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**Problem of Virial Expansion:**- Virial expansion is a
*polynomial*in density . It is a continuous non-singular function of the density. We know however, that the density cannot exceed the value of the closed packing 0.74, therefore the equation of state should diverge. Empirical recipe: let's cook some divergent function and fit it with the known behavior at low densities. **Padé Approximants:**- Let us write
The expansion at small should coincide with virial expansion!
If we know
*N*=*n*+*m*virial coefficients, (*n*,*m*)-Padé approximant can be constructed. (3,3) approximant describes the simulation (*P*,*V*,*T*) data for hard spheres a lot better, than the corresponding virial expansion with 6 virial coefficients. This is however empirical and ambiguous approach. Alternative description is necessary.

© 1997

Thu Sep 25 23:59:09 EDT 1997