Application of the p-version of the finite-element method to global-local problems

A brief survey is given of some recent developments in finite-element analysis technology which bear upon the three main research areas under consideration in this workshop: (1) analysis methods; (2) software testing and quality assurance; and (3) parallel processing. The variational principle incorporated in a finite-element computer program, together with a particular set of input data, determines the exact solution corresponding to that input data. Most finite-element analysis computer programs are based on the principle of virtual work. In the following, researchers consider only programs based on the principle of virtual work and denote the exact displacement vector field corresponding to some specific set of input data by vector u(EX). The exact solution vector u(EX) is independent of the design of the mesh or the choice of elements. Except for very simple problems, or specially constructed test problems, vector u(EX) is not known. Researchers perform a finite-element analysis (or any other numerical analysis) because they wish to make conclusions concerning the response of a physical system to certain imposed conditions, as if vector u(EX) were known

A Mean Field Platform for Excited State Quantum Chemistry

We present a mean field theory for excited states that is broadly analogous to ground state Hartree-Fock theory. Like Hartree-Fock, our approach is deterministic, state-specific, applies a variational principle to a minimally correlated ansatz, produces energy stationary points, relaxes the orbital basis, has a Fock-build cost-scaling, and can serve as the foundation for correlation methods such as perturbation theory and coupled cluster theory. To emphasize this last point, we pair our mean field approach with an excited state analogue of second order Moller-Plesset theory and demonstrate that in water, formaldehyde, neon, and stretched lithium fluoride, the resulting accuracy far exceeds that of configuration interaction singles and rivals that of equation of motion coupled cluster.Comment: 6 page

Solution of geometrically nonlinear statics problems by the p-version of the finite element method

This project is concerned with the possibility of using computers for the simulation of structural systems with the same degree of reliability as full scale physical experiments. Reliable numerical simulation will make it possible to reduce the costs of engineering and improve the quality of engineering decisions based on computed information. An error of idealization is an error between the actual physical quantities on which engineering decisions are based (e.g., maximum principal stress, first natural frequency, etc.) and the same data corresponding to the exact solution of the mathematical model. An error of discretization is an error between the quantities of interest corresponding to the exact and approximate solutions of a mathematical model. A high degree of reliability can be achieved in numerical simulation only if both the errors of idealization and errors of discretization can be shown to be small

Implications of Particle Acceleration in Active Galactic Nuclei for Cosmic Rays and High Energy Neutrino Astronomy

We consider the production of high energy neutrinos and cosmic rays in radio-quiet active galactic nuclei (AGN) or in the central regions of radio-loud AGN. We use a model in which acceleration of protons takes place at a shock in an accretion flow onto a supermassive black hole, and follow the cascade that results from interactions of the accelerated protons in the AGN environment. We use our results to estimate the diffuse high energy neutrino intensity and cosmic ray intensity due to AGN. We discuss our results in the context of high energy neutrino telescopes under construction, and measurements of the cosmic ray composition in the region of the ``knee'' in the energy spectrum at $\sim 10^7$ GeV.Comment: 37 pages of compressed and uuencoded postscript; hardcopy available on request; to be published in Astroparticle Physics; ADP-AT-94-

An exactly size consistent geminal power via Jastrow factor networks in a local one particle basis

The accurate but expensive product of geminals ansatz may be approximated by a geminal power, but this approach sacrifices size consistency. Here we show both analytically and numerically that a size consistent form very similar to the product of geminals can be recovered using a network of location specific Jastrow factors. Upon variational energy minimization, the network creates particle number projections that remove the charge fluctuations responsible for size inconsistency. This polynomial cost approach captures strong many-electron correlations, giving a maximum error of just 1.8 kcal/mol during the double-bond dissociation of H2O in an STO-3G atomic orbital basis.Comment: Updated the original arXiv submission to include improvements resulting from journal peer review. 5 pages, 4 figures, 1 tabl

Quantum Black Holes, Elliptic Genera and Spectral Partition Functions

We study M-theory and D-brane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinite-dimensional Lie algebras, elliptic genera, and Hilbert schemes, and describe their relations to elliptic modular forms. The common feature in our examples lie in the modular properties of the characters of certain representations of the pertinent affine Lie algebras, and in the role of spectral functions of hyperbolic three-geometry associated with q-series in the calculation of elliptic genera. We present new calculations of supergravity elliptic genera on local Calabi-Yau threefolds in terms of BPS invariants and spectral functions, and also of equivariant D-brane elliptic genera on generic toric singularities. We use these examples to conjecture a link between the black hole partition functions and elliptic cohomology.Comment: 42 page