Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering

Radio Spectra and NVSS Maps of Decametric Sources

We constructed radio spectra for ~1400 UTR-2 sources and find that 46% of them have concave curvature. Inspection of NVSS maps of 700 UTR sources suggests that half of all UTR sources are either blends of two or more sources or have an ultra-steep spectrum (USS). The fraction of compact USS sources in UTR may be near 10%. Using NVSS and the Digitized Sky Survey(s) we expect to double the UTR optical identification rate from currently ~19%.Comment: 2 pages, no figures; to appear in Proc. "Observational Cosmology with the New Radio Surveys", eds. M. Bremer, N. Jackson & I. Perez-Fournon, Kluwer Acad. Pres

Extreme Events in Resonant Radiation from Three-dimensional Light Bullets

We report measurements that show extreme events in the statistics of resonant radiation emitted from spatiotemporal light bullets. We trace the origin of these extreme events back to instabilities leading to steep gradients in the temporal profile of the intense light bullet that occur during the initial collapse dynamics. Numerical simulations reproduce the extreme valued statistics of the resonant radiation which are found to be intrinsically linked to the simultaneous occurrence of both temporal and spatial self-focusing dynamics. Small fluctuations in both the input energy and in the spatial phase curvature explain the observed extreme behaviour.Comment: 5 pages, 5 figures, submitte

University of Colorado: 1971 Summer Field Season in East Baffin Island

Research was continued by University of Colorado faculty and graduate students in the area of Cumberland Peninsula. Baffin Island, Northwest Territories. The work was divided into four main phases: 1) studies on the glacial chronology of the Penny Ice Cap and local mountain ice caps; 2) the mass balance of the Boas Glacier; 3) air-sea interactions using ground stations, instrumented aircraft and satellite data; and 4) evaluation of climatic trends. ..

A Convergent Method for Calculating the Properties of Many Interacting Electrons

A method is presented for calculating binding energies and other properties of extended interacting systems using the projected density of transitions (PDoT) which is the probability distribution for transitions of different energies induced by a given localized operator, the operator on which the transitions are projected. It is shown that the transition contributing to the PDoT at each energy is the one which disturbs the system least, and so, by projecting on appropriate operators, the binding energies of equilibrium electronic states and the energies of their elementary excitations can be calculated. The PDoT may be expanded as a continued fraction by the recursion method, and as in other cases the continued fraction converges exponentially with the number of arithmetic operations, independent of the size of the system, in contrast to other numerical methods for which the number of operations increases with system size to maintain a given accuracy. These properties are illustrated with a calculation of the binding energies and zone-boundary spin- wave energies for an infinite spin-1/2 Heisenberg chain, which is compared with analytic results for this system and extrapolations from finite rings of spins.Comment: 30 pages, 4 figures, corrected pd

Exchange Frequencies in the 2d Wigner crystal

Using Path Integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a ``clean'' 2d Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for r_s \leq 175 \pm 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic

Counts and Colors of Faint Galaxies in the U and R Bands

Ground-based counts and colors of faint galaxies in the U and R bands in one field at high Galactic latitude are presented. Integrated over flux, a total of 1.2x10^5 sources per square degree are found to U=25.5 mag and 6.3x10^5 sources per square degree to R=27 mag, with d log N/dm ~ 0.5 in the U band and d log N/dm ~ 0.3 in the R band. Consistent with these number-magnitude curves, sources become bluer with increasing magnitude to median U-R=0.6 mag at 24<U<25 mag and U-R=1.2 mag at 25 < R < 26 mag. Because the Lyman break redshifts into the U band at z~3, at least 1.2x10^5 sources per square degree must be at redshifts z<3. Measurable U-band fluxes of 73 percent of the 6.3x10^5 sources per square degree suggest that the majority of these also lie at z < 3. These results require an enormous space density of objects in any cosmological model.Comment: 17 pages, MNRAS in pres

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application