated glasses and measure crack surface roughness by atomic force microscopy. The ability of tuning the phase domain size by thermal treatment allows us to test thoroughly the predictions of crack front depinning models about the scaling properties of crack surface roughness. It appears that, in the range of validity of these depinning models developed for the fracture of brittle materials, our experimental results show a quantitative agreement with theoretical predictions: Beyond the characteristic size of disorder, the roughness of crack surfaces obeys the logarithmic scaling early predicted by Ramanathan, Ertaş, and Fisher [Phys. Rev. Lett. 79, 873 (1997)].

Universal depinning force fluctuations of an elastic line: application to finite temperature behavior

The depinning of an elastic line in a random medium is studied via an extremal model. The latter gives access to the instantaneous depinning force for each successive conformation of the line. Based on conditional statistics the universal and nonuniversal parts of the depinning force distribution can be obtained. In particular the singular behavior close to a (macroscopic) critical threshold is obtained as a function of the roughness exponent of the front. We show, moreover, that the advance of the front is controlled by a very tenuous set of subcritical sites. Extension of the extremal model to a finite temperature is proposed, the scaling properties of which can be discussed based on the statistics of depinning force at zero temperature. In particular a new temperature-dependent correlation length is shown to become relevant.