A bound for the spectral radius of a matrix
Bound for spectral radius of matrix derived by constructing integral equation with degenerate kernel
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Bound for spectral radius of matrix derived by constructing integral equation with degenerate kernel
Integral formulation of scattering theory extended to Coulomb interactions by expanding Green function and treating kernel singularities
Hard X-ray pulse identification with formation of brilliant kernel /11-12 September 1968/ flare by comparision with optical data
Linear compressibility assumption incorporated into third order multiple integral representation of nonlinear creep of polyurethane, reducing time independent kernel functions
Complex matrix eigenvalues bound derivation by constructing integral equation with degenerate kernel
Nonlinear operator for determining complete continuity when kernel is function of variables
Total radiative interchange kernel measurements, describing remote excitation/detection
The Backus-Gilbert theory is applied to the problem of the vertical sounding of the atmosphere by means of remote radiation measurements. An application is made to spectral intervals 2.8/cm wide in the 667/cm band of CO2, and tradeoff curves are presented which quantitatively define the relationship between intrinsic vertical resolution and random error in temperature profile estimates. It is found that for a 1-2K random error with state-of-the-art instrumentation, the intrinsic vertical resolution ranges from approximately 0.5 local scale height (l.s.h.) in the lower troposphere to 2 l.s.h. in the upper stratosphere with approximately 2 l.s.h. resolution in the vicinity of the tropopause. These values are somewhat smaller than the widths of the radiactive transfer kernels at similar levels. Increasing the number of spectral intervals from 7 to 16 is found to produce only a marginal improvement in vertical resolution.
Parametric tradeoff analyses of a wide spectrum of alternate tank configurations to minimize both primary and secondary, direct and scattered radiation sources emanating from the NERVA are reported. The analytical approach utilizing point kernel techniques is described and detailed data are presented on the magnitude of neutron/gamma doses for different locations. Single-tank configurations utilizing smaller cone angles and end cap radii were found to minimize integral radiation levels, hence, stage shielding-weight penalties for shuttle missions. Hybrid configurations employing an upper tank with a reduced cone angle and end cap radius result in low integral payload doses primarily due to the increased separation distance caused by the elongation of the larger capacity upper tank. A preliminary radiation damage assessment is discussed of possible reusable nuclear shuttle materials, components, and subsystems, and the possible effects of the radiation environment on various phases of RNS mission operations.
Radiation analyses were performed and shielding weight requirements were estimated for various candidate vehicle and payload configurations for use with the reusable nuclear shuttle. The analyses included both point kernel and Monte Carlo approaches. The effects on reduced shield weight were determined for propellant ranks with pointed conical tank bottoms and for one case of a cluster of small tanks. This later case, however, had an arrangement which had no center tank in the upper tier of tanks. This effect negated most of the gain of going to the smaller tanks. A range of shield weights is presented for various light and heavy manned payload configurations when used in conjunction with a single liquid hydrogen propellant tank, 33 ft in diameter with a 15 deg conical tank bottom.
A practical method for computing the effectiveness of a space nuclear shield perforated by small tubing and cavities is reported. Performed calculations use solutions for a two dimensional transport code and evaluate perturbations of that solution using last flight estimates and other kernel integration techniques. In general, perturbations are viewed as a change in source strength of scattered radiation and a change in attenuation properties of the region.
Government-sponsored study and development efforts were directed toward design and implementation of high level programming languages suitable for future aerospace applications. The study centered around an evaluation of the four most pertinent existing aerospace languages. Evaluation criteria were established, and selected kernels from the current Saturn 5 and Skylab flight programs were used as benchmark problems for sample coding. An independent review of the language specifications incorporated anticipated future programming requirements into the evaluation. A set of language requirements was synthesized from these activities.
The activities and results of a study for the definition of flight program language requirements are described. A set of detailed requirements are presented for a language capable of supporting onboard application programming for the Marshall Space Flight Center's anticipated future activities in the decade of 1975-85. These requirements are based, in part, on the evaluation of existing flight programming language designs to determine the applicability of these designs to flight programming activities which are anticipated. The coding of benchmark problems in the selected programming languages is discussed. These benchmarks are in the form of program kernels selected from existing flight programs. This approach was taken to insure that the results of the study would reflect state of the art language capabilities, as well as to determine whether an existing language design should be selected for adaptation.
The efforts and results are summarized for a study to establish requirements for a flight programming language for future onboard computer applications. Several different languages were available as potential candidates for future NASA flight programming efforts. The study centered around an evaluation of the four most pertinent existing aerospace languages. Evaluation criteria were established, and selected kernels from the current Saturn 5 and Skylab flight programs were used as benchmark problems for sample coding. An independent review of the language specifications incorporated anticipated future programming requirements into the evaluation. A set of detailed language requirements was synthesized from these activities. The details of program language requirements and of the language evaluations are described.
The work performed in the following areas is summarized: (1) Analysis of Realistic nuclear-propelled vehicle was analyzed using the Marshall Space Flight Center computer code package. This code package includes one and two dimensional discrete ordinate transport, point kernel, and single scatter techniques, as well as cross section preparation and data processing codes, (2) Techniques were developed to improve the automated data transfer in the coupled computation method of the computer code package and improve the utilization of this code package on the Univac-1108 computer system. (3) The MSFC master data libraries were updated.
Detailed descriptions are presented of the input data for each of the MSFC computer codes applied to the analysis of a realistic nuclear propelled vehicle. The analytical techniques employed include cross section data, preparation, one and two dimensional discrete ordinates transport, point kernel, and single scatter methods.
Integrations over solid angle and frequency are performed in the expressions for the radiant heat flux and local energy loss of a line in a region of strong variations of the source function in one direction. Approximations are given for coefficients and kernels in the resulting forms which involve integrals over the physical coordinate.
The Backus-Gilbert theory, originally developed for analysis of inversion problems associated with the physics of the solid earth, was applied to the problem of the vertical sounding of the atmosphere by means of remote radiation measurements. An application was made to spectral intervals 2.8/cm wide in the 667/cm band CO2, and tradeoff curves are presented which quantitatively define the relationship between intrinsic vertical resolution and random error in temperature profile estimates. It is found that for a 1-2 K random error with state-of-the-art instrumentation, the intrinsic vertical resolution ranges from approximately 0.5 locale scale height (l.s.h.) in the lower troposphere to greater than 2 l.s.h. in the upper stratosphere with approximately 1 l.s.h. resolution in the vicinity of the tropopause. These values are somewhat smaller than the widths of the radioactive transfer kernels at similar levels. Increasing the number of spectral intervals from 7 to 16 is found to produce only a marginal improvement in vertical resolution.