Chaotic behaviour of trajectories for the asteroidal resonances

A systematic study of the main asteroidal resonances of the third and fourth order is performed using mapping techniques. For each resonance one-parameter family of surfaces of section is presented together with a simple energy graph which helps to understand and predict the changes in the surfaces of section within the family. As the truncated Hamiltonian for the planar, elliptic, restricted three-body problem is used for the mapping, the method is expected to fail for high eccentricities. We compared, therefore, the surfaces of section with trajectories calculated by symplectic integrators of the fourth and six order employing the full Hamiltonian. We found a good agreement for small eccentricities but differences for the higher eccentricities (e 0.3).     

Mapping and dynamical systems

This paper reviews various mapping techniques used in dynamical astronomy. It is mostly dealing with symplectic mappings. It is shown that used mappings can be usually interpreted as symplectic integrators. It is not necessary to introduce any functions it is just sufficient to split Hamiltonian into integrable parts. Actually it may be shown that exact mapping with function in the Hamiltonian may be non-symplectic. The application to the study of asteroid belt is emphasised but the possible use of mapping in planetary evolution studies, cometary and other problems is shortly discussed.     

The basic cycle of solar activity and the global magnetic field and active phenomena distribution

We have compared the latitudinal distributions of polar faculae, green coronal emission maxima, prominences and of a new index of enhanced geomagnetic recurrence with the distribution of magnetic fields during the cycles Nos. 20 and 21.We did not find a distinct high-latitude initial stage of an extended cycle in the corona, prominences and polar faculae distribution. On the contrary, it seems that the polar faculae and their following polarity magnetic fields represent the last evolutionary phase of a magnetic activity cycle lasting 15–17 years. The enhanced recurrent geomagnetic activity seems to be related to the old cycle fields.All studied phenomena clearly display two types of latitudinal distribution: the polar belts, into which the old following polarity fields have been transported from the equatorial belt where both the polarities developin situ simultaneously, but in which the leading polarity fields only remain, crossing the equator during the minimum of activity, to play the same role on the opposite hemispheres in the new cycle.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Particle beams as a source of noise storm depression?

The February 5, 1986 flare-related radio continuum depression is studied, compared with other noise storm depression events and discussed in the framework of current type I storm models. The influence of flare plasma flow or shocks and of superthermal electrons on noise storm radiation is considered. The presence of fast drifting emission features just before and during the decrease of the intensity, the association between the depression onset and the microwave burst maximum, the simultaneous appearance of the intensity minimum over a broad spectral range as well as preflare evidence of an interconnection of the flare site and the noise storm source are arguments for a preference of the role of beams of superthermal electrons. We distinguish abrupt and slow depressions (Figure 5). The abrupt depressions are in agreement with Melrose's (1980) predictions. Slow depressions can only be understood by invoking the diffusion of super-thermal electrons through the magnetic field carrying the storm source.     

Cosmologic member λ in the light of present physical conceptions

In this paper, in a historical retrospect, the problem of the hypothetical cosmologic member is discussed. Under the assumption that the Universe is an ultrastable actual manifestation of a unique fundamental substance-physical vacuum, the extremality of actual properties of the Universe admits only of two values . In the de Sitter evolution phase, has an undetermined character. In the Friedmann one, =0.     

Degradation of Geopotential Recovery from Short Repeat-Cycle Orbits: Application to GRACE Monthly Fields

Throughout 2004 the GRACE (Gravity Recovery And Climate Experiment) orbit contracted slowly to yield a sparse repeat track of 61 revolutions every 4 days on 19 September 2004. As a result, we show from linear perturbation theory that geopotential information previously available to fully resolve a gravity field every month of 120× 120 (degree by order) in spherical harmonics was compressed then into about one-fourth of the necessary observation space. We estimate from this theory that the ideal gravity field resolution in September 2004 was only about 30 × 30. More generally, we show that any repeat-cycle mission for geopotential recovery with full resolution L × L requires the number of orbit-revolutions-to-repeat to be greater than 2L.     

