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Mathematical analysis technique generalizes a root squaring and root cubing method into a general root powering method. The introduction of partitioned polynomials into this general root powering method simplifies the coding of the polynomial transformations into input data suitable for processing by computer. The method includes analytic functions.
Food cubes exhibit flavor and quality stability for periods of four weeks in 100 deg F environment. They are suitable for field rations, emergency rations or snacks and should interest the food processing industry.
A mathematical analysis of the tradeoffs and requirements was performed to develop an improved array design which will give stronger returns at lower elevation angles and reduce pulse spread in the return. It was determined that a zenith angle of 75deg can be obtained with an array with an area of 0.28 sq m, if the array is shaped on the surface of a 45 deg cone whose axis is coincident to the satellite axis. The total weight of the truncated pyramid array with 270 cube corners is calculated to be not more than 50% greater than the GEOS 2 array, while the efficiency is increased 275%.
Results of plasmapause measurements made onboard S cubed A (explorer 45) satellite are presented. Data cover model calculations made to explain the observed probe potential behavior, comparison of satellite data with VLF data to establish that certain effects seen are interpretable as the plasmapause, and plasmapause behavior during the December 17, 1971 magnetic storm.
A method first presented by Goodman is used to derive an equation for the statistical effects associated with laser returns from satellites having retroreflecting arrays of cube corners. The effect of the distribution on the returns of a satellite-tracking system is illustrated by a computation based on randomly generated numbers.
The satellite coordinate system necessary to describe the location and orientation of each cube corner in the array is discussed. The method of optical testing is described along with the gain function, and computational methods for deriving the gain function and experimental values for it. The velocity aberration is derived as a function of satellite orbit, a complete method for cross section evaluation is described, and finally the radar equation is described.
Test procedure for optimum cube design records beam-return patterns photographically.
Cube corner retroreflectors with nominal dihedral angles of 90 deg 0 min 1.5 sec were fabricated, tested, and analyzed to determine the return energy in the annular ring of the far field diffraction pattern required by the Laser Geodynamic Satellite. Performance was assessed for variations in the dihedral angles, optical surfaces, and thermal environment. Despite relatively high independent axial and radial sensitivities, the changes caused by the anticipated thermal environment were found to be negligible; however, there were substantial variations between the analytical predictions and measured performance.-
The array is built from a large number (hundreds or thousands) of microprocessors or microcomputers linked through a switching network into an indirect binary n-cube array. Control is two level, the array operating synchronously, or in lock step, at the higher level, and with the broadcast commands being locally interpreted into rewritable microinstruction streams in the microprocessors and in the switch control units. The key to the design is the switching array. By properly programming it, the array can be made into a wide variety of virtual arrays which are well adapted to a wide range of applications. It is believed that the flexibility of the switching array can be used to obtain fault avoidance, which appears necessary in any highly parallel design.
In this paper, the geometric ray tracing theory for the scattering of light by hexagonal cylinders to cubes and parallelepipeds has been modified. Effects of the real and imaginary parts of the refractive index and aspect ratio of the particle on the scattering phase function and the degree of linear polarization are investigated. Causes of the physical features in the scattering polarization patterns are identified in terms of the scattering contribution due to geometric reflections and refractions. The single-scattering phase function and polarization data presented in this paper should be of some use for the interpretation of observed scattering and polarization data from planetary atmospheres and for the physical understanding of the transfer of radiation in an atmosphere containing nonspherical particles.
Lidar cross section of some typical types of cube-corner retroreflectors (CCRs) having a three corner mirror system is investigated for the case that the CCR is tilted from the normal illumination axis. Analytic expressions for the effective aperture area for the two typical window types (circular and hexagonal) of CCRs are obtained for the case that the CCR is tilted. The range of incidence angle in which only the total reflection occurs at all three uncoated corner mirrors has been found to vary considerably with the orientation of CCR and the refractive index of the CCR prism. The analytical expression for the far-field diffraction pattern of a tilted CCR is obtained by taking different polarization transformation of the six sectors of the effective reflecting aperture into account. This expression is essential when evaluating the lidar cross section of a moving CCR which is tilted in general. Formulas for the angles defining the six sectors have also been obtained.
The paper presents a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinate. The current J is taken to be proportional to the cube of the magnetostatic potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of similarity solution examples are displayed depending on the values of the similarity parameters. Each similarity parameter corresponds to a symmetry of the underlying nonlinear elliptic equation for A. The similarity parameters also determine the source currents for the potential field solution of the family. The solutions show the interplay between the gravitational force, the J & B force (B, magnetic field induction) and the gas pressure gradient.
