First- and second-order density matrices of symmetry-projected single-determinant wavefunctions.
Density matrices of symmetry projected single determinant wave functions for finite groups, considering many particle system
Harriman, J. E.↗
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Results for “symmetry projection”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Program Computes Universal Transverse Mercator Projection
Computer program produces Gauss-Kruger (constant meridional scale) transverse Mercator projection, used to construct U.S. Army's universal transverse Mercator (UTM) grid system. Capable of mapping entire Northern Hemisphere of Earth (and, by symmetry of projection, entire Earth) accurately with respect to single principal meridian. Mathematically insensitive to proximity to pole or equator and insensitive to departure of meridian from central meridian. Useful to any mapmaking agency. FORTRAN 77 program developed on IBM PC-series computer equipped with Intel Math Coprocessor.
Wallis, David E.↗
Impact of Magnetic Draping, Convection, and Field Line Tying on Magnetopause Reconnection Under Northward IMF
We simulate a northward IMF cusp reconnection event at the magnetopause using the OpenGGCM resistive MHD code. The ACE input data, solar wind parameters, and dipole tilt belong to a 2002 reconnection event observed by IMAGE and Cluster. Based on a fully three-dimensional skeleton separators, nulls, and parallel electric fields, we show magnetic draping, convection, ionospheric field line tying play a role in producing a series of locally reconnecting nulls with flux ropes. The flux ropes in the cusp along the global separator line of symmetry. In 2D projection, the flux ropes the appearance of a tearing mode with a series of 'x's' and 'o's' but bearing a kind of 'guide field' that exists only within the magnetopause. The reconnecting field lines in the string of ropes involve IMF and both open and closed Earth magnetic field lines. The observed magnetic geometry reproduces the findings of a superposed epoch impact parameter study derived from the Cluster magnetometer data for the same event. The observed geometry has repercussions for spacecraft observations of cusp reconnection and for the imposed boundary conditions reconnection simulations.
Wendel, Deirdre E.↗
Prospects for three-dimensional projective and tomographic imaging radar networks
Results of a study demonstrating the feasibility of broadband and speckle-free projective imaging of a complex shaped scattering object in the 6-17 GHz range with centimeter resolution are presented. It is shown how angular, spectral, and polarization diversities can be combined in the data acquisition process with a unique target-derived reference technique to access the three-dimensional Fourier space of the scatterer cost-effectively. Imagea retrieval algorithms, based on the projection slice theorem and knowledge of object symmetry, are utilized in obtaining images of a model aircraft with near optical resolution. The implications for high-resolution three-dimensional tomographic imaging radar networks are discussed.
Farhat, N. H.↗
Frequency Stratification of the Nonthermal Emission in Blazars
Research supported by this grant involved theoretical investigations of the multifrequency nonthermal emission from the relativistic jets in blazars, which are quasars and related objects with highly variable brightness. In the initial stage of the project, one-dimensional, conical (i.e., spherical symmetry between the jet axis and surface is assumed) jet models were used to explain the multi-waveband spectra and variability of blazars. The results were applied to two flares observed in the object PKS 2155-304, leading to the conclusion that the distinct differences in the observed characteristics of the two flares can be explained with the same jet model if two different physical parameters (the magnetic field in the first flare and the efficiency of acceleration of electrons to high energies in the second) varied.
Marscher, Alan P.↗
Sines and Cosines. Part 1 of 3
Applying the concept of similarities, the mathematical principles of circular motion and sine and cosine waves are presented utilizing both film footage and computer animation in this 'Project Mathematics' series video. Concepts presented include: the symmetry of sine waves; the cosine (complementary sine) and cosine waves; the use of sines and cosines on coordinate systems; the relationship they have to each other; the definitions and uses of periodic waves, square waves, sawtooth waves; the Gibbs phenomena; the use of sines and cosines as ratios; and the terminology related to sines and cosines (frequency, overtone, octave, intensity, and amplitude).
