Errors in finite-difference computations on curvilinear coordinate systems

Curvilinear coordinate systems were used extensively to solve partial differential equations on arbitrary regions. An analysis of truncation error in the computation of derivatives revealed why numerical results may be erroneous. A more accurate method of computing derivatives is presented

Transformation of two and three-dimensional regions by elliptic systems

The research during this period continued to expand the class of numerical algorithms that can be accurately and efficiently implemented on overlapping grids. Whereas previous calculations have been used to solve elliptic equations and to find the steady-state solution of parabolic equations, the present work is aimed towards developing time-accurate solution techniques for parabolic and hyperbolic equations. The primary difficulty here is in the correct treatment of the interior boundary nodes that must be updated at each iteration. The implementation of explicit methods is straightforward. However, the common practice of lagging these values when using an implicit methods leads to inconsistencies in the difference equation. One way to avoid this problem is to alternately calculate with an implicit and an explicit method on each subgrid. With this procedure, the explicit method generates boundary values at the next time level which are then used by the implicit step. It can be shown that when a backward implicit method is combined with a forward explicit method, the composite method is second order accurate and unconditionally stable for linear problems. A second area in which progress can be reported is in the distribution of grid points on curves and surfaces

Elliptic systems and numerical transformations

Properties of a transformation method, which was developed for solving fluid dynamic problems on general two dimensional regions, are discussed. These include construction error of the transformation and applications to mesh generation. An error and stability analysis for the numerical solution of a model parabolic problem is also presented

Quasiconformal mappings and grid generation

A finite difference scheme is developed for constructing quasiconformal mappings for arbitrary simply and doubly connected regions. Computational grids are generated to reduce elliptic equations to canonical form. Examples of conformal mappings on surfaces are also included

Transformation of two and three-dimensional regions by elliptic systems

Finite difference methods for composite grids were analyzed. It was observed that linear interpolation between grids would suffice only where low order accuracy was required. In the context of fluid flow, this would be in regions where the flow was essentially free stream. Higher order interpolation schemes were also investigated. The well known quadratic and cubic interpolating polynomials would increase the formal accuracy of the overall numerical algorithm. However, it can also be shown that the stability of the algorithm may be adversely affected. Further numerical results are needed in order to assess the nature of this instability induced by the interpolation procedure. Finally, error analysis and the order of difference expressions on general curvilinear coordinates are discussed

A Narrowband Imaging Survey for High Redshift Galaxies in the Near Infrared

A narrowband imaging survey of 276 square minutes of arc was carried out at near infrared wavelengths to search for emission line objects at high redshifts. Most of the fields contained a known quasar or radio galaxy at a redshift that placed one of the strong, restframe optical emission lines (H-alpha, [O III], H-beta, or [O II]) in the bandpass of the narrowband filter. The area weighted line flux limit over the entire survey was 3.4x10e-16 erg/cm2/s (3-sigma), while the most sensitive limits reached 1.4x10e-16 erg/cm2/s. Integrating the volume covered by all four optical emission lines in each image yields a total comoving volume surveyed of 1.4x10e5 cubic megaparsecs. Considering only H-alpha emission in the K band (2.05 < z < 2.65), where the survey is most sensitive, the survey covered a comoving volume of 3.0x10e4 cubic megaparsecs to a volume-weighted average star formation rate of 112 M-solar/yr (for Ho = 50 km/s/Mpc, Omega = 1). This is the most extensive near-infrared survey which is deep enough to have a reasonable chance at detecting strong line emission from an actively star-forming population of galaxies, when d against simple models of galaxy formation. One emission line candidate was identified in this survey, and subsequently confirmed spectroscopically.Comment: To appear in the Astronomical Journal, November 1996. 23 pages, including 2 tables and 7 figure

Centaur operations at the space station

A study was conducted on the feasibility of using a Centaur vehicle as a testbed to demonstrate critical OTV technologies at the Space Station. Two Technology Demonstration Missions (TDMs) were identified: (1) Accommodations, and (2) Operations. The Accommodations TDM contained: (1) berthing, (2) checkout, maintenance and safing, and (3) payload integration missions. The Operations TDM contained: (1) a cryogenic propellant resupply mission, and (2) Centaur deployment activities. A modified Space Station Co-Orbiting Platform (COP) was selected as the optimum refueling and launch node due to safety and operational considerations. After completion of the TDMs, the fueled Centaur would carry out a mission to actually test deployment and help offset TDM costs. From the Station, the Centaur could carry a single payload in excess of 20,000 pounds to geosynchronous orbit or multiple payloads

Locality and Translations in Braided Ribbon Networks

An overview of microlocality in braided ribbon networks is presented. Following this, a series of definitions are presented to explore the concept of microlocality and the topology of ribbon networks. Isolated substructure of ribbon networks are introduced, and a theorem is proven that allows them to be relocated. This is followed by a demonstration of microlocal translations. Additionally, an investigation into macrolocality and the implications of invariants in braided ribbon networks are presented.Comment: 12 pages, 12 figure