On convexity of solutions of ordinary differential equations

We prove a result on the convex dependence of solutions of ordinary differential equations on an ordered finite-dimensional real vector space with respect to the initial data.Comment: 10 page

Three atmospheric dispersion experiments involving oil fog plumes measured by lidar

The Wave Propagation Lab. participated with the U.S. Environmental Protection Agency in a series of experiments with the goal of developing and validating dispersion models that perform substantially better that models currently available. The lidar systems deployed and the data processing procedures used in these experiments are briefly described. Highlights are presented of conclusions drawn thus far from the lidar data

Ultra-bright source of polarization-entangled photons

Using the process of spontaneous parametric down conversion in a novel two-crystal geometry, one can generate a source of polarization-entangled photon pairs which is orders of magnitude brighter than previous sources. We have measured a high level of entanglement between photons emitted over a relatively large collection angle, and over a 10-nm bandwidth. As a demonstration of the source intensity, we obtained a 242-$\sigma$ violation of Bell's inequalities in less than three minutes.Comment: 4 pages, 5 encapsulated Postscript figures. To appear in Physical Review A (Rapid Communication

Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms

The random phase approximation (RPA) for the correlation energy functional of density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as for instance their inability to account for dispersion forces. First results for atoms, however, indicate that the RPA overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the KS Hamiltonian. In this contribution, three simple extensions of the RPA are examined, (a) its augmentation by an LDA for short-range correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlation energies as well as the ionization potentials resulting from the extensions (a) and (c) for closed sub-shell atoms are clearly superior to those obtained with the unmodified RPA. Quite some effort is made to ensure highly converged RPA data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular for the inherent frequency integration, should also be useful for applications of RPA-type functionals to more complex systems.Comment: 11 pages, 7 figure

Angular Distribution of Photoelectrons in Three Photon Ionisation of Sodium

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