Compression yielding tests were performed at 760 C on crystals of the Ni base superalloys Rene 150 and a modified MAR-M247, both having two different Co concentrations. For both alloy bases, increasing Co concentration was shown to decrease the critical resolved shear stress for octahedral slip, but to have little effect on that for cube slip. The results suggest that decreasing complex stacking fault energy in the gamma-prime with increasing Co could account for the observed effects.
Production of finely divided cubes of boron involves vacuum-deposition technology and requires making of template. Template supports pattern of checkered squares 25 micrometers on side, which are etched 25 micrometers into template material. Template coasted uniformly with paralyene or some similar vacuum coating with low coefficient of adhesion. Intended application to solid rocket fuels, explosives, and pyrotechnics; process used for other applications, from manufacture of pharmaceuticals to processing of nuclear materials.
Graph partitioning is a topic of extensive interest, with applications to parallel processing. In this context graph nodes typically represent computation, and edges represent communication. One seeks to distribute the workload by partitioning the graph so that every processor has approximately the same workload, and the communication cost (measured as a function of edges exposed by the partition) is minimized. Measures of partition quality vary; in this paper we consider a processor's cost to be the sum of its computation and communication costs, and consider the cost of a partition to be the bottleneck, or maximal processor cost induced by the partition. For a general graph the problem of finding an optimal partitioning is intractable. In this paper we restrict our attention to the class of k-art n-cube graphs with uniformly weighted nodes. Given mild restrictions on the node weight and number of processors, we identify partitions yielding the smallest bottleneck. We also demonstrate by example that some restrictions are necessary for the partitions we identify to be optimal. In particular, there exist cases where partitions that evenly partition nodes need not be optimal.
The software described in this document provides I/O functions to be used with Moderate Resolution Spectroradiometer (MODIS) level 1 and 2 data, and could be easily extended to other data sources. This data is in a scan cube data format: a 3-dimensional ragged array containing multiple bands which have resolutions ranging from 250 to 1000 meters. The complexity of the data structure is handled internally by the library. The I/O calls allow the user to access any pixel in any band through 'C' structure syntax. The high MODIS data volume (approaching half a terabyte per day) has been a driving factor in the library design. To avoid recopying data for user access, all I/O is performed through dynamic 'C' pointer manipulation. This manual contains background material on MODIS, several coding examples of library usage, in-depth discussions of each function, reference 'man' type pages, and several appendices with details of the included files used to customize a user's data product for use with the library.
We used the Goddard Space Flight Center, Acousto-Optic Tunable Filter (AOTF) Camera to obtain near-IR spectral image sets of Mars over the 1.6-3.6 micron region during the April 1999 opposition. A complete image set consists of 280 images with a spectral full-width-half maximum of 10 wavenumbers (fixed in frequency), 90 images in H-band (1.55-1.80 micron), 115 images in K-band (1.95-2.50 micron) and 75 images in L-band (2.90-3.70 micron). The short-wavelength limit is set by transmission of AOTF cell and long-wavelength limit is imposed by sensitivity of PICNIC, 256x256, HgCdTe array detector. We will discuss the new array performance and provide preliminary interpretations of some of these results. These measurements were part of a 4-observatory coordinated effort whose overall objective was to assemble a photometrically calibrated, spectrally complete ground-based image cube over the visible and near-IR spectral region. To accomplish this, four observing teams conducted the investigations with instruments spanning 0.4 to 5.0 micron. The instruments and observing facilities were (a) AOTF camera at Apache Point Observatory, 3.5m, f/10, Nasymth focus (this abstract). Primary science targets included the 3 micron water-of hydration feature and CO2, H2O ice (polar regions and clouds); (b) Visible/NIR interference-filter (24 filters) camera at Lowell Observatory, 72" telescope. 430-1050 nm. Science targets were Fe(2+), Fe(3+) mineralogy and coarse grain hematite search; (c) NMSU Tortugas Mountain Observatory, 60 cm telescope, CCD photometry with same filter set as Lowell; (d) KPNO cryogenic grating/slit spectrometer (CRSP/SALLY) at KPNO 2.1 m, f/15 Cassegrain focus (see abstract by D. Glenar, et. al., this meeting). Selected wavelengths in 3-5 micron region (L, M band). Science targets included water-of-hydration feature (3-4 micron long wave extension) and sulfate mineralogy. Observers participating in this campaign included Dave Glenar, John Hillman, Gordon Bjoraker and Fred Espenak from GSFC, Nancy Chanover, Jim Murphy and A. S. MurTell from NMSU, Leslie Young from BU, Diana Blaney from JPL and Dick Joyce from KPNO.
Flip cube (constructed of heavy plastic) displays 11 graphics representing current projects or demos from 5 NASA centers participating in Supercomputing '98 (SC98). Included with the images are the URLS and names of the NASA centers.