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Critical slowing down and hyperuniformity on approach to jamming
Steven Atkinson1, Ge Zhang2, Adam B Hopkins3
1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review. E
|August 31, 2016
Summary
Strict jamming and hyperuniformity in frictionless hard-disk packings are closely linked. Standard protocols often fail to create truly jammed states, even when appearing so, highlighting the need for improved packing algorithms.
Area of Science:
- Physics of disordered materials
- Statistical mechanics
- Computational physics
Background:
- Hyperuniformity describes suppressed density fluctuations in matter at critical points.
- A link exists between strict jamming (mechanical rigidity) and hyperuniformity in frictionless hard-particle packings.
- Studying large systems is crucial for accessing long-range behavior and ensuring true jamming.
Purpose of the Study:
- To modify a rigorous linear programming method for testing jamming in hard-disk packings.
- To compare the efficacy of this rigorous jamming test against standard methods like the 'pressure-leak' test.
- To investigate the relationship between packing protocols, jamming, and hyperuniformity in two-dimensional systems.
Main Methods:
- Modification of the rigorous linear programming method by Donev et al. for jamming detection.
- Application of the modified method to test putatively jammed packings of hard disks in two dimensions.
- Analysis of packing protocols and their ability to generate strictly jammed and hyperuniform configurations.
Main Results:
- The modified rigorous jamming test is superior to standard methods for ascertaining jamming.
- Standard packing protocols often fail to reliably create jammed packings for modest system sizes (N≈10³).
- Deviations from hyperuniformity in maximally random jammed (MRJ) packings correlate with the inability to ensure strict jamming, suggesting a strong link between the two phenomena.
Conclusions:
- Strict jamming and hyperuniformity are intrinsically linked in frictionless hard-disk packings.
- Existing packing protocols struggle to generate reliably jammed and hyperuniform configurations due to 'critical slowing down' effects.
- The development of algorithms for producing large, disordered, strictly jammed, and rattler-free packings is a significant challenge and an important future direction.
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