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Distance of closest approach of two arbitrary hard ellipsoids

Peter Palffy-Muhoray ,Xiaoyu Zheng ,Wilder Iglesias ²
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.

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