Hard hyperspheres: Difference between revisions
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{{ | '''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== | ||
<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]
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]
- ↑ Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics 126 224505 (2007)
- ↑ C. D. Estrada and M. Robles "Fluid–solid transition in hard hypersphere systems", Journal of Chemical Physics 134 044115 (2011)
- ↑ 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)
- ↑ 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)
- Related reading