Hard hyperspheres

Hard hyperspheres are hard spheres in more than three dimensions ($D$).

Volume

The volume of an n-sphere of unit diameter is given by

$v_n=\frac{(\pi /4{)}^{n/2}}{\mathrm{\Gamma }(1+n/2)}$

where $\mathrm{\Gamma }(m)$ is the Gamma function.

Structure factor

Structure factor

Liquid-solid transition

The liquid-solid transition for $D=4,5$ and $6$ .

Virial coefficients

Hard sphere: virial coefficients for odd dimensions

Percus–Yevick equation

The Percus Yevick equation

References

Related reading

• 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)