Periodic orbits and their bifurcations in a 3-D system

We study some simple periodic orbits and their bifurcations in the Hamiltonian . We give the forms of the orbits, the characteristics of the main families, and some existence diagrams and stability diagrams. The existence diagram of the family 1a contains regions that are stable (S), simply unstable (U), doubly unstable (DU) and complex unstable (). In the regionsS andU there are lines of equal rotation numberm/n. Along these lines we have bifurcations of families of periodic orbits of multiplicityn. When these lines reach the boundary of the complex unstable region, they are tangent to it. Inside the region there are linesm/n, along which the orbits 1a, describedn-times, are doubly unstable; however, along these lines there are no bifurcations ofn-ple periodic orbits. The families bifurcating from 1a exist only in certain regions of the parameter space (, ). The limiting lines of these regions join at particular points representing collisions of bifurcations. These collisions of bifurcations produce a nonuniqueness of the various families of periodic orbits. The complicated structure of the various bifurcations can be understood by constructing appropriate stability diagrams.     

Effect of perturbed potentials on the non-linear stability of libration pointL 4 in the restricted problem

The non-linear stability of the libration pointL ₄ in the restricted problem has been studied when there are perturbations in the potentials between the bodies. It is seen that the pointL ₄ is stable for all mass ratios in the range of linear stability except for three mass ratios depending upon the perturbing functions. The theory is applied to the following four cases:

On the electron density in an active region observed by SERTS

Emission lines from an active region, observed by SERTS, have been used to determine electron densities from theoretical curves for Mgvii, Siviii, and Siix density-sensitive line ratios. Density diagnostics of Alviii 285.46/323.52 line emissivity ratio has also been investigated.     

The near infrared camera on the W.M. Keck telescope

The near infrared camera (NIRC) was used for a science demonstration run on the Keck telescope during 16–24 March 1993. The camera used a 256×256 InSb array manufactured by Santa Barbara Research Corporation. Observations were obtained using narrowband and broad band filters from 1 to 2.4 microns, and grisms with a spectral resolution of 0.6 percent in the J, H and K atmospheric windows. The instrument was fully background limited over the entire wavelength range. The sky background was quite low, reaching 14.3 mag/square arc sec in the broadband K _s filter. The image quality of the camera + telescope was excellent, being seeing limited in the range 0.5–0.9.The science demonstration observations of the NIRC on the Keck Telescope included observations of the most distant galaxy known, 4C41.17 at a redshift z=3.8 and the most luminous object known, the IRAS source FSC10214+4724 at a redshift z=2.29. Observations of the radio galaxy address the problem of the alignment effect in high redshift radio galaxies as well as the environments of such systems. FSC10214+4724 appears to be a merging galaxy that is at least 5×10⁸ years old.Based on observations obtained at the W.M.Keck Observatory, which is operated jointly by the California Institute of Technology and the University of CaliforniaThe W.M. Keck Observatory is operated as a scientific partnership between the California Institute of Technology and the University of California. It was made possible by the generous gift of the W.M. Keck foundation and the support of its president, Howard Keck.     

Theoretical emission line strengths for Ov compared to EUV solar observations

RecentR-matrix calculations of electron impact excitation rates in Ov are used to derive the emission line intensity ratios (in energy units) $$\begin{gathered} R_1 = I(2s2p^{ 3} P - 2p^{2 3} P)/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(761.1\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ ), \hfill \\ R_2 = I(2s^{2 1} S_0 - 2s2p^{ 3} P_1 )/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(1218.4\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ ), \hfill \\ \end{gathered} $$ and $$R_3 = I(2s2p^{ 1} P_1 - 2p^{2 1} S_0 )/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(774.5\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ )$$ as a function of electron temperature (T _e) and density (N _e). These results are presented as plots ofR ₁ vsR ₂, andR ₁ vsR ₃, which should allowboth N _e andT _e to be deduced for the Ov line emitting region of a plasma. Electron densities derived from the (R ₁,R ₂) and (R ₁,R ₃) diagrams in conjunction with observational data for several solar features obtained with the Harvard S-055 spectrometer on boardSkylab are found to be compatible, and in good agreement with values ofN _e estimated from line ratios in species formed at similar electron temperatures to Ov. In addition, values ofT _e determined from (R ₁,R ₂) and (R ₁,R ₃) are generally close to that expected theoretically. These results provide experimental support for the accuracy of the diagnostic calculations presented in this paper, and hence the atomic data used in their derivation.     

