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Marginal stability in jammed packings: quasicontacts and weak contacts.
Yoav Kallus1, Salvatore Torquato2
1Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 13, 2014
Summary
Maximally random jammed sphere packing reveals that quasicontacts, pairs of spheres near contact, significantly impact dynamic stability. Their abundance grows faster than contacts in high dimensions, influencing packing density estimates.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Maximally random jammed (MRJ) sphere packing represents systems at the edge of mechanical stability (isostaticity).
- Traditional stability analysis often overlooks quasicontacts, which are pairs of spheres close to touching.
Purpose of the Study:
- To investigate the non-trivial effects of quasicontacts on the dynamic stability of jammed sphere packings.
- To re-evaluate packing density estimates in high dimensions by including quasicontacts.
Main Methods:
- Analysis of quasicontact and contact distributions in d-dimensional MRJ sphere packings.
- Revisiting prior calculations by incorporating the influence of quasicontacts.
- Examining quasicontact roles in Bravais lattice packings and the Edwards ensemble.
Main Results:
- The abundance of quasicontacts increases faster than contacts in MRJ packings.
- Including quasicontacts provides a revised estimate for packing density in high dimensions, suggesting a lower bound.
- Quasicontacts are crucial in stable Bravais lattice packings and challenge the Edwards ensemble's predictions for contact force distributions.
Conclusions:
- Quasicontacts are essential for understanding dynamic stability in jammed systems, not just static stability.
- The inclusion of quasicontacts refines our understanding of high-dimensional packing densities.
- Jammed lattices highlight limitations of static ensembles in capturing dynamic properties like contact force distributions.
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