Virial expansion for mixtures: some examples & recent results

Abstract: Mayer's expansion is an expansion of the pressure in powers of the activity (fugacity) in equilibrium statistical mechanics; the virial expansion is an expansion in powers of the density. Rigorous convergence results have been available for decades, nevertheless for mixtures the theory of density expansions is less advanced than the theory of activity expansions. I will review the setting, and discuss some recent results for the virial expansion for mixtures (multi-species systems) and illustrate them with three concrete models: mixtures of hard spheres of different sizes, non-overlapping rods of different lengths, and a hierarchical mixture of cubes in $Z^d$. The last two examples are helpful toy models for which concrete formulas are available and phase transitions can be studied. Based in part on joint works with Tobias Kuna, Stephen Tate, Dimitrios Tsagkarogiannis and Daniel Ueltschi.

mathematical physics

Audience: researchers in the discipline

( video )

One world IAMP mathematical physics seminar

Series comments: In order to receive announcements, please send an email to IAMPseminars@gmail.com with “subscribe” in the subject line.