A verification of some methods to determine the fluxes of momentum,sensible heat,and water vapour using standard deviation and structure parameter of scalar meteorological quantities

A set of micro-meteorological data collected over a horizontal, uniform terrain (the plain of La Crau, France) in June 1987 is analysed. Conditions were predominantly sunny and arid, while due to the Mistral the wind speed could exceed 10 m/s. Verification of several methods to evaluate surface fluxes of heat, momentum and water vapour from the standard deviation of temperature, wind and specific humidity is presented. Also, a similar approach using the structure parameter of temperature is considered. These methods are all based on Monin-Obukhov (M-O) similarity theory. It is found that the standard deviation of temperature, vertical and horizontal wind speed as well as the structure parameter for temperature behave according to M-O similarity. It is shown that the sensible heat flux and friction velocity can be determined from a fast response thermometer and a cup anemometer. Also, it appears that the analytic solution of the set of governing equations as derived by the first author yields good results. M-O theory does not appear to work for the standard deviation of specific humidity. This may be due to the relative importance of large eddies.     

On the sampling of airborne measurements of radiative properties of cloud fields: Results from International Cirrus Experiment (ICE), 1987

Summary During the first pilot phase of the International Cirrus Experiment (ICE) in September/October 1987 radiation measurements were carried out above and below broken cloud fields over the German Bight. Analyses of the measurements of 25.9.1987 (broken cumulus cloud field) showed an unexpected high absorption of solar radiation but not those of 28.9.1987 (stratocumulus/stratus cloud field). This might be explained by a partial negligence of cloud side factor under the viewing geometry of the pyranometer and other reasons. The light guide effect (leakage) within holes can account for the depletion of cloud reflectance and the enhancement of cloud transmittance at large cloud cover, as observed during the measurements on 28.9.1987. The fluctuation of the irradiances, which can be characterized by the intermittency parameter, has been related to the corresponding cloud cover by a regression equation. On the condition of similarity, this scaling parameter derived from sample measurements could be extrapolated to that of the whole cloud field. Thus, the estimation of the irradiance spectrum for the whole cloud field may be possible, from samples taken with aircraft and imaging data.With 5 Figures     

Correlation methods in fingerprint detection studies

This investigation addresses two general issues regarding the role of pattern similarity statistics in greenhouse warming detection studies: normalization, and the relative merits of centered versus uncentered statistics. A pattern correlation statistic is used to search for the greenhouse warming signals predicted by five different models in the observed records of land and ocean surface temperature changes. Two forms of this statistic were computed: R (t), which makes use of nonnormalized data, and (t), which employs point-wise normalized data in order to focus the search on regions where the signal-to-noise ratio is large. While there are no trends in the R (t) time series, the time series of (t) show large positive trends. However, it is not possible to infer from the (t) results that the observed pattern of temperature change is, in fact, becoming increasingly similar to the model-predicted signal. This is because point-wise normalization of the observed and simulated mean change fields by a single common field introduces a common factor effect, which means that the quantities being compared should show some similarity a priori. This does not necessarily make normalization inapplicable, because the detection test involves seeking a trend in the similarity statistic. We show, however, that trends in (t) must arise almost completely from the observed data, and cannot be an indicator of increasing observed data/signal similarity. We also compare the information provided by centered statistics such as R(t) and the uncentered C(t) statistic introduced by Barnett. We show that C(t) may be expressed as the weighted sum of two terms, one proportional to R(t) and the other proportional to the observed spatial mean. For near-surface temperatures, the spatial average term dominates over the R(t) term. In this case the use of C(t) is equivalent to the use of spatial-mean temperature. We conclude that at present, the most informative pattern correlation statistic for detection purposes is R(t), the standard product-moment correlation coefficient between the observed and model fields. Our failure to find meaningful trends in R(t) may be due to the fact that the signal is being obscured by the background noise of natural variability, and/or because of incorrect model signals or sensitivities.     

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

Ethnicity as a cause of migration in Eastern Europe

Migration within and from Eastern Europe has recently risen as a topic of significance on the European political agenda. One aspect of this complex migration matrix relates to ethnic unrest. This paper examines the scale and spatial ramifications of this movement on a part of the continent recently freed from communist rule.An attempt is made to divide the ethnic quilt of Eastern Europe into those countries with few such problems and those with many. It is possible then to define areas of active migration (hot spots) from those of potential migration (inflammable spots) based on predictions from the current situation.Active ethnic migration results from the present political/military instability in the western Balkans, where refugees have left for other parts of Europe to escape the present Croat-Serb-Muslim conflict. War escalation could encourage potential ethnic migration from Kosovo, the Sandzak and Vojvodina regions,and Macedonia within the former Yugoslavia. Future disquiet elsewhere could stimulate ethnic groups such as the Turks in Bulgaria,and the Hungarian minorities in Slovakia and Romania to join this migration movement scenario.