Latest revision |
Your text |
Line 1: |
Line 1: |
| '''Hard hyperspheres''' are [[hard sphere model | hard spheres]] in more than three dimensions (<math>D</math>).
| | {{Stub-general}} |
| ==Volume== | | ==Volume== |
| The volume of an ''n''-sphere of unit diameter is given by | | The volume of a <math>d</math> sphere of unit diameter is given by |
|
| |
|
| :<math>v_n=\frac{(\pi / 4)^{n/2}}{\Gamma(1+ n/2)}</math> | | :<math>v_d=\frac{(\pi / 4)^{d/2}}{\Gamma(1+ d/2)}</math> |
|
| |
|
| where <math>\Gamma(m)</math> is the [[Gamma function]]. | | where <math>\Gamma(m)</math> is the [[Gamma function]]. |
| ==Structure factor== | | ==See also== |
| [[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>
| | *[[Hard sphere: virial coefficients]] |
| ==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/>
| | #[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
| | #[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)] |
| *[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]] |