Random generation of periodic hard ellipsoids based on molecular dynamics: A computationally-efficient algorithm

This paper presents a computationally-efficient algorithm for generating random periodic packings of hard ellipsoids. The algorithm is based on molecular dynamics where the ellipsoids are set in translational and rotational motion and their volumes gradually increase. Binary collision times are computed by simply finding the roots of a non-linear function. In addition, an original and efficient method to compute the collision time between an ellipsoid and a cube face is proposed. The algorithm can generate all types of ellipsoids (prolate, oblate and scalene) with very high aspect ratios (i.e., >10). It is the first time that such packings are reported in the literature. Orientations tensors were computed for the generated packings and it has been shown that ellipsoids had a uniform distribution of orientations. Moreover, it seems that for low aspect ratios (i.e., ⩽10), the volume fraction is the most influential parameter on the algorithm CPU time. For higher aspect ratios, the influence of the latter becomes as important as the volume fraction. All necessary pseudo-codes are given so that the reader can easily implement the algorithm.