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It was previously shown (author, 1969) that the regions of absolute stability in the parameter space can be determined when the parameters appear on the right-hand side of the system equations, i.e., the regular case. Here, the effect on absolute stability of a small parameter attached to higher derivatives in the equations (the singular case) is studied. The Lur'e-Postnikov class of nonlinear systems is considered.
Solar irradiance measurements by instruments (Eppley Angstrom Pyrheliometers) reproducing the International Pyrheliometric Scale (IPS) have been compared with measurements made simultaneously by a number of JPL Active Cavity Radiometers (ACR) and the Practical Absolute Cavity Radiometer (PACRAD). The results of these tests demonstrate a systematic difference between the absolute radiation scale as defined by the ACR and PACRAD measurements and the IPS.
An experimental examination of the absolute intensity, polarization, and relative line intensities of rotational Raman scattering (RRS) from N2, O2, and CO2 is reported. The absolute scattering intensity for N2 is characterized by its differential cross section for backscattering of incident light at 647.1 nm, which is calculated from basic measured values. The ratio of the corresponding cross section for O2 to that for N2 is 2.50 plus or minus 5 percent. The intensity recent for N2, O2, and CO2 are shown to compare favorably to values calculated from recent measurements of the depolarization of Rayleigh scattering plus RRS. Measured depolarizations of various RRS lines agree to within a few percent with the theoretical value of 3/4. Detailed error analyses are presented for intensity and depolarization measurements. Finally, extensive RRS spectra at nominal gas temperatures of 23 C, 75 C, and 125 C are presented and shown to compare favorably to theoretical predictions.
Absolute photon-flux measurements in the vacuum ultraviolet have extended to short wavelengths by use of rare-gas ionization chambers. The technique involves the measurement of the ion current as a function of the gas pressure in the ion chamber. The true value of the ion current, and hence the absolute photon flux, is obtained by extrapolating the ion current to zero gas pressure. Examples are given at 162 and 266 A. The short-wavelength limit is determined only by the sensitivity of the current-measuring apparatus and by present knowledge of the photoionization processes that occur in the rate gases.
A two-channel spectrometer was calibrated in the wavelength region 1200-3400 A and flown on an Aerobee rocket to observe the stars alpha Lyr, eta UMa, and zeta Oph. Standard tungsten lamps provided the absolute calibration down to 2250 A, and a photodiode calibrated by the National Bureau of Standards was the reference at shorter wavelengths. The molecular branching-ratio technique of relative calibration using the gases CO, NO, and N2 was a check on the absolute calibration. The flux from eta UMa agrees with the prediction of a hydrogen line blanketed model atmosphere within 10% between 1700 and 3400 A and within 4% over most of this wavelength region.
A radiometer for the remote measurement of sea surface temperature is described. The development of an instrument capable not only of high relative accuracy (i.e., resolution) but also of high absolute precision is considered. The concepts underlying the design of an instrument capable of an absolute accuracy of a few tenths degrees Kelvin in the measurement of brightness temperature at S band are described. The role of the antenna is discussed, and the importance of high ohmic and beam efficiencies is stressed. The hardware itself is fully described, along with an outline concerning the design of a unique cryogenically cooled termination used to calibrate the whole radiometer, including antenna. Finally, some test results are presented that show that the design goals for the instrument have been closely approached.
Orbital solutions were obtained for the early-type eclipsing binary LY Aurigae from the light curves obtained with the OAO-2 by Heap and from the V light curve obtained from ground-based observations by Mayer and Horak. The solutions take into account the existence of a nearby companion not accounted for by previous investigators. The spectroscopic observations by Mayer and Batten were used to compute absolute dimensions for the binary orbit and for each component. This binary system presents an unique opportunity to determine accurately the absolute dimensions of an O9.5 III star.
Work has been conducted to reduce substantially uncertainties concerning the line strengths for carbon and sulfur. Two or more independent methods were used to measure thermodynamic variables and to calibrate detectors for absolute sensitivity and spectral response. The absolute transition probabilities of 124 visible and infrared lines of C I, S I, and S II were measured in a consistent way.
The main interaction of the earth's interior with the lithosphere is as a material source and sink. An absolute reference frame defined by minimizing the translational motion of tectonic plate boundaries differs by 0.6 cm/year from a frame defined by hot spot traces and by 0.4 cm/year from the frame defined by the most plausible model of drag forces on the plates. The rms absolute translational velocities are about 2 cm/year for ocean-ocean plate boundaries and 1.5 cm/year for ocean-continent plate boundaries. The close agreement between the source and sink and the drag-dependent definitions suggests that the lithosphere, as a stress guide, to some extent controls the locations of its sources and sinks.
Results are presented for an experimental application of the laminar flow-through/resonance technique, which allows direct observations of the absolute concentration of atoms and radicals in the earth's upper atmosphere. Atomic resonance fluorescence was used in conjunction with a parachute-borne flow-through module deployed from a balloon at a height of 40 km to determine the concentration of ground-state atomic oxygen at 40 to 25 km in the atmosphere. The equipment is described, and the measurements and experimental uncertainties are plotted. It is shown that the observed absolute concentration of ground-state atomic oxygen is similar to that predicted by model calculations, and it is concluded that this technique provides a simple and direct means of measuring atomic and radical concentrations in the part-per-trillion range in unperturbed stratospheric samples.
