Robe's restricted three-body problem with drag

Robe's restricted three-body problem is investigated with regards to the effects of a linear drag force. In particular. the stability of the model's equilibrium points is studied in this respect. Two scenarios are envisaged: the one originally discussed by Robe himself and the one suggested by him and recently analyzed by the present authors, that assumes for the fluid body the structure of a Roche's ellipsoid.     

Untersuchungen mit der Elektronen-Mikrosonde an zonargebauten Mineralen der Pyromorphitgruppe

Zusammenfassung Natürliche Glieder der Pyromorphitgruppe wurden mit einer Elektronen-Mikrosonde untersucht. Bei allen untersuchten Proben tritt gegenseitige isomorphe Ersetzung des Phosphors, Arsens oder Vanadins auf. Die fast reinen Endglieder zeigen dabei einen ziemlich gleichmäßigen, geringfügigen Einbau der Nebenkomponente unabhängig vom optischen Zonarbau, während für die Mischglieder starke zonare Schwankungen in der chemischen Zusammensetzung in Abhängigkeit von den optisch erkennbaren Zonen typisch sind.In einem Falle wird zonar Blei isomorph durch Kalzium ersetzt. Der Chlorgehalt scheint von keiner der übrigen Komponenten abhängig zu sein und unterliegt nur z.T. zonaren Schwankungen. Zonarbau durch Farbänderungen und Einbau von Fremdpartikeln, fast nur bei den Mischgliedern zu finden, bedingt zumeist entsprechende zonare chemische Veränderungen der Phosphor-, Arsen- oder Vanadingehalte. Zonarbau infolge unterschiedlicher optischer Orientierung kann sowohl ohne chemische Zonen vorkommen (bei den Endgliedern), als auch mit gleichlaufenden Veränderungen der Komponenten bei den Mischgliedern.Zonarbau als Folge unterschiedlicher optischer Orientierung, Felderteilung und Zweiachsigkeit haben nach den vorliegenden Untersuchungen nicht isomorphen Ersatz als Ursache; Veränderungen der physikalischen Bedingungen während oder Sekundärvorgänge nach Beendigung des Wachstums der Kristalle könnten eine Rolle gespielt haben. In Frage kommt auch eine Abweichung von der hexagonalen Symmetrie; eine kürzlich von U. Keppler (Karlsruhe) durchgeführte Einkristall-Untersuchung einer Mimetesit-Zone ergab für diese eine monokline Symmetrie (im Druck).Das Auftreten von diffusen Reflexen oder Doppellinien in den Röntgendiagrammen der Mischglieder kann zwanglos durch die gegenläufigen Schwankungen der Phosphor-, Arsen- oder Vanadin-Gehalte gedeutet werden.

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Electron microprobe investigation of members of the pyromorphite group with zoned structure

Natural members of the pyromorphite group, pyromorphite Pb₅(PO₄)₃Cl, mimetite Pb₅(AsO₄)₃Cl, kampylite Pb₅(PO₄, AsO₄)₃Cl, and vanadinite Pb₅(VO₄)₃Cl were investigated by the electron microprobe method. Mutual isomorphic replacement of P, V and As was observed even in the purest available end members occurring in nature. The frequently appearing zoned structure, observed in thin sections, may or may not coincide with corresponding chemical changes with respect to the V, As or P contents, mainly for the intermediate members, while for the rather pure end members nearly no connection was found between optical zones and chemical composition (also as to the division of basal sections into six triangular areas).

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Den Herren Prof. Dr. F. Laves, Zürich, und Prof. Dr. H. Wondratschek, Karlsruhe, danken wir für die Ermöglichung dieser Arbeit und für das fördernde Interesse. Der Deutschen Forschungsgemeinschaft danken wir für die finanzielle Unterstützung dieser Arbeit durch eine Beihilfe.     

A discussion of the Cepheid amplitude behaviour in the instability strip

An analysis is presented which seeks to reveal the possible causes for discrepancy in the results on the dependence of Cepheid amplitudes on star positions in the instability strip noted by different investigators.A comparison of the data used in two of these investigations—that of Yakimova (1970) and that of Sandage and Tammann (1971)—shows that it is most unlikely to be able to explain completely the conflicting results obtained in these studies. But if we analyse the data of Sandage and Tammann following the approach of Yakimova — namely, by considering the Cepheids in only one stellar system and taking into account the stellar colours in maximum light — we obtain Yakimova's result: the light amplitude is the larger, the nearer to the low temperature edge of the instability strip a Cepheid is. Therefore, it appears that differences between the various approaches contribute greatly to the different results of Sandage and Tammann and Yakimova (and the other investigators).     

Geochronology and petrology of recent volcanics in the eastern Aegean Sea (West Anatolia and Lesvos Island)

During the lower and middle Miocene the western Anatolia and the eastern Aegean Sea were dominated by a calcalkaline volcanism associated with minor acid and basic volcanics. The basic subcrustal volcanics consist mainly of alkali basalts and hawaiites (9.7–11.9 m.y.), nepheline hawaiites and nepheline trachyandesites (Kula area from 1.1 m.y. to the recent times). The rhyolitic volcanics (12.5 m.y.) derived by a partial melting process in the upper crust (⁸⁷Sr/⁸⁶Sr=0.7121). The calcalkaline suite (16.2–21.5 m.y., mean value⁸⁷Sr/⁸⁶Sr=0.708) shows a trend from latite-andesites to dacites and rhyodacites; a latite andesite system related to a sinking slab of lithosphere and constituted by a mixing of oceