Distance of closest approach

The maximum packing density of hard particles, an important problem of ongoing interest,[1] depends on their distance of closest approach.

The interactions of particles typically depend on their separation, and the distance of closest approach plays an important role in determining the behavior of condensed matter systems.

The one anisotropic shape whose excluded volume can be expressed analytically is the spherocylinder; the solution of this problem is a classic work by Onsager.

Vieillard Baron first investigated this problem, and although he did not obtain a result for the distance of closest approaches, he derived the overlap criterion for two ellipses.

His final results were useful for the study of the phase behavior of hard particles and for the packing problem using Monte Carlo simulations.

Although overlap criteria have been developed,[8][9] analytic solutions for the distance of closest approach and the location of the point of contact have only recently become available.