Hard hyperspheres
Hard hyperspheres are hard spheres in more than three dimensions (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D} ).
Volume
The volume of an n-sphere of unit diameter is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_n=\frac{(\pi / 4)^{n/2}}{\Gamma(1+ n/2)}}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Gamma(m)} is the Gamma function.
Structure factor
Liquid-solid transition
The liquid-solid transition for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D=4, 5} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6} [2].
Virial coefficients
Hard sphere: virial coefficients for odd dimensions [3]
Percus–Yevick equation
The Percus Yevick equation [4]
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