  The distance of closest approach of hard particles is a key parameter of
their interaction and plays an important role in the resulting phase behavior.
For non-spherical particles, the distance of closest approach depends on
orientation, and its calculation is surprisingly difficult. Although overlap
criteria have been developed for use in computer simulations [1, 2], no
analytic solutions have been obtained for the distance of closest approach of
ellipsoids in 3-D, or, until now, for ellipses in 2-D. We have derived an
analytic expression for the distance of closest approach of the centers of two
arbitrary hard ellipses as function of their orientation relative to the line
joining their centers. We describe our method for solving this problem,
illustrate our result, and discuss its usefulness in modeling and simulating
systems of anisometric particles such as liquid crystals.
