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Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings
Aleksandar Donev1, Salvatore Torquato, Frank H Stillinger
1Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
Disordered hard-sphere packings are strictly isostatic, with contacts equaling degrees of freedom. This study reveals new insights into interparticle forces and pair correlation functions at jamming.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Understanding jamming in hard-sphere packings is crucial for granular materials.
- The pair correlation function (g(2)(r)) and interparticle force distributions (P(f)) are key metrics.
Purpose of the Study:
- To theoretically and computationally investigate jamming in hard-sphere packings.
- To analyze the pair correlation function around contact and interparticle force distributions.
- To clarify the isostatic nature of jammed packings.
Main Methods:
- Computational analysis of hard-sphere packings.
- Theoretical derivation of connections between force distributions and pair correlation functions.
- Shared-neighbor analysis of contact networks.
Main Results:
- Disordered packings are strictly isostatic (contacts = degrees of freedom).
- A power-law divergence with exponent -0.4 was observed in the near-contact pair correlation function.
- A maximum and non-zero probability of zero force were found in interparticle force distributions.
Conclusions:
- The study confirms the isostatic nature of jammed packings, even with ordering.
- New relationships between force distributions and pair correlation functions were established.
- The findings shed light on granular media physics and jamming phenomena.