Statistical mechanics of jammed packings of spheres
Item
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Title
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Statistical mechanics of jammed packings of spheres
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Identifier
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d_2009_2013:028936263cf8:11501
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identifier
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11954
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Creator
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Jin, Yuliang,
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Contributor
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Hernan A. Makse
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Date
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2012
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics | Statistics | granular matter | jamming | sphere packing | statistical mechanics
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Abstract
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The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. There are presently numerous experiments showing that randomly packing spheres of equal size into a container consistently results in a static configuration with a density of 0.64. The ubiquity of random close packing (RCP) rather than the equilibrium crystalline array at 0.74 begs a new statistical framework. Here we introduce a general volume ensemble statistical approach for jammed packings of spheres. This approach provides a thermodynamic definition of RCP: RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the "freezing point'' in a first-order phase transition between ordered and disordered packing phases. We generalize the theory to jammed packings of high dimensional and different size spheres. The asymptotic high-dimensional scaling of the RCP density is consistent with that of other approaches, such as replica theory and density functional theory. The theory predicts the density of random close packing and random loose packing (RLP) of polydisperse systems for a given distribution of sphere size. The present mean-field approach may help to treat packing problems of non-spherical particles, and could serve as a starting point to understand the higher-order correlations present in jammed packings.
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.
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Program
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Physics
