We investigate three different local approximations for nonlinear gravitational instability in the framework of cosmological Lagrangian fluid dynamics of cold dust. By local we mean that the evolution is described by a set of ordinary differential equations in time for each mass element with no coupling to other mass elements aside from those implied by the initial conditions. We first show tha...

We investigate the system of D-dimensional hard spheres in D-dimensional space, where D>3. For the fluid phase of these hyperspheres, we generalize scaled-particle theory to arbitrary D and furthermore use the virial expansion and the Percus-Yevick integral equation. For the crystalline phase, we adopt cell theory based on elementary geometrical assumptions about close-packed lattices. Regardle...

Let S denote the convex hull of m full-dimensional ellipsoids in Rn. Given > 0 and δ > 0, we study the problems of computing a (1 + )-approximation to the minimum volume covering ellipsoid of S and a (1 + δ)n-rounding of S. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in ...

In high bit rate optical fiber communication systems, Polarization mode dispersion (PMD) is one of the main factors to signal distortion and needs to be compensated. PMD monitoring system is the key integral part of an adaptive PMD compensator. The degree of polarization (DOP) ellipsoid obtained by using a polarization scrambler can be used as a feedback signal for automatic PMD compensation. G...

Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered inf...

Mean squared displacements and velocity auto correlation functions are calculated using molecular dynamics for hard spheres under a range of conditions (i) for the equilibrium fluid below freezing; (ii) for the metastable fluid above freezing; and (iii) for the hard sphere crystal, both in the metastable region between freezing and melting, and in the stable region above melting. In addition, s...

Corresponding to each convex (or more general) subset of n-dimensional Euclidean space, Rn, there is a unique ellipsoid with the following property. The moment of inertia of the ellipsoid and the moment of inertia of the convex set are the same about every 1-dimensional subspace of Rn. This ellipsoid is called the Legendre ellipsoid of the convex set. The Legendre ellipsoid is a well-known conc...