## Viscoelastic Interfaces Driven in Disordered Media: Applications to FrictionThis book offers an in-depth study of two well-known models of “avalanche” dynamics, modified minimally by the inclusion of relaxation. Many complex systems respond to continuous inputs of energy by accumulation of stress over time, interrupted by sudden energy releases called avalanches. The first model studied is the viscoelastic interface driven over disorder, which is shown to display the fundamental features of friction. In the mean-field limit, the friction force derived semi-analytically is compatible with laboratory experiments (displaying both velocity weakening and contact aging). In two dimensions, large-scale numerical simulations are in good agreement with the basic features of real earthquakes (Gutenberg-Richter Law, aftershock migration). The second model is a non-Markovian variant of Directed Percolation, in which we observe that the universality class is only partly modified by relaxation, a promising finding with respect to our first model. |

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### Contents

1 | |

7 | |

3 Application of Friction to Seismic Faults | 49 |

4 Elastic Interfaces Driven in Disordered Media | 67 |

5 Viscoelastic Interfaces Driven in Disordered Media | 113 |

A NonMarkovian Variant | 167 |

7 General Perspectives | 191 |

Appendix A
Additional Proofs and Heuristics | 193 |

### Other editions - View all

Viscoelastic Interfaces Driven in Disordered Media: Applications to Friction François P. Landes No preview available - 2015 |

Viscoelastic Interfaces Driven in Disordered Media: Applications to Friction François P. Landes No preview available - 2016 |

### Common terms and phrases

active aftershocks asperities avalanche average behaviour block Brownian Motion cellular automaton characteristic earthquakes consider constant correlation corresponds critical critical exponents dashpots decrease defined deformation depends depinning model depinning transition dimensions disorder distribution DP process driving dynamics earthquakes effect elastic depinning elastic interface equation evolution exponents ferromagnetic finite fracture friction law fthi function geophysics granular materials Gutenberg-Richter law increase infinitesimal interactions jump Langevin equation Laplacian lattice length scales main shock mean field mechanisms microscopic motion neighbours numerical observed oscillations parameters phase transition plastic power-law psubs purely elastic quenched disorder random regime relaxation relevant roughness RSF laws scaling relations Sect seismic faults self-affine Self-Organized Criticality shear simple simulations sliding slip solid Springer static friction stationary statistical stick-slip stress drop surface tectonic plates term threshold trigger universality class variable viscoelastic interface zero