Low-field variation of magnetic susceptibility measured by the KLY-4S Kappabridge and KLF-4A magnetic susceptibility meter: Accuracy and interpretational programme

The KLY-4S Kappabridge and KLF-4A Magnetic Susceptibility Meter enable automated measurement of susceptibility variation with field in the ranges of 2–450 A/m and 5–300 A/m (in effective values), respectively. Unfortunately, the measurement accuracy decreases with decreasing field and it is not easy to decide whether the susceptibility variation at the lowest fields is natural phenomenon or results from measuring errors. To overcome this problem, the accuracies of both the above instruments were investigated experimentally using artificial specimens (mixture of pure magnetite and plaster of Paris) with variable susceptibilities ranging from 1 × 10⁻⁵ to 5 × 10⁻². The complete curve of the field variation of susceptibility of each specimen was measured 10 times and the relative error was calculated for each field. In the KLY-4S Kappabridge, in specimens with susceptibilities higher than 100 × 10⁻⁶, the relative errors are lower than 3% in all fields and lower than 1% in the fields stronger than 10 A/m. In the KLF-4A Magnetic Susceptibility Meter, in relatively strongly magnetic specimens with susceptibilities 5 × 10⁻⁴ to 5 × 10⁻², the relative error is less than 1.5% in the entire field range. While the former instrument is convenient for investigating almost all rock types, the latter instrument is convenient for measuring moderately and strongly magnetic specimens. To facilitate work with field variation of susceptibility curves, showing variable accuracies with field, the programme FieldVar was written. One of its options is plotting the measured data with corresponding field-variable error bars. In this way, a tool is offered for interpreting such susceptibility changes that are sound and reasonable from the point of view of measuring accuracy.     

Interaction of Weak Shock Waves with Current Sheets in an Active Region to Produce Nanoflares and Chains of Type I Radio Bursts

Interaction of weak shock waves with a current sheet is investigated by a two-dimensional numerical magnetohydrodynamic model. In accordance with solar coronal conditions, a ratio of thermal to magnetic pressures of 0.1 and a shock Alfvén Mach number slightly above 1 are considered. It is found that even weak shock waves trigger magnetic field reconnection in current sheets. Based on this result, it is suggested that drifting chains of type I radio bursts are radio manifestations of the interactions of weakly super-Alfvénic shock waves with pre-existing current sheets distributed in an active region. This model of type I noise storms is then discussed in connection with the concept of nanoflares (localized reconnections) and the heating of the solar corona.     

Modelling climate change impacts on maize growth and development in the Czech Republic

Summary The crop growth model CERES-Maize is used to estimate the direct (through enhanced fertilisation effect of ambient CO₂) and indirect (through changed climate conditions) effects of increased concentration of atmospheric CO₂ on maize yields. The analysis is based on multi-year crop model simulations run with daily weather series obtained alternatively by a direct modification of observed weather series and by a stochastic weather generator. The crop model is run in two settings: stressed yields are simulated in water and nutrient limited conditions, potential yields in water and nutrient unlimited conditions. The climate change scenario was constructed using the output from the ECHAM3/T42 model (temperature), regression relationships between temperature and solar radiation, and an expert judgement (precipitation). Results: (i) After omitting the two most extreme misfits, the standard error between the observed and modelled yields is 11%. (ii) The direct effect of doubled CO₂: The stressed yields would increase by 36–41% in the present climate and by 61–66% in the 2 × CO₂ climate. The potential yields would increase only by 9–10% as the improved water use efficiency does not apply. (iii) The indirect effect of doubled CO₂: The stressed yields would decrease by 27–29% (14–16%) at present (doubled) ambient CO₂ concentration. The increased temperature shortens the phenological phases and does not allow for the optimal development of the crop. The simultaneous decrease of precipitation and increase of temperature and solar radiation deepen the water stress, thereby reducing the yields. The reduction of the potential yields is significantly smaller as the effect of the increased water stress does not apply. (iv) If both direct and indirect effects of doubled CO₂ are considered, the stressed yields should increase by 17–18%, and the potential yields by 5–14%. (v) The decrease of the stressed yields due to the indirect effect may be reduced by applying earlier planting dates. Received March 9, 2001 Revised September 25, 2001     

