Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions

By N. Clisby, B. McCoy. 2005

189 citations recorded by the source corpus.

We evaluate the virial coefficients Bk for $$k\leq 10$$ for hard spheres in dimensions $$D=2,\cdots,8.$$ Virial coefficients with k even are found to be negative when $$D\geq 5. $$ This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when $$D\geq 5$$. Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 for D = 4, and there is a distinct possibility that negative virial coefficients will also eventually occur for D = 3.

Subfields: Biomedical Engineering, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/c5de7f73ebfde6d8866f1d1194974a93cfd6171e

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In Biomedical Engineering

1. Salvatore Torquato
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In Condensed Matter Physics

1. Salvatore Torquato
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In Materials Chemistry

1. Salvatore Torquato
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Citations in the corpus

• Jammed hard-particle packings: From Kepler to Bernal and beyond (2010, methodology): “For hard spheres in dimensions 1 ≤ d ≤ 8, these coefficients for low orders 1 ≤ n ≤ 3 are known exactly, and accurate numerical estimates are available for n+1 ≤ 10 (Clisby and McCoy, 2006).”