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Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings.

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Date
2010-11
Authors
Jin, Yuliang
Charbonneau, Patrick
Meyer, Sam
Song, Chaoming
Zamponi, Francesco
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Abstract
The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song et al., Nature (London) 453, 629 (2008)] is generalized to arbitrary dimension d using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling ϕ∼d2(-d) is consistent with that of other approaches, such as replica theory and density-functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.
Type
Journal article
Subject
Models, Theoretical
Probability
Thermodynamics
Permalink
https://hdl.handle.net/10161/12594
Published Version (Please cite this version)
10.1103/PhysRevE.82.051126
Publication Info
Jin, Yuliang; Charbonneau, Patrick; Meyer, Sam; Song, Chaoming; & Zamponi, Francesco (2010). Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings. Phys Rev E Stat Nonlin Soft Matter Phys, 82(5 Pt 1). pp. 051126. 10.1103/PhysRevE.82.051126. Retrieved from https://hdl.handle.net/10161/12594.
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Scholars@Duke

Charbonneau

Patrick Charbonneau

Professor of Chemistry
Professor Charbonneau studies soft matter. His work combines theory and simulation to understand the glass problem, protein crystallization, microphase formation, and colloidal assembly in external fields.
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