Phase behavior of hard spherical caps

Phase Behavior of Dispersions of Hard Spherical Particles

Codes in spherical caps

We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are consi...

Equilibrium phase behavior of polydisperse hard spheres.

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energies for the fluid and solid phases. Cloud and shadow curves are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid ...

A characteristic property of spherical caps

It is proved that given H ≥ 0 and an embedded compact orientable constant mean curvature H surface M included in the half space z ≥ 0, not everywhere tangent to z = 0 along its boundary ∂M = γ ⊂ {z = 0}, the inequality H ≤ (min κ) ( min √ 1 − (κg/κ) ) is satisfied, where κ and κg are the geodesic curvatures of γ on z = 0 and on the surface M , respectively, if and only if M is a spherical cap o...

Almost Optimal Pseudorandom Generators for Spherical Caps

Halfspaces or linear threshold functions are widely studied in complexity theory, learning theory and algorithm design. In this work we study the natural problem of constructing pseudorandom generators (PRGs) for halfspaces over the sphere, aka spherical caps, which besides being interesting and basic geometric objects, also arise frequently in the analysis of various randomized algorithms (e.g...