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Related Experiment Video

Updated: Jul 17, 2026

Cutting Procedures, Tensile Testing, and Ageing of Flexible Unidirectional Composite Laminates

Cutting Procedures, Tensile Testing, and Ageing of Flexible Unidirectional Composite Laminates

Published on: April 27, 2019

Frequency distribution of mechanically stable disk packings.

Guo-Jie Gao¹, Jerzy Bławzdziewicz, Corey S O'Hern

¹Department of Mechanical Engineering, Yale University, New Haven, Connecticut 06520-8284, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 7, 2007

Summary

Mechanically stable packings of disks are not equally probable. Their frequencies grow exponentially with packing fraction and are influenced by geometrical properties, not just local energy barriers.

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Area of Science:

Physics, specifically condensed matter physics and statistical mechanics.
Computational physics and materials science.

Background:

Understanding the statistical properties of jammed matter is crucial for granular systems.
Previous thermodynamic descriptions assumed equal probability for mechanically stable packings.

Purpose of the Study:

To numerically investigate the relative frequencies of mechanically stable (MS) packings in small systems of frictionless bidisperse disks.
To determine if MS packings are equally probable and to explore factors influencing their frequencies.

Main Methods:

Generating MS packings through compression/decompression and energy minimization in systems up to 14 particles.
Analyzing frequency distributions within packing-fraction intervals.
Introducing thermal fluctuations to estimate energy barriers between packings.
Examining displacement fluctuations to assess local configuration space basins.

Main Results:

MS packings are not equally probable; their frequency distribution grows exponentially with packing fraction.
Frequencies within intervals vary by many orders of magnitude, independent of the generation algorithm.
A positive correlation exists between packing frequencies and energy barrier heights, though with significant scatter.
Displacement modes scale with eigenvalues, suggesting packing frequencies are not solely determined by local configuration space volume.

Conclusions:

The frequency distribution of MS packings is strongly influenced by geometrical properties of the configuration space.
Energy barriers and local basin geometry play a role, but other undetermined variables also affect packing probabilities.
Findings challenge assumptions in current thermodynamic descriptions of granular systems.