Hard hyperspheres
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Hard hyperspheres are hard spheres in more than three dimensions (\(D\)).
Contents |
[edit] Volume
The volume of an n-sphere of unit diameter is given by
\[v_n=\frac{(\pi / 4)^{n/2}}{\Gamma(1+ n/2)}\]
where \(\Gamma(m)\) is the Gamma function.
[edit] Structure factor
[edit] Liquid-solid transition
The liquid-solid transition for \(D=4, 5\) and \(6\)
[edit] Virial coefficients
Hard sphere: virial coefficients for odd dimensions
[edit] Percus–Yevick equation
The Percus Yevick equation
[edit] References
- ↑ 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
