Viscoelastic Interfaces Driven in Disordered Media and Applications to Friction
arXiv:1508.03548 · doi:10.1007/978-3-319-20022-4
Abstract
Many complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by sudden energy releases called avalanches. Recently, it has been pointed out that several basic features of avalanche dynamics are induced at the microscopic level by relaxation processes, which are neglected by most models. During my thesis, I studied two well-known models of avalanche dynamics, modified minimally by the inclusion of some forms of relaxation. The first system is that of a viscoelastic interface driven in a disordered medium. In mean-field, we prove that the interface has a periodic behaviour (with a new, emerging time scale), with avalanche events that span the whole system. We compute semi-analytically the friction force acting on this surface, and find that it is compatible with classical friction experiments. In finite dimensions (2D), the mean-field system-sized events become local, and numerical simulations give qualitative and quantitative results in good agreement with several important features of real earthquakes. The second system including a minimal form of relaxation consists in a toy model of avalanches: the Directed Percolation process. In our study of a non-Markovian variant of Directed Percolation, we observed that the universality class was modified but not completely. In particular, in the non-Markov case an exponent changes of value while several scaling relations still hold. This picture of an extended universality class obtained by the addition of a non-Markovian perturbation to the dynamics provides promising prospects for our first system.
Thesis defended in Sept. 2014. Minor additions in the introduction and minor corrections to the bibliographical references. Received the Springer Theses award (2015). Springer Theses (2015). eBook ISBN: 978-3-319-20022-4. Hardcover ISBN: 978-3-319-20021-7
References in corpus (18)
- Fractional Laplacian in Bounded Domains
- Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
- The dependence of the dry friction threshold on rupture dynamics
- The effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions
- On the velocity-strengthening behavior of dry friction
- Width distribution of contact lines on a disordered substrate
- Creep dynamics of elastic manifolds via exact transition pathways
- Viscoelastic Effects in Avalanche Dynamics: A Key to Earthquake Statistics
- Creep motion of an elastic string in a random potential
- Time dependent elastic response to a local shear transformation in amorphous solids
- Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition
- Growing correlations and aging of an elastic line in a random potential
- Self-Sustained Reaction Fronts in Porous Media
- Rate- and State-Dependent Friction Law and Statistical Properties of Earthquakes
- Aftershock production rate of driven viscoelastic interfaces
- Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
- Shearing a glass and the role of pin-delay in models of interface depinning
- Field theory of disordered systems -- Avalanches of an elastic interface in a random medium