Apostol, Tom M.↗
A Symmetric Time-Varying Cluster Rate of Descent Model
A model of the time-varying rate of descent of the Orion vehicle was developed based on the observed correlation between canopy projected area and drag coefficient. This initial version of the model assumes cluster symmetry and only varies the vertical component of velocity. The cluster fly-out angle is modeled as a series of sine waves based on flight test data. The projected area of each canopy is synchronized with the primary fly-out angle mode. The sudden loss of projected area during canopy collisions is modeled at minimum fly-out angles, leading to brief increases in rate of descent. The cluster geometry is converted to drag coefficient using empirically derived constants. A more complete model is under development, which computes the aerodynamic response of each canopy to its local incidence angle.
Ray, Eric S.↗
HP-9810A calculator programs for plotting the 2-dimensional motion of cyclindrical payloads relative to the shuttle orbiter
The HP-9810A calculator programs described provide the capability to generate HP-9862A plotter displays which depict the apparent motion of a free-flying cyclindrical payload relative to the shuttle orbiter body axes by projecting the payload geometry into the orbiter plane of symmetry at regular time intervals.
Wilson, S. W.↗
Identification of forbidden transitions in the nu-4 band of (N-14)H3 by intracavity laser-Stark spectroscopy
These transitions are forbidden in the sense that they follow the selection rule delta K = + or - 2, which violates the usual rule that delta K = + or - 1 for a perpendicular band of a symmetric top, where K is the projection of the total angular momentum onto the molecular symmetry axis. The assignments are based for the most part on laser-Stark measurements made with a CO laser and an intracavity Stark cell. The procedure followed in making the assignments is described. Attention is called to the significance of these new lines in the analysis of the nu-4 vibrational state and in an improved determination of the ground-state rotational and centrifugal distortion constants.
Weber, W. H.↗
Comparison of four stable numerical methods for Abel's integral equation
The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.
Murio, Diego A.↗
Calculation of autoionization of He and H/-/ using the projection-operator formalism
Improved calculations are reported for the first several autoionization states of the lower symmetries of He and H(-). Unshifted energies are calculated by diagonalizing QHQ using a Hylleraes basis with more terms than previously used; shifts, widths, and photoabsorption shape parameters are obtained with the additional use of exchange-approximate nonresonant continuum functions. Previous calculations of H(-) resonances are reviewed and slightly augmented by applying various nonresonant continua and correcting small errors. A comparison is made between the calculations and experimental results and is found to be very satisfactory except for the lowest 1P autoionization state of He, which is shown to need a more accurate experimental determination.
Bhatia, A. K.↗
Projective-symmetric spaces
Cartanian symmetrical property of Riemannian projective-symmetric spaces - tensor geometry
CARTAN SPACE↗
An improved method of Nusselt number calculation
A novel method for calculating the Nusselt number, Nu, in a steady-state Rayleigh-Benard convection problem is presented, in which calculations are done for a square box with constant temperature, free-slip boundary conditions at the top and bottom, and a reflection symmetry along the side walls. The element heat flux is obtained by averaging over the entire element; element heat fluxes are then projected to the adjacent nodes. Compared with previous methods, the approach reduces the calculated depth variation in horizontally averaged flux by more than a factor of 10 and shows more rapid convergence of Nu as a function of grid size.
Ho-Liu, Phyllis↗
Multicolor surface photometry of powerful radio galaxies. II - Morphology and stellar content
Results on the morphology, photometric structure, and colors of 72 powerful radio galaxies (PRGs) are presented. It is found that galaxy interactions and mergers play an important role in the PRG phenomenon. Over 50 percent of the sample galaxies display optical morphological deviations from elliptical symmetry at high levels of surface brightness. About 20 percent of the galaxies have a second nucleus less than 10 kpc in projection from the main nucleus. The fraction of PRGs in a common envelope with neighboring galaxies is even larger. Surface brightness profiles for galaxies with weak or no emission lines are typically shallower in slope than normal radio-quiet elliptical galaxies, but similar to the brightest cluster galaxies. Surface brightness profiles for strong emission (SE) galaxies are more diverse in form. The SE PRGs have unusually blue average colors relative to giant elliptical galaxies. These colors are spatially extended and not merely due to light from a bright nucleus or extended emission-line gas.
