In this paper, continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the n-dimensional space are introduced. Two different models for the non-overlapping and models for the inclusion of ellipsoids within half-spaces and ellipsoids are presented. By applying a simple multi-start strategy combined with a clever choice of starting guesses and a nonline...

Given two ellipsoids, we show that their characteristic equation has at least two negative roots and that the ellipsoids are separated by a plane if and only if their characteristic equation has two distinct positive roots. Furthermore, the ellipsoids touch each other externally if and only if the characteristic equation has a positive double root. An advantage of this characterization is that ...

dipolar-dephasing method provides some information about the strength of dipolar coupling in solids. dipolar dephasing technique measures the time for a polarized carbon nucleus to lose its magnetization once the proton locking field is terminated. the dynamics of guest molecules adsorbed within the cavities and channels of nonporouszeolite strongly depend on the structure and chemical composit...

Using classical density functional theory (DFT) in a modified mean-field approximation we investigate the fluid phase behavior of quasi-two dimensional dipolar fluids confined to a plane. The particles carry three-dimensional dipole moments and interact via a combination of hard-sphere, van-der-Waals, and dipolar interactions. The DFT predicts complex phase behavior involving firstand second-or...

We extend the notion of minimal volume ellipsoid containing a convex body in $$\mathbb {R}^{d}$$ to setting logarithmically concave functions. consider vast class functions whose superlevel sets are concentric ellipsoids. For fixed function from this class, we set all its “affine” positions. any log-concave f on {R}^{d},$$ belonging positions, and find one with integral under condition that it ...

Dipolar-dephasing method provides some information about the strength of dipolar coupling in solids. Dipolar dephasing technique measures the time for a polarized carbon nucleus to lose its magnetization once the proton locking field is terminated. The dynamics of guest molecules adsorbed within the cavities and channels of nonporouszeolite strongly depend on the structure and chemical composit...

Distributions of ellipsoids are often used to simulate the optical properties of non-ellipsoidal atmospheric particles, such as dust. In this work, the applicability of ellipsoids for retrieving the refractive index of dust-like target model particles from scattering data is investigated. This is a pure modeling study, in which stereogrammetrically retrieved model dust shapes are used as target...