Distance of closest approach of two arbitrary hard ellipsoids
Liquid Crystal Institute, Kent State University
Dept. of Mathematical Sciences, KSU
2Liquid Crystal Institute, KSU
The distance of closest approach of particles with hard cores is a key parameter in statistical theories
and computer simulations of liquid crystals and colloidal systems. In this paper, we provide a new
algorithm to calculate the distance of closest approach of two ellipsoids of arbitrary shape and orientation.
This algorithm is based on our previous analytic result for the distance of closest approach of 2D ellipses.
The method consists of determining the intersection of the ellipsoids with the plane containing the line
joining their centers and rotating the plane. The distance of closest approach of the two ellipses formed
by the intersection is a periodic function of the plane orientation, whose maximum corresponds to the
distance of closest approach of the two ellipsoids.