Smith, Eric P.↗
Polar heating and the shape of Venus
Observations of an increase of the brightness temperature of Venus towards the poles are reported. Measurements of the deviations from circular symmetry of radio emission at 6 cm were made with a two-element interferometer near a time of inferior conjunction with Venus. The projected baseline lengths of the planet at the first null of the visibility function imply that the planet is either larger (by about 7 km) or brighter (by about 5 K) at the poles than at the equator. Possible causes of polar heating include a strong downwelling of the Venusian atmosphere at the poles and a slight topographical flattening relative to the gravitational equipotentials. Calculations of brightness temperature variations for a planet with a topographical oblateness of about 0.6 km are shown to agree with the observations, however the possibility of this oblateness being due to a fossil rotational bulge is argued against.
Pechmann, J. B.↗
Unsteady Diffusion Flames: Ignition, Travel, and Burnout (SUBCORE Project: Simplified Unsteady Burning of Contained Reactants)
An experimental apparatus for the examination of a planar, virtually strain-rate-free diffusion flame in microgravity has been designed and fabricated. Such a diffusion flame is characterized by relatively large spatial scale and high symmetry (to facilitate probing), and by relatively long fluid-residence time (to facilitate investigation of rates associated with sooting phenomena). Within the squat rectangular apparatus, with impervious, noncatalytic isothermal walls of stainless steel, a thin metallic splitter plate subdivides the contents into half-volumes. One half-volume initially contains fuel vapor diluted with an inert gas, and the other, oxidizer diluted with another inert gas-so that the two domains have equal pressure, density, and temperature. As the separator is removed, by translation in its own plane, through a tightly fitting slit in one side wall, a line ignitor in the opposite side wall initiates a triple-flame propagation across the narrow layer of combustible mixture formed near midheight in the chamber. The planar diffusion flame so emplaced is quickly disrupted in earth gravity. In microgravity, the planar flame persists, and travels ultimately into the half-volume containing the stoichiometrically deficient reactant; the flame eventually becomes extinguished owing to reactant depletion and heat loss to the walls.
Fendell, Francis↗
Joint US/Soviet docking mission.
The purpose and objectives of the joint Apollo/Soyuz experimental test flight, the technical requirements and anticipated solutions necessary to meet the objectives, the mission plan, the flight vehicles, the schedule, and the expected results of successfully completing such a project are discussed. The androgynous feature of the docking system is provided by a symmetrical distribution of all elements which are directly connected during docking, relative to the axis of reverse symmetry. Both the American and Russian systems are designed to serve as either the active or passive system for docking and undocking.
Scott, D. R.↗
ProperCAD: A portable object-oriented parallel environment for VLSI CAD
Most parallel algorithms for VLSI CAD proposed to date have one important drawback: they work efficiently only on machines that they were designed for. As a result, algorithms designed to date are dependent on the architecture for which they are developed and do not port easily to other parallel architectures. A new project under way to address this problem is described. A Portable object-oriented parallel environment for CAD algorithms (ProperCAD) is being developed. The objectives of this research are (1) to develop new parallel algorithms that run in a portable object-oriented environment (CAD algorithms using a general purpose platform for portable parallel programming called CARM is being developed and a C++ environment that is truly object-oriented and specialized for CAD applications is also being developed); and (2) to design the parallel algorithms around a good sequential algorithm with a well-defined parallel-sequential interface (permitting the parallel algorithm to benefit from future developments in sequential algorithms). One CAD application that has been implemented as part of the ProperCAD project, flat VLSI circuit extraction, is described. The algorithm, its implementation, and its performance on a range of parallel machines are discussed in detail. It currently runs on an Encore Multimax, a Sequent Symmetry, Intel iPSC/2 and i860 hypercubes, a NCUBE 2 hypercube, and a network of Sun Sparc workstations. Performance data for other applications that were developed are provided: namely test pattern generation for sequential circuits, parallel logic synthesis, and standard cell placement.
Ramkumar, Balkrishna↗