Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings.
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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.
Published Version (Please cite this version)10.1103/PhysRevE.82.051126
Publication InfoCharbonneau, Patrick; Jin, Y; Meyer, S; Song, C; & 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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Associate 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.