Periodic orbits and escapes in dynamical systems

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central ??bumpy?? black hole. When the energy reaches its escape value, a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy.     

THE BEAVER-HARRISON,BEAVER COUNTY,UTAH L6 CHONDRITE

The Beaver-Harrison, Utah chondrite (find July 24, 1979), a single, shock-veined stone of 925 grams, consists of major olivine (Fa_25.0), low-Ca pyroxene (En_77.3Fs_21.1Wo_1.6) and metallic nickel-iron; minor troilite and plagioclase (Ab_82.6An_11.1Or_6.3), accessory high-Ca pyroxene (En_47.0Fs_8.5Wo_44.5), chromite (Cm_8.7Sp_10.6Uv_9.4Pc_0.6Hc_0.7), chlorapatite and whitlockite; and hydrous ferric oxide of terrestrial weathering origin. Mineral compositions indicate L-group classification, and homogeneity of minerals, highly recrystallized texture and presence of clear plagioclase suggest that the meteorite belongs to petrologic type 6.     

Spatial and temporal variations of EUV coronal bright points

This paper reports results of an analysis of Skylab observations of coronal bright points made in EUV spectral lines formed in the chromosphere, chromospheric-coronal transition region and corona. The most important result is that the observed bright points exhibited large variations in EUV emission over time scales as short as 5.5 min, the temporal resolution of the data. In most cases strong enhancements in the coronal line were accompanied by strong enhancements in the chromospheric and transition region lines. The intensity variations appear to take place within substructures of the bright points, which most likely consist of miniature loops evolving on time scales of a few minutes. Coronal cooling times derived from the data are consistent with an intermittent, impulsive coronal heating mechanism for bright points.     

The use of invariant manifolds for transfers between unstable periodic orbits of different energies

Techniques from dynamical systems theory have been applied to the construction of transfers between unstable periodic orbits that have different energies. Invariant manifolds, trajectories that asymptotically depart or approach unstable periodic orbits, are used to connect the initial and final orbits. The transfer asymptotically departs the initial orbit on a trajectory contained within the initial orbit’s unstable manifold and later asymptotically approaches the final orbit on a trajectory contained within the stable manifold of the final orbit. The manifold trajectories are connected by the execution of impulsive maneuvers. Two-body parameters dictate the selection of the individual manifold trajectories used to construct efficient transfers. A bounding sphere centered on the secondary, with a radius less than the sphere of influence of the secondary, is used to study the manifold trajectories. A two-body parameter, κ, is computed within the bounding sphere, where the gravitational effects of the secondary dominate. The parameter κ is defined as the sum of two quantities: the difference in the normalized angular momentum vectors and eccentricity vectors between a point on the unstable manifold and a point on the stable manifold. It is numerically demonstrated that as the κ parameter decreases, the total cost to complete the transfer decreases. Preliminary results indicate that this method of constructing transfers produces a significant cost savings over methods that do not employ the use of invariant manifolds.     

Metabolic plasticity of nitrogen assimilation by Porphyra umbilicalis (Linnaeus) Kützing

The physical stresses associated with emersion have long been considered major factors determining the vertical zonation of intertidal seaweeds.We examined Porphyra umbilicalis(Linnaeus) Kützing thalli from the vertical extremes in elevation of an intertidal population(i.e.upper and lower intertidal zones) to determine whether Porphyra thalli acclimate to different vertical elevations on the shore with different patterns of nitrate uptake and nitrate reductase(NR) and glutamine synthetase(GS) activities in response to different degrees of emersion stress.We found that the nitrate uptake and NR recovery in the emersed tissues took longer in lower intertidal sub-population than in upper intertidal sub-population;and GS activity was also significantly affected by emersion and,interestingly,such an activity was enhanced by emersion of thalli from both upper and lower intertidal zones.These results suggested that intra-population variability in post-emersion recovery of physiological functions such as nutrient uptake and NR activity enables local adaptation and contributes to the wide vertical distribution of P.umbilicalis.The high GS activity during periodic emersion stress may be a protective mechanism enabling P.umbilicalis to assimilate nitrogen quickly when it again becomes available,and may also be an evidence of photorespiration during emersion.     

