Ground State Asymptotics of a Dilute, Rotating Gas

We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the so-called Gross-Pitaevskii (GP) limit of a dilute gas. Analyzing both the absolute and the bosonic ground state of the system we show, in particular, their different behavior for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.Comment: LaTeX2e, 37 page

Proof of Bose-Einstein Condensation for Dilute Trapped Gases

The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schroedinger equation; the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional. This is the first rigorous proof of BEC in a physically realistic, continuum model.Comment: Revised version with some simplifications and clarifications. To appear in Phys. Rev. Let

A two - grid, fourth order method for nonlinear fourth order boundary value problems

A fourth order convergent finite difference method is developed for the numerical solution of the nonlinear fourth order boundary value problem y(iv)(x) = f(x,y), a<x <b, y(a) = A0 , y"(a) = B0 , y(b) = A1, y" (b) = B1 . The method is based on a second order convergent method which is used on two grids, fourth order convergence being obtained by considering a linear combination of the individual results relating to the two grids. Special formulas are developed for application to grid points adjacent to the boundaries x = a and x = b , the principal parts of the local truncation errors of these formulas being the same as that of the second order method used at other points of each grid. Modifications to these special formulas are noted for problems with boundary conditions of the form y (a) = Ao , y'(a) = Co , y(b) = A1, y'(b) =c1

Global extrapolation procedures for linear partial differential equations

Global extrapolation procedures, in space and time are considered for the numerical Solution of linear partial differential equations. Global extrapolation procedures in time only are reviewed. The procedures are tested on three problems from the literature, one of which has a nonlinear source term

Method accurately measures mean particle diameters of monodisperse polystyrene latexes

Photomicrographic method determines mean particle diameters of monodisperse polystyrene latexes. Many diameters are measured simultaneously by measuring row lengths of particles in a triangular array at a glass-oil interface. The method provides size standards for electronic particle counters and prevents distortions, softening, and flattening

The Top Quark: Experimental Roots and Branches of Theory

The CDF and D0 experiments at the Fermilab Tevatron have discovered the top quark and provided first measurements of many of its properties. The small top sample gathered by Run I leaves open many possibilities for top physics beyond the standard model. Run II and the LHC (and eventually an LC) promise to deepen our knowledge of the top quark and its relationship to electroweak symmetry breaking.Comment: 14 pages, 9 figures; talk presented at HCP200

Plasma-sprayed metal-glass fluoride coatings for lubrication to 1170 K (1650 F)

Plasma spray of Nichrome matrix composite contains dispersed glass for oxidation protection and calcium fluoride for lubrication. Coatings can be applied to bearing journals and bearing bores. Coating was easily machinable and had excellent bond strength on substrate metal