title: Spontaneous instabilities and stick-slip motion in a generalized Hébraud-Lequeux model.
abstract: We revisit the Hébraud-Lequeux (HL) model for the rheology of jammed materials and argue that a possibly important time scale is missing from HL's initial specification. We show that our generalization of the HL model undergoes interesting oscillating instabilities for a wide range of parameters, which lead to intermittent, stick-slip flows under constant shear rate. The instability we find is akin to the synchronization transition of coupled elements that arises in many different contexts (neurons, fireflies, financial bankruptcies, etc.). We hope that our scenario could shed light on the commonly observed intermittent, serrated flows of glassy materials under shear.
authors.affiliation: CFM, 23 rue de l'Université, 75007, Paris, France and Ecole Polytechnique, 91120 Palaiseau, France.
authors.forename: Jean-Philippe
authors.initials: JP
authors.lastname: Bouchaud
authors.affiliation: Laboratoire de Mathématiques Appliquées aux Systèmes, CentraleSupélec, 92290 Châtenay-Malabry, France. stanislao.gualdi@gmail.com.
authors.forename: Stanislao
authors.initials: S
authors.lastname: Gualdi
authors.affiliation: Université Pierre et Marie Curie - Paris 6, Laboratoire de Physique Théorique de la Matière Condensée, 4, Place Jussieu, Tour 12, 75252 Paris Cedex 05, France.
authors.forename: Marco
authors.initials: M
authors.lastname: Tarzia
authors.affiliation: Laboratoire de Physique Théorique, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75231 Paris Cedex 05, France.
authors.forename: Francesco
authors.initials: F
authors.lastname: Zamponi