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NASA NTRS1972

Numerical stability in problems of linear algebra.

Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

Babuska, I.↗

NASA NTRS1972

Lava filled craters and the thermal history of the lunar surface.

Discussion of a hypothesis according to which two separate phases of lunar crust heating could be responsible for the formation of Mare Smythii and Tsiolkovsky crater, two lava-filled relatively recent lunar features which cannot be easily explained by other hypotheses. A small-crater count in eight flat floored larger craters is conducted in an attempt to support the two-phase heating hypothesis, on a theory that the distribution of the smaller craters by size may indicate a recurrence of lunar crust heating. Further counts are suggested for a more substantiated conclusion.

Beals, C. S.↗

NASA NTRS1972

On the elliptic restricted three-body problem.

This article describes the most important features of the elliptic restricted three-body problem. The methods of numerical integration with recurrent power series are developed for both the equations of motion and the variational equations. The conditions for the existence of periodic orbits and families of periodic orbits are also outlined in detail, and finally illustrated with a family of symmetric periodic orbits.

Broucke, R.↗

NASA NTRS1972

Corotation of an intermittent solar wind source

The measured electron content of the solar wind in mid-1970 exhibited a region of relatively high electron density that reappeared at intervals of about 27.8 days. It is shown that the repeating event cannot be reconciled with the concept of a long-enduring steady flow, even though the recurrence period is close to the rotation period of the sun. This evidence of transients is inferred from the short duration of each appearance of the interval of higher density; each should last for roughly one corotation interval if it is caused by a steady stream. The radio path was approximately 0.8 AU long, and the corotation interval exceeded 3 days. Other aspects of the content data patterns support the view that such transient events are common in the solar wind. The mid-1970 repeating event is an unusually good example of the intermittent character of flow regions in the solar wind that fluctuate on a time scale of days but endure as identifiable regions for many months. A sputtering corotating source of thin solar plasma streams could explain this series of events; it could also be explained in terms of a stream that is steady in density and speed but undulating north-south so that it passes into and out of the 0.8 AU radio path in a matter of a day or less.

Croft, T. A.↗

NASA NTRS1972

Solar flare predictions and warnings

The real-time solar monitoring information supplied to support SPARCS equipped rocket launches, the routine collection and analysis of 3.3-mm solar radio maps, short-term flare forecasts based on these maps, longer-term forecasts based on the recurrence of active regions, and an extension of the flare forecasting technique are summarized. Forecasts for expectation of a solar flare of class or = 2F are given and compared with observed flares. A total of 52 plage regions produced all the flares of class or = 1N during the study period. The following results are indicated: of the total of 21 positive forecasts, 3 were correct and 18 were incorrect; of the total of 31 negative forecasts, 3 were incorrect and 28 were correct; of a total of 6 plage regions producing large flares, 3 were correctly forecast and 3 were missed; and of 46 regions not producing any large flares, 18 were incorrectly forecast and 28 were correctly forecast.

White, K. P., III↗

NASA NTRS1972

Solar flare forecasts based on mm-wavelength measurements

Solar radio temperature contour maps at a wavelength of 3.3 mm are analyzed to develop a method of forecasting solar flares of classes 1N and 1B. Fundamental to the analysis is the demonstration that most of the radio sources associated with the sunspot-plage systems are not spatially resolved by the radio telescope and, hence, only the peak temperature enhancements due to these local radio sources are employed. Evidence is presented indicating that flare-prone plage regions, which belong to recurrent families of flare-productive regions, exhibit a relationship between flare production and radio temperature characteristics considerably unlike that exhibited by virgin plage regions. The results are interpreted by means of graphs which permit the inference of class 1B or 1N flare probabilities based on the peak temperature enhancements measured at 3.3 mm. In particular, the forecast obtained is the probability that a given flare-prone plage region will produce a class 1B or 1N flare (two quoted probabilities) during the period of its disk transit.

White, K. P., III↗

NASA NTRS1972

Sampling functions for geophysics

A set of spherical sampling functions is defined such that they are related to spherical-harmonic functions in the same way that the sampling functions of information theory are related to sine and cosine functions. An orderly distribution of (N + 1) squared sampling points on a sphere is given, for which the (N + 1) squared spherical sampling functions span the same linear manifold as do the spherical-harmonic functions through degree N. The transformations between the spherical sampling functions and the spherical-harmonic functions are given by recurrence relations. The spherical sampling functions of two arguments are extended to three arguments and to nonspherical reference surfaces. Typical applications of this formalism to geophysical topics are sketched.

Giacaglia, G. E. O.↗

NASA NTRS1973

ERTS Applications in earthquake research and mineral exploration in California

Examples that ERTS imagery can be effectively utilized to identify, locate, and map faults which show geomorphic evidence of geologically recent breakage are presented. Several important faults not previously known have been identified. By plotting epicenters of historic earthquakes in parts of California, Sonora, Mexico, Arizona, and Nevada, we found that areas known for historic seismicity are often characterized by abundant evidence of recent fault and crustal movements. There are many examples of seismically quiet areas where outstanding evidence of recent fault movements is observed. One application is clear: ERTS-1 imagery could be effectively utilized to delineate areas susceptible to earthquake recurrence which, on the basis of seismic data alone, may be misleadingly considered safe. ERTS data can also be utilized in planning new sites in the geophysical network of fault movement monitoring and strain and tilt measurements.

