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Computer techniques used for determination of periods of brightness change in variable stars are discussed, with emphasis on the Lafler-Kinman method and a presentation of Kholopov's own method based on brightness extremes.
The solution of the one-dimensional Ginzburg-Landau equation is presented for the case of a linear, periodic, superconducting weak-link system. With respect to currents below a critical value, four solutions for the spatially dependent order parameter are obtained.
The use of artificial periodic structures, consisting of spatial modulations of the linear and nonlinear susceptibilities of a nonlinear optical medium, to achieve phase matching in second-harmonic generation is analyzed. Dispersion relations and approximate formulas for the second-harmonic fields generated under various conditions are obtained and used to evaluate the experimental situation.
A class of second order linear time-invariant systems which are unstable for any constant feedback but which are stabilized by a two level periodic feedback is identified. Necessary and sufficient conditions for this type of stabilization are found. In addition, the sensitivity of the closed-loop system to changes in feedback gains is investigated.
The short period luni-solar theory of Kozai is generalized for arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements are derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.
An investigation is conducted concerning the trapping of gas and its effect on the structure of the magnetic field. The aligned and orthogonal cases are discussed in detail. In each case, there are small collection zones which are both microscopically and macroscopically stable. By determining where macroscopic stability changes to instability, the separatrix between closed and open field lines is investigated together with the sizes and shapes of the polar caps. This information makes it possible to reexamine the period-pulse-width distribution and to compare it with observational data.
The apparent strength of CO2 absorptions in the spectrum of Venus varies by 20% in a period of 4 days. The variations are synchronous over the disk, and thus represent a fundamental dynamical mode of the atmosphere.
Analytical solutions for quasi-periodic orbits about the translunar libration point are obtained by using the method of Lindstedt-Poincare and computerized algebraic manipulations. The solutions include the effects of nonlinearities, lunar orbital eccentricity, and the sun's gravitational field. For a small-amplitude orbit, the orbital path as viewed from the earth traces out a Lissajous figure. This is due to a small difference in the fundamental frequencies of the in-plane and out-of-plane oscillations. However, when the amplitude of the in-plane oscillation is greater than 32,379 km, there is a corresponding value of the out-of-plane amplitude that will produce a path where the fundamental frequencies are equal. This synchronized trajectory describes a 'halo orbit' of the moon.
Investigation of the long-period V/R variation in some Be stars studied by McLaughlin (1966) and others, based on the assumption that the variation is caused by the apsidal motion of an elliptical ring in which the emitting atoms revolve around the star according to Kepler's laws of motion. The results indicate that the behavior of the V/R variation depends upon both the eccentricity and the lateral extent of the gaseous ring. However, if the ring is narrower than a certain limit, the dependence on the width is negligible. In such a case, the eccentricity of the ring can be determined by the observed amplitude of the V/R variation. Based on this model, the radial-velocity curves of both emission edges and central absorption are derived. It is found that they all have the same amplitude, which also depends on the eccentricity, and that all are changing in phase with the V/R variation.
The statistical significance of anisotropies in the distribution of orbital orientations among the long-period and nearly parabolic comets is evaluated. It is suggested that these anisotropies are not the result of observational selection effects. A numerical model for the distribution of orbital orientations is constructed, based on Oort's theory of comet origin and the assumption that the observed anisotropies are caused by multiple planetary perturbations over the course of many perihelion passages. The model, which is restricted to comets with perihelion distances less than 0.3 AU, does not predict any significant anisotropies.
A study has been made of a dynamical system composed of a pendulum and a harmonic oscillator, in order to show the remarkable resemblance with many classical celestial mechanics problems, in particular, the restricted three-body problem. It is shown that the well-known investigations of periodic orbits can be applied to the present dynamics problem.
In the generally stably stratified lower stratosphere, SST exhaust plumes could spend a significant length of time in a relatively undispersed state. This effort has utilized invariant modeling techniques to simulate the separate and combined effects of atmospheric turbulence, turbulent diffusion, and chemical reactions of SST exhaust materials in the lower stratosphere. The primary results to date are: (1) The combination of relatively slow diffusive mixing and rapid chemical reactions during the Phase III wake period minimizes the effect of SST exhausts on O3 depletion by the so-called NOx catalytic cycle. While the SST-produced NO is substantially above background concentrations, it appears diffusive mixing of NO and O3 is simply too slow to produce the O3 depletions originally proposed. (2) The time required to dilute the SST exhaust plume may be a significant fraction of the total time these materials are resident in the lower stratosphere. If this is the case, then prior estimates of the environmental impact of these materials must be revised significantly downward.
The circadian rhythm hardware activities from 1965 through 1973 are considered. A brief history of the programs leading to the development of the combined Skylab SO71/SO72 Circadian Periodicity Experiment (CPE) is given. SO71 is the Skylab experiment number designating the pocket mouse circadian experiment, and SO72 designates the vinegar gnat circadian experiment. Final design modifications and checkout of the CPE, integration testing with the Apollo service module CSM 117 and the launch preparation and support tasks at Kennedy Space Center are reported.
Phase lag, maximal slow phase velocity, and beat frequency were measured in periodic Coriolis star nystagmus. The results have been described by Steinhausen's model of the semicircular canal system. Estimates of the biophysical constants have been obtained. It is concluded that this model is a good functional approximation for describing, and also for interpreting, the behavior of the system.
The results of recent studies on higher order, integrative processes in the central nervous system are reported. Attempts were made to determine whether these processes exhibit any ongoing rhythmicity which might manifest itself in alterations of attention and alertness. Experiments were also designed to determine if a periodicity approximating that of the REM could be detected in various parameters of brain electrical activity.
The variability of stratospheric meridional winds is examined in both space and time. Height-latitude sections for January along 70 deg E and 90 deg W show a divergence zone above 50 km near 60 deg N and an intense convergence zone 40 km near 50 deg N over North America. This latter structure, with southward winds in the Arctic and northward winds at mid-latitudes over North America, persists from October through April. Tidal winds dominate all other circulation features in summer at all latitudes, and throughout the year at low latitudes. To help understand the observed patterns of variability, long-term periodic features are analyzed. The quasi-biennial oscillation, annual wave, and four-month wave have amplitudes of about 10, 20, and 10 m/sec respectively in the Arctic near 45 km. The phase of the annual wave changes by nearly 180 deg in a narrow zone near 45 deg N. The semiannual wave has an amplitude of 10 m/sec. 50 deg N above 50 km equinoctial phase dates in the region of maximum amplitude. This polar semiannual wave corresponds closely to that previously found in the zonal wind.
Infrared observations at an effective wavelength of 3.5 microns of a selected group of long period variable (LPV) stars are presented. Mira type and semiregular stars of M, S, and C spectral classifications were monitored throughout the full cycle of variability. Although the variable infrared radiation does not exactly repeat in intensity or time, the regularity is sufficient to produce mean 3.5 micron light curves. The 3.5 micron maximum radiation lags the visual maximum by about one-seventh of a cycle, while the minimum 3.5 micron intensity occurs nearly one-half cycle after infrared maximum. In some stars, there are inflections or humps on the ascending portion of the 3.5 micron light curve which may also be seen in the visual variations.
The optimal Bayes detector for a general periodic waveform having uniform delay and additive white Gaussian noise is examined. It is shown that the detector is much more complex than that for the well known cases of pure sine waves (i.e. classical noncoherent detection) and narrowband signals. An interpretation of the optimal processing is presented, and several implementations are discussed. The results have application to the noncoherent detection of optical square waves.