The Precambrian tectogenesis in the Bohemian Massif

The Cadomian and Variscan tectogeneses are two distinctive and easily distinguished cycles of a long-term geological process leading to the almost complete crustal consolidation of the Bohemian Massif. The internal parts of the massif are those of the main development of the Upper Proterozoic geosyncline and the intensive Cadomian metamorphism and plutonism.The Precambrian of the Bohemian Massif is divided into two principal regional chronostratigraphic units: the Moldanubian and the Brioverian; the age of the boundary between them is estimated at about 1000 Ma B. P. The Brioverian is subdivided into three units: the Lower, Middle and Upper. The Moldanubian is provisionally subdivided into two units: the Lower and the Upper.The maximum of the metamorphic activity of the Cadomian cycle falls approximately within the sedimentation interval of the Middle Brioverian, and that of the Variscan cycle in the Devonian. Compared with the Cadomian regional metamorphism which attained mostly amphibolite to granulite facies, the Variscan metamorphism generally did not exceed greenschist facies.The origin of the granitoid rocks of the massif is closely associated with the metamorphic processes of the two above-mentioned cycles. Cadomian granitoids are represented mostly by rocks of granodiorite-tonalite and durbachite types whereas the Variscan intrusives are dominated by rocks of granitic composition.

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Zusammenfassung Die assyntische und variszische Orogenese sind die wesentlichen strukturprägenden Ereignisse im Böhmischen Massiv. Die internen Teile des Massives sind aus der jung-proterozoischen Geosynklinale hervorgegangen und während der assyntischen Gebirgsbildung metamorphisiert und von Magmatiten durchdrungen worden. Das Präkambrium des Böhmischen Massives ist in zwei chronostratigraphische Einheiten zu gliedern: das Moldanubium und das Brioverian. Die Grenze liegt etwa bei 1000 Mill. Jahren. Das Brioverian läßt sich in drei Einheiten gliedern und das Moldanubium in zwei Einheiten.Das Maximum der metamorphen Überprägung während der assyntischen Orogenese fällt in die Sedimentationslücke im mittleren Brioverian; im variszischen Zyklus erfolgt die Metamorphose im Devon. Die assyntische Metamorphose erreicht Amphibolit- bis Granulitfazies, die variszische geht nicht über eine Grünschieferfazies hinaus.Die magmatischen Gesteine sind eng mit den beiden Orogenesen verbunden. Die assnytischen Magmatite sind vorwiegend Granodiorit-Tonalite und Durbachite, während die variszischen Magmatite aus Graniten bestehen.

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Résumé Les tectogenèses cadomienne et varisque sont deux cycles différents, bien discernables, d'un processus géologique de longue durée, qui a conduit à la cosolidation presque complète du Massif de Bohème. La partie interne du Massif est celle du développement principal du géosynclinal protérozoïque supérieur et du métamorphisme et du plutonisme cadomiens.Le Précambrien du Massif de Bohème se divise en deux unités chronostratigraphiques régionales: le Moldanubien et le Briovérien. On estime l'âge de la limite entre elles à 1000 millions d'années environ. Le Briovérien est subdivisé en trois unités: inférieure, moyenne et supérieure. Le Moldanubien est divisé provisoirement en deux unités: inférieure et supérieure.La culmination de l'activité métamorphique du cycle cadomien tombe à peu près dans l'intervalle de sédimentation du Briovérien moyen, celle du cycle varisque dans le Dévonien. Comparé avec le métamorphisme régional cadomien qui le plus souvent a atteint le faciès amphibolite, le métamorphisme varisque, en général, n'a pas dépassé le faciès schistes verts.L'origine des roches granitoïdes du Massif et associée avec les processus métamorphiques des deux sus-dits cycles. Les granitoïdes cadomiens sont représentés pour la plupart par des roches du type des granodiorites-tonalites et durbachites, tandis que parmi les roches intrusives varisques prédominent des roches de composition granitique.

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