Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings.
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.
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https://hdl.handle.net/10161/12594Published Version (Please cite this version)
10.1103/PhysRevE.82.051126Publication 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.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
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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