Heights of formation of non-magnetic solar lines suitable for velocity studies

Heights of formation of lines that do not exhibit Zeeman splitting are calculated using an LTE, partial non-LTE, and full non-LTE approach. Non-magnetic (g=0) lines are valuable for velocity investigations in quiet-Sun magnetic field regions, and a knowledge of their formation heights is useful for obtaining three dimensional velocity profiles in these regions. Presently at Sacramento Peak Observatory. Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

EUV analysis of an active region

A sequence of extreme ultraviolet (EUV) spectroheliograms of McMath region No. 10283 were obtained by the Harvard College Observatory experiment on OSO-6. The lines Ovi λ1032 Mg × λ625, Si xii λ499 and Fe xvi λ 335 were used to determine coronal temperatures and densities above the active region. A comparison of theoretical and observed line ratios yielded coronal temperatures of 2.2 to 2.3 × 10⁶K above the active region and 2.0 to 2.1 × 10⁶K in the surrounding area. The temperatures derived from ratios involving the O vi intensities are systematically higher than the others. This is attributed to an error in the theoretical O vi intensities. The intensities observed above the limb are compared with intensities predicted with a simple model based on cylindrical geometry. The overall agreement shows that the assumption of an iso-thermal corona in hydrostatic equilibrium above the active region is a reasonable working hypothesis and that the adopted geometrical model for the electron density distribution is adequate.     

A technique to deduce atmospheric temperature and constituent profiles from a planet's limb radiance profile

The concept is described of deducing the temperature and constituent profile of a planetary atmosphere from orbiter measurements of the planet's ir limb radiance profile. Expressions are derived for the weighting functions associated with the limb radiance profile for a Goody random band model. Analysis of the weighting functions for the Martian atmosphere indicates that a limb radiance profile in the 15 μm CO₂ band can be used to determine the Martian atmospheric temperature profile from 20 to 60 km. Simulation of the Martian limb radiance profile in the rotational water vapor band indicates that Martian water vapor mixing ratios can be inferred from limb radiance observations in a water vapor band.     

An analysis of the distribution of boulders in the vicinity of small lunar craters

Nine Orbiter 3 high-resolution photographs were examined at three sites for distributions of boulders around craters 110 m in diameter; three kinds of distributions were noted. Some had boulders inside and far outside (designated), others had boulders only inside or on their ramparts (), and some had no detectable boulders (). Additionally, shapes or morphologies of craters were classified according to their resemblance to one of three Jaffe models (1965); a third classification involved the depth of particulate overlay (Jaffe, 1965). Crater morphologies were classified (A) if they were relatively shallow with sharp, raised rims, (B) if they were rimless and shallow, and (C) if they were relatively deep and had low, broad rims. The data suggested that there were strong relationships between crater types and boulder distributions in which, generally, A-type was related to the-distribution, B-type to-distribution, and C-type to-distribution. Plots of numbers of craters of each crater type and each kind of boulder distribution versus steps of overlay for each site and for the totality of craters considered indicated that neither boulder distribution nor crater type represented orderly progression of age or erosional evolution. The apparent overlays for the A's and C's and for the's and's were similar, implying similar ages or stages of erosion. It is suggested that they represent two kinds of primary craters and that the A's are of impact origin while the C's are of volcanic origin. The B's probably represent later stages of erosion of the C's and possibly of some A's.Now at the University of Maryland.Receipt delayed by postal strike in Great Britain.     

Lyman-alpha observations of Comet West (1975n)

Images of Comet West in atomic hydrogen (1216 Å) emission were obtained from a sounding rocket on 1976 March 5.5 (R = 0.38 AU). The hydrogen production rate derived from the fit of a simple radial-outflow model to the observed inner isophotes was 3.2 × 10³⁰ atoms/sec. The outer isophotes did not fit the predictions of the complex dynamic model of Keller and Meier, partly because of optical depth effects, but also because the nucleus was breaking up at about this time and it is quite possible that additional hydrogen was being emitted from smaller chunks of the nucleus distributed along the orbit. The above production rate, taken with data on C and O obtained simultaneously by Feldman and Brune, gives Q_H: Q_o: Q_c = 8:3.5:1. For Comet Kohoutek we obtained the ratio 7:1.7:1. The difference, if real, may be due to minor differences in composition or evolution, but in any case it appears that the two comets are similar.