Depinning in a two-layer model of plastic flow
Pierre Le Doussal1, M. Cristina Marchetti2, Kay Jörg Wiese1
1CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
2Physics Department, Syracuse University, Syracuse NY 13244, USA
Abstract
We study a model of two layers, each
consisting of a d-dimensional elastic object driven over a random
substrate, and mutually interacting through a viscous coupling. For
this model, the mean-field theory (i.e. a fully connected model)
predicts a transition from elastic depinning to hysteretic plastic
depinning as disorder or viscous coupling is increased. A functional
RG analysis shows that any small inter-layer viscous coupling
destablizes the standard (decoupled) elastic depinning FRG fixed point
for d ≤ 4, while for d > 4 most aspects of the mean-field theory are
recovered. A one-loop study at non-zero velocity indicates, for d < 4,
coexistence of a moving state and a pinned state below the elastic
depinning threshold, with hysteretic plastic depinning for periodic
and non-periodic driven layers. A 2-loop analysis of quasi-statics
unveils the possibility of more subtle effects, including a new
universality class for non-periodic objects. We also study the model
in d = 0, i.e. two coupled particles, and show that hysteresis does
not always exist as the periodic steady state with coupled layers can
be dynamically unstable. It is also proved that stable pinned
configurations remain dynamically stable in presence of a viscous
coupling in any dimension d. Moreover, the layer model for periodic
objects is stable to an infinitesimal commensurate density
coupling. Our work shows that a careful study of attractors in phase
space and their basin of attraction is necessary to obtain a firm
conclusion for dimensions d = 1, 2, 3.
arXiv:0801.0137 [pdf]
Phys. Rev. B 78, 224201 (2008) [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.