Approximate solutions for isothermal flows behind strong spherical shocks with variable energy

Self-similar unsteady flows with zero temperature gradient behind strong spherical shocks propagating in non-uniform perfect gas at rest are investigated. The total energy of the flow is assumed to be varying with the shock radius obeying a power law. Approximate solutions in a closed analytical form are obtained using the integral method. Also these solutions are shown to be useful to calculate easily and quickly the shock temperature, X-ray surface brightness and luminosity which are important in astrophysical problems. It is found that these approximate solutions are in close agreement with numerical solutions.     

A study on the bio-hydro mechanical effects of the tree roots on the Agaclı coal reclaimed – forested land

The research area that is in the north of Istanbul (Turkey) and it is a land of open pit coal mining residuals reclaimed and turned to forest in 1988–1989. The materials that are open pit mine spoils are formed by sandy loam, sandy clay loam, heavy loam and clay (noncalcareous Pliocene I sediments). Pseudoacacia (Robinia pseudoacacia), Maritima Pine (Pinus pinaster) and Stone Pine (Pinus pinea) are planted on these materials. The aims of this research were to determine the strength of the material provided by tree roots and evaluate the performance of the forestation practices at lands especially where open pit coal mining spoil (residual) materials piled up. The research has been performed at two stages. The first one was hydro-mechanical effect concerned about material moisture depletion as a result of transpiration and the second one was bio-mechanical effects due to strength parameters of the roots and their growth pattern within the material. All results were evaluated in relation to tensile strength and displacement curves due to pre and post failure behaviors of materials and root systems. The results showed the increase of the displacement of the material was the significant indicator of the bio-mechanics tensile strength of the material provided by the tree roots. The fast growing type of tree roots have stabilized the material up to a depth for 80–100 cm by covering the coal residual materials within 12 years.     

Some Homogeneous Bianchi type IX Viscous Fluid Cosmological Models with a Varying Λ

Some Bianchi type IX viscous fluid cosmological models are investigated. To get a solution, a supplementary condition between metric potentials is used. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density, whereas the coefficient of shear viscosity is considered as proportional to scale of expansion in the model. The cosmological constant Λ is found to be positive and is a decreasing function of time, which is supported by results from recent supernovae observations. Some physical and geometric properties of the models are also discussed.     

Tourism resources and their development in Maldive Islands

Maldive Islands are characterized by a unique coral nature and thus they posses unique tourism resources though in a one-sided way, namely in the submarine and littoral environment of the islands, lagoons and reefs, associated with the year-round tropical climate. Therefore, not only divers and snorklers enjoy the profuse underwater resources, but also beach tourists are attracted by the nature of the beaches and the climatic conditions as well. This environment really guarantees relaxation and recreation. Tourism in Maldives which was introduced in 1972 only, has successfully developed so far. Proof is given by the rapidly growing number of tourists and tourist resorts (islands) over the past 10 year period. On the European market, Maldives today rank among the most attractive tourist destinations in the tropics. Maldives offer large natural resources for tourism to be further developed in the future. The sensitive environment does however call for most considerate measures.     

Notes on the Julianehåb granite of eqaluit Peninsula,Julianehåb district,Southern Greenland

Summary The Julianehåb granite has its greatest extent between Kobbermine Bay and Igaliko Fjord. His formation took place over a long space of time in the Precambrian. It is possible to distinguish Ketilidian (older) and Sanerutian (younger) granites. The older types are supposed to be autochthonous, whereas the younger show traces of older granites. In the Sanerutian period a strong reactivation is recognizable which even led to allochthonous intrusions.

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Zusammenfassung Der Julianehåb Granit hat seine größte Ausdehnung zwischen Kobbermine Bugten und Igaliko Fjord. Seine Bildung erstreckte sich über lange Zeiträume im Präkambrium. Es lassen sich Ketilidische (ältere) und Sanerutische (jüngere) Granite abgliedern. Während die älteren Typen meist durch synorogene Granitisation (autochthon) erklärbar sind, lassen die jüngeren teilweise noch Spuren von älteren Graniten erkennen. Im Sanerut ist jedenfalls eine starke Reaktivierung des Grundgebirges zu verzeichnen, die auch zu allochthonen Intrusionen führte.

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Dedicated to Prof.H. Leitmeier on the occasion of his 80th birthday.     

Principal component maps instead of trend surface maps for modal and chemical data of granitoid rock bodies

Summary Trend surface analysis may be an unsuitable method for the design of contour maps and of petrogenetic models for granitoid rock bodies. In granitoid bodies we are often dealing with several successive and superimposed petrogenetic processes, which lead to very complex regional patterns of modal or chemical data. Before drawing the contour map of a rock body it is of advantage, therefore, to separate the superimposed components of the complex pattern. The trend surface analysis allows only for the separation of the geometrically simple parts from those showing a more complex, or even random, distribution. Principal component analysis permits us to break multivariate data down into those components which are independent and result from different petrogenetic processes. For each of the most important eigenvectors which are calculated from the covariance matrix of data one contour map is drawn. The number of contour maps is therefore low and their interpretation relatively easy. The advantage of the principal comoponent analysis is demonstrated by its application to twelve granitoid rock bodies.

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Hauptkomponenten-Karten statt Trend Surface-Karten für modale und chemische Daten von granitoiden Gesteinskörpern

Zusammenfassung Die trend surface-Analyse ist als Methode zur Anfertigung von Konturkarten und Aufstellung petrogenetischer Modelle für granitoide Gesteinskörper nicht sehr geeignet. In granitoiden Gesteinskörpern haben wir es oft mit mehreren sich überlagernden oder aufeinander folgenden petrogenetischen Prozessen zu tun, die zu komplizierten regionalen Mustern modaler oder chemischer Daten führen. Bevor eine Konturkarte gezeichnet wird, ist es daher von Vorteil, das komplexe Muster in seine sich überlagernden Komponenten zu zerlegen. Die trend surface-Analyse gestattet nur die Trennung eines geometrisch einfacheren von einem komplizierteren Teil. Die Hauptkomponenten-Analyse ermöglicht es uns, die multivariaten Daten in jene unabhängigen Komponenten zu zerlegen, die auf den Einfluß verschiedener petrogenetischer Prozesse im Gesteinskörper zurückgehen. Für die größten der aus der Kovarianz-Matrix der Daten berechneten Eigenvektoren wird je eine Konturkarte gezeichnet. Die Anzahl der Konturkarten ist daher gering und ihre Interpretation relativ einfach. Die Vorteile der Hauptkomponenten-Analyse werden durch ihre Anwendung auf zwölf granitoide Gesteinskörper demonstriert.

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With 13 Figures