We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on the function used to measure the size of the ellipsoid. Simple examples with non-unique minimal or maximal ellipsoids conclude this article. MSC 2000: 52A27, 52A20

We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation measured along their intercenter vector. This directional distance is derived from the elliptic contact function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modeling arbitrary mixtures of elliptic particles, whether hard or s...

Depletion-induced interactions between colloids in colloid-polymer mixtures depend in range and strength on size, shape, and concentration of depletants. Crowding by colloids in turn affects shapes of polymer coils, such as biopolymers in biological cells. By simulating hard-sphere colloids and random-walk polymers, modeled as fluctuating ellipsoids, we compute depletion-induced potentials and ...

We construct symplectic embeddings in dimension 2n ≥ 6 of ellipsoids into the product of a 4-ball or 4-dimensional cube with Euclidean space. A sequence of the embeddings are seen to be optimal by a quantitative version of the embedding obstructions introduced in [8]. In the limiting case when our ellipsoids approach a cylinder we recover an embedding of Guth, [7]. However for compact ellipsoid...

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 nonspherical 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 [Vieillard-Baron, J. Chem. Phys. 56...

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...