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| '''Hard hyperspheres''' are [[hard sphere model | hard spheres]] in more than three dimensions (<math>D</math>).
| | {{Stub-general}} |
| ==Volume==
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| The volume of an ''n''-sphere of unit diameter is given by
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| :<math>v_n=\frac{(\pi / 4)^{n/2}}{\Gamma(1+ n/2)}</math>
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| where <math>\Gamma(m)</math> is the [[Gamma function]].
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| ==Structure factor==
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| [[Structure factor]] <ref>[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)]</ref>
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| ==Liquid-solid transition==
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| The [[Solid-liquid phase transitions |liquid-solid]] transition for <math>D=4, 5</math> and <math>6</math> <ref>[http://dx.doi.org/10.1063/1.3530780 C. D. Estrada and M. Robles "Fluid–solid transition in hard hypersphere systems", Journal of Chemical Physics '''134''' 044115 (2011)]</ref>.
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| ==Virial coefficients==
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| [[Hard sphere: virial coefficients]] for odd dimensions <ref>[http://dx.doi.org/10.1063/1.2951456 René D. Rohrmann, Miguel Robles, Mariano López de Haro, and Andrés Santos "Virial series for fluids of hard hyperspheres in odd dimensions", Journal of Chemical Physics '''129''' 014510 (2008)]</ref>
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| ==Percus–Yevick equation==
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| The [[Percus Yevick]] equation <ref>[http://dx.doi.org/10.1063/1.2991338 M. Adda-Bedia, E. Katzav, and D. Vella "Solution of the Percus–Yevick equation for hard hyperspheres in even dimensions", Journal of Chemical Physics '''129''' 144506 (2008)]</ref>
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| ==References== | | ==References== |
| <references/>
| | #[http://dx.doi.org/10.1063/1.2743031 Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics '''126''' 224505 (2007)] |
| ;Related reading
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| *[http://dx.doi.org/10.1063/1.3622597 Jarosław Piasecki, Piotr Szymczak, and John J. Kozak "Structural transitions in hypersphere fluids: Predictions of Kirkwood's approximation", Journal of Chemical Physics '''135''' 084509 (2011)]
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| [[category: models]] | | [[category: models]] |