A series of active cavity radiometers (ACRs) are described which have been developed as standard detectors for the accurate measurement of irradiance in absolute units. It is noted that the ACR is an electrical substitution calorimeter, is designed for automatic remote operation in any environment, and can make irradiance measurements in the range from low-level IR fluxes up to 30 solar constants with small absolute uncertainty. The instrument operates in a differential mode by chopping the radiant flux to be measured at a slow rate, and irradiance is determined from two electrical power measurements together with the instrumental constant. Results are reported for measurements of the solar constant with two types of ACRs. The more accurate measurement yielded a value of 136.6 plus or minus 0.7 mW/sq cm (1.958 plus or minus 0.010 cal/sq cm per min).
A low-pressure hydrogen discharge lamp was calibrated for radiant intensity in the vacuum ultraviolet spectral region on an absolute basis and was employed as a laboratory standard source in spectrograph calibrations. This calibration was accomplished through the use of a standard photodiode detector obtained from the National Bureau of Standards together with onsite measurements of spectral properties of optical components used. The stability of the light source for use in the calibration of vacuum ultraviolet spectrographs and optical systems was investigated and found to be amenable to laboratory applications. The lamp was studied for a range of operating parameters; the results indicate that with appropriate peripheral instrumentation, the light source can be used as a secondary laboratory standard source when operated under preset controlled conditions. Absolute intensity measurements were recorded for the wavelengths 127.7, 158.0, 177.5, and 195.0 nm for a time period of over 1 month, and the measurements were found to be repeatable to within 11 percent.
Relative and absolute populations of 19 levels in beam-foil-excited neutral helium at 0.275 MeV have been measured. The singlet angular-momentum sequences show dependences on principal quantum number consistent with n to the -3rd power, but the triplet sequences do not. Singlet and triplet angular-momentum sequences show similar dependences on level excitation energy. Excitation functions for six representative levels were measured in the range from 0.160 to 0.500 MeV. The absolute level populations increase with energy, whereas the neutral fraction of the beam decreases with energy. Further, the P angular-momentum levels are found to be overpopulated with respect to the S and D levels. The overpopulation decreases with increasing principal quantum number.
The absolute energy distribution in the ultraviolet is given for the stars alpha Vir, eta UMa, and alpha Leo. The calibration is based on absolute heterochromatic photometry between 2920 and 1370 A carried out with an Aerobee sounding rocket. The fundamental radiation standard is the synchrotron radiation from 240-MeV electrons in a certain synchrotron storage ring. On the basis of the sounding-rocket calibration, the preliminary OAO-2 spectrometer calibration has been revised; the fluxes for the three program stars are tabulated in energy per second per square centimeter per unit wavelength interval.
The laboratory measurements of absolute Rayleigh scattering cross sections as a function wavelength are reported for gas molecules He, Ne, Ar, N2, H2, O2, CO2, CH4 and for vapors of most commonly used freons CCl2F2, CBrF3, CF4, and CHClf2. These cross sections are determined from the measurements of photon scattering at an angle of 54 deg 44 min which yield the absolute values independent of the value of normal depolarization ratios. The present results show that in the spectral range 6943-3638A deg, the values of the Rayleigh scattering cross section can be extrapolated from one wavelength to the other using 1/lambda (4) law without knowing the values of the polarizabilities. However, such an extrapolation can not be done in the region of shorter wavelengths.
It has already been shown that the Fe II absolute oscillator strengths (f-values) measured by Warner (1967) contain a systematic error, the magnitude of which depends on the energy of the transition's upper level. The present paper demonstrates that this error affects all of Warner's oscillator strengths for the second spectra of the iron group and develops a correction formula for Warner's results. A comparison of the corrected f-values with other measured f-values for Ti II, V II, and Fe II indicates that the correction improves the usefulness of Warner's data and that the corrected f-values have no large systematic dependence on wavelength, level energy, or line strength. Solar abundances for iron-group elements computed using the original and corrected f-values are compared with recently suggested abundances, and it is found that the corrected f-values yield more consistent results. Semiempirical oscillator strengths calculated by Kurucz and Peytremann (1975) for Fe I, Ti II, and V II are also compared with measured data to evaluate the accuracy of the calculations. It is found that the absolute scales of these results are roughly correct, but some of them are subject to very large errors.
The absolute integrated intensity of the IR vibration-rotation nu-1 SO2 band was measured using the linear portion of the curve of growth. Infrared spectroscopic-absorption cell measurements were performed on sulfur dioxide at partial pressures less than 0.15 torr with nitrogen added to give a total pressure of 705 torr, the path length being 4 mm. The absolute integrated intensity was determined to be 112.0 plus or minus 2.6/cm/sq (atm cm) at 296 K at the 95% confidence level.
The absolute intensity of the 4-0 vibration band of CO is measured in spectra obtained using a 25-m base-path multiple-traversal absorption cell and a 5-m scanning spectrometer. The intensities of individual vibration-rotation lines in this band are determined from measurements of their equivalent widths, and absolute values for the rotationless transition moment and the vibration-rotation interaction factor are derived from the measured line strengths. The experimentally obtained vibration-rotation function is compared with a theoretical curve; agreement between theory and experiment is found to be good for the P-branch but poor for the R-branch. It is noted that numerical solutions to the radial Schroedinger equation lead to vibration-rotation function values that are in good agreement with the experiment.