Hard hyperspheres: Difference between revisions

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==Volume==
'''Hard hyperspheres''' are [[hard sphere model | hard spheres]] in more than three dimensions.
The volume of a <math>d</math> sphere of unit diameter is given by  
The volume of an ''n''-sphere of unit diameter is given by  


:<math>v_d=\frac{(\pi / 4)^{d/2}}{\Gamma(1+ d/2)}</math>
:<math>v_n=\frac{(\pi / 4)^{n/2}}{\Gamma(1+ n/2)}</math>


where <math>\Gamma(m)</math> is the [[Gamma function]].
where <math>\Gamma(m)</math> is the [[Gamma function]].

Revision as of 10:45, 16 October 2008

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Hard hyperspheres are hard spheres in more than three dimensions. The volume of an n-sphere of unit diameter is given by

where is the Gamma function.

See also

References

  1. Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics 126 224505 (2007)
  2. 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)
  3. 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)