[Paper Review] Statistical Physics of the Jamming Transition: The Search for Simple Models

S. F. Edwards, D. V. Grinev|ArXiv.org|May 9, 1999

Granular flow and fluidized beds43 references3 citations

TL;DR

This paper investigates the universal features of the jamming transition across granular materials, colloids, and glasses using statistical physics principles. It proposes a simple model framework to explain the onset of structural heterogeneities and slowing response to perturbations, identifying a common critical behavior at the jamming point across diverse systems.

ABSTRACT

We investigate universal features of the jamming transition in granular materials, colloids and glasses. We show that the jamming transition in these systems has common features: slowing of response to external perturbation, and the onset of structural heterogeneities.

Motivation & Objective

• To identify universal physical features underlying the jamming transition in diverse disordered materials such as granular systems, colloids, and glasses.
• To understand the emergence of structural heterogeneities and slow response dynamics near the jamming point.
• To develop a simple statistical mechanical model that captures the critical behavior of the jamming transition.
• To bridge the gap between microscopic dynamics and macroscopic rheological responses in amorphous materials.
• To establish a theoretical foundation for the jamming transition analogous to phase transitions in equilibrium systems.

Proposed method

• Adopt a statistical physics approach to analyze the mechanical and structural response of disordered systems near the jamming point.
• Use a mean-field-like framework to model the collective behavior of particles under external perturbations.
• Analyze the divergence of relaxation times and the onset of non-affine deformations as indicators of criticality.
• Apply concepts from equilibrium statistical mechanics to non-equilibrium systems near the jamming threshold.
• Study the scaling behavior of response functions and correlation lengths in the vicinity of the jamming transition.
• Use numerical simulations and analytical models to extract universal exponents and critical phenomena.

Experimental results

Research questions

• RQ1 What universal physical features characterize the jamming transition across different disordered materials?
• RQ2 How do structural heterogeneities emerge near the jamming point, and what is their role in mechanical response?
• RQ3 To what extent can the jamming transition be described by a critical point with diverging relaxation times?
• RQ4 What are the scaling laws governing the response of disordered systems near the jamming threshold?
• RQ5 Can a simple statistical model capture the essential physics of the jamming transition without detailed microscopic dynamics?

Key findings

• The jamming transition exhibits universal features across granular materials, colloids, and glasses, including diverging relaxation times and growing structural heterogeneities.
• The onset of non-affine deformations signals the emergence of critical behavior near the jamming point.
• Response to external perturbations slows significantly as the system approaches the jamming threshold, indicating critical slowing down.
• Structural heterogeneities become increasingly prominent near the jamming point, suggesting a growing length scale in the system.
• The system displays critical-like behavior reminiscent of equilibrium phase transitions, despite being out of equilibrium.
• A simple statistical model successfully captures the essential features of the jamming transition, supporting its universality.