Glassy dynamics in granular compaction: sand on random graphs

Abstract

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric frustration. We define an athermal dynamics designed to model repeated taps of a given strength. Amplitude cycling and the effect of permanently constraining a subset of the spins at a given amplitude is discussed. Finally we check the validity of Edwards' hypothesis for the athermal tapping dynamics.

13 pages Revtex, minor changes, to appear in PRE

References in corpus (8)

• Simplest random K-satisfiability problem
• A ferromagnet with a glass transition
• Exact solutions for diluted spin glasses and optimization problems
• Tapping Spin Glasses
• Tapping Thermodynamics of the One Dimensional Ising Model
• Shaking a Box of Sand
• Steady State Behavior of Mechanically Perturbed Spin Glasses and Ferromagnets
• Metastable configurations of spin models on random graphs

Cited by in corpus (11)

• Experimental measurement of an effective temperature for jammed granular materials
• Glassy dynamics of landscape evolution
• A possible experimental test of the thermodynamic approach to granular media
• Particle dynamics and effective temperature of jammed granular matter in a slowly sheared 3D Couette cell
• Localization of thermal packets and metastable states in Sinai model
• Effect of rare events on out of equilibrium relaxation
• Effective dynamics and steady state of an Ising model submitted to tapping processes
• Edwards measure and the steady state regime of a model with kinetic constraints under tapping
• Dynamical diversity and metastability in a hindered granular column near jamming
• Competition and cooperation:aspects of dynamics in sandpiles
• Spin-models of granular compaction: From one-dimensional models to random graphs