Large scale numerical simulations of "ultrametric" long-range depinning

Abstract

The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for a drastic reduction of the numerical complexity of the problem. Based on large scale simulations, two to three orders of magnitude larger than previously considered, we obtain a very precise determination of critical exponents which are shown to be indistinguishable from their Euclidean metric counterparts. Moreover the scaling functions are shown to be unchanged. The choice of an ultrametric distance thus does not affect the universality class of the depinning transition and opens the way to an analytic real space renormalization group approach.

arXiv commentsubmitted to Phys. Rev. E

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Cited by in corpus (8)

• Crack propagation through phase separated glasses: effect of the characteristic size of disorder
• Depinning exponents of the driven long-range elastic string
• Universal depinning force fluctuations of an elastic line: Application to finite temperature behavior
• Cracks in random brittle solids: From fiber bundles to continuum mechanics
• Geometry of Gaussian signals
• Material-independent crack arrest statistics: Application to indentation experiments
• Universal width distributions in non-Markovian Gaussian processes
• Kinetic roughening of a soft dewetting line under quenched disorder - a numerical study