Steady states of two-dimensional granular systems are unique, stable, and sometimes satisfy detailed balance
-
Published:2023-08-01
Issue:34
Volume:56
Page:345001
-
ISSN:1751-8113
-
Container-title:Journal of Physics A: Mathematical and Theoretical
-
language:
-
Short-container-title:J. Phys. A: Math. Theor.
Author:
Myhill Alex D CORCID,
Blumenfeld RaphaelORCID
Abstract
Abstract
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse analytically and numerically the steady states of this theory in systems of arbitrary density and report the following. (1) We discover that all such dynamics almost certainly possess only one physical steady state, which may or may not satisfy detailed balance. (2) We show rigorously that, if a detailed balance solution is possible then it is unique. The above two results correct an erroneous conjecture in the literature. (3) We show rigorously that the detailed-balance solutions in very dense systems are globally stable, extending the local stability found for these solutions in the literature. (4) In view of recent experimental observations of robust detailed balance steady states in very dilute cyclically sheared systems, our results point to a self-organisation of process rates in dynamic granular systems.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference23 articles.
1. Moving through scales of flow and transport in soil;Vogel;J. Hydrol.,2003
2. The transmission of stress in an aggregate;Edwards;Physica D,1989
3. Heterogeneities in granular materials;Mehta;Phys. Today,2009
4. Structure and dynamics of granular materials perturbed by external fields;Gerasymov;Uk. J. Phys.,2010