Abdel-Gawad, M.↗

NASA NTRS1973

The numerical solution of ordinary differential equations by the Taylor series method

A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

Silver, A. H.↗

NASA NTRS1973

Solar flare predictions and warnings

The real-time solar monitoring information supplied to support SPARCS-equipped rocket launches, the routine collection and analysis of 3.3-mm solar radio maps, short-term flare forecasts based on these maps, longer-term forecasts based on the recurrence of active regions, and results of the synoptic study of solar active regions at 3.3-mm wavelength are presented. Forecasted flares in the 24-hour forecasts were 81% accurate, and those in the 28-day forecasts were 97% accurate. Synoptic radio maps at 3.3-mm wavelength are presented for twenty-three solar rotations in 1967 and 1968, as well as synoptic flare charts for the same period.

White, K. P., III↗

NASA NTRS1972

Venus - Atmospheric rotation.

Photographs of Venus taken in ultraviolet light from Sept. 29, 1963, to May 29, 1971, indicate a general planet-wide circulation in the upper atmosphere of that planet having velocities which varied with time from -87 to -127m/sec at the equator. Positional measurements on 67 pairs of photographs which show the recurrence of similar patterns after intervals of one to three rotations suggest an asymmetric bimodal distribution of these velocities. The ultraviolet markings appear to be randomly distributed and quite ephemeral in nature, rarely enduring in a recognizable pattern for more than 20 days and usually much less. Attention is directed to an apparent but fictitious mean sidereal rotation period of approximately 4.06 days derived from observations which are made at a single station and span many months or years. Under such conditions this fictitious value for the rotation period is produced by the commensurability of the one-day period of earth and the assumed four-day period of the atmosphere of Venus.

Scott, A. H.↗

NASA NTRS1973

Recursive formulas for the partial fraction expansion of a rational function with multiple poles.

The coefficients in the partial fraction expansion considered are given by Heaviside's formula. The evaluation of the coefficients involves the differential of a quotient of two polynomials. A simplified approach for the evaluation of the coefficients is discussed. Leibniz rule is applied and a recurrence formula is derived. A coefficient can also be determined from a system of simultaneous equations. Practical methods for the performance of the computational operations involved in both approaches are considered.

Chang, F.-C.↗

NASA NTRS1973

Interhemispheric comparison of atmospheric circulation features as evaluated from Nimbus satellite data

Reiter, E. R.↗

NASA NTRS1973

A contribution to the synoptic climatology of the extratropics

A relationship is established between relative geostrophic vorticity on an isobaric surface and the Laplacian of the underlying layer-mean temperature. This relationship is used to investigate the distribution of vorticity and baroclinicity in a jet-stream model which is constantly recurrent in the winter troposhere. The investigation shows that the baroclinic and vorticity fields of the extratropical troposphere must be bifurcated with two extrema in the middle and subpolar latitudes. This pattern is present in daily tropospheric meridional cross-sections. The reasons for the disappearance of bifurcation in the time-and-longitude averaged distributions are discussed. The implications of the geographical distribution for the maintenance of the observed kinetic energy and baroclinicity distributions in the extratropical troposphere in winter are discussed. It is shown that the subtropical and subpolar ridges are nearly antiparallely distributed as is required by the observed distribution of temporal r.m.s. vorticity at the jet-stream level.

Srivatsangam, S.↗

NASA NTRS1974

Thermal surveillance of active volcanoes

The author has identified the following significant results. By the end of 1973, aerial infrared scanner traverses for thermal anomaly recordings of all Cascade Range volcanoes were essentially completed. Amplitude level slices of the Mount Baker anomalies were completed and compiled at a scale of 1:24,000, thus producing, for the first time, an accurate map of the distribution and intensity of thermal activity on Mount Baker. The major thermal activity is concentrated within the crater south of the main summit and although it is characterized by intensive solfataric activity and warm ground, it is largely subglacial, causing the development of sizable glacier perforation features. The outgoing radiative flux from the east breach anomalies is sufficient to account for the volume of ice melted to form the glacier perforations. DCP station 6251 has been monitoring a thermally anomalous area on the north slope of Mount Baker. The present thermal activity of Mount Baker accounts for continuing hydrothermal alteration in the crater south of the main summit and recurrent debris avalanches from Sherman Peak on its south rim. The infrared anomalies mapped as part of the experiment SR 251 are considered the basic evidence of the subglacial heating which was the probable triggering mechanism of an avalanche down Boulder Glacier on August 20-21, 1973.

Friedman, J. D.↗

NASA NTRS1973

Parts, Materials, and Processes Experience Summary

The ALERT program, a system for communicating common problems with parts, materials, and processes, is condensed and catalogued. Expanded information on selected topics is provided by relating the problem area (failure) to the cause, the investigations and findings, the suggestions for avoidance (inspections, screening tests, proper part applications), and failure analysis procedures. The basic objective of ALERT is the avoidance of the recurrence of parts, materials, and processed problems, thus improving the reliability of equipment produced for and used by the government.

Source record↗

NASA NTRS1974

Chromospheric flares and sudden commencements of geomagnetic storms

A catalogue of flare activity was compiled during 1957-1967 (the solar activity cycle). By comparing all reliable SC during this period with chromospheric flares, the following conclusions are drawn; (1) There is no statistically significant correlation between SC and chromospheric flares. (2) The assumption that a shock wave propagates throughout the entire hemisphere is unjustified and contradicts the fact of recurrence of SC. (3) A statistically significant correlation was established between SC and chromospheric flares, that is, a relationship between a SC and the moment that a flare active region transits the Central Meridian. (4) SC are caused by shock waves or tangential discontinuities formed at the western boundary of the quasisteady directed corpuscular flux or at the boundary between sectors.

Nesmyanovich, A. T.↗

NASA NTRS1974

Relationships between solar activity and climate change

Recurrent droughts are related to the double sunspot cycle. It is suggested that high solar activity generally increases meridional circulations and blocking patterns at high and intermediate latitudes, especially in winter. This effect is related to the sudden formation of cirrus clouds during strong geomagnetic activity that originates in the solar corpuscular emission.

Roberts, W. O.↗