Hard hyperspheres: Difference between revisions

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{{Stub-general}}
'''Hard hyperspheres''' are [[hard sphere model | hard spheres]] in more than three dimensions (<math>D</math>).
==Volume==
The volume of an ''n''-sphere of unit diameter is given by
 
:<math>v_n=\frac{(\pi / 4)^{n/2}}{\Gamma(1+ n/2)}</math>
 
where <math>\Gamma(m)</math> is the [[Gamma function]].
==Structure factor==
[[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>
==Liquid-solid transition==
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>.
==Virial coefficients==
[[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>
==Percus–Yevick equation==
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>
==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)]
<references/>
;Related reading
*[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)]
[[category: models]]
[[category: models]]

Latest revision as of 11:38, 1 September 2011

Hard hyperspheres are hard spheres in more than three dimensions ().

Volume[edit]

The volume of an n-sphere of unit diameter is given by

where is the Gamma function.

Structure factor[edit]

Structure factor [1]

Liquid-solid transition[edit]

The liquid-solid transition for and [2].

Virial coefficients[edit]

Hard sphere: virial coefficients for odd dimensions [3]

Percus–Yevick equation[edit]

The Percus Yevick equation [4]

References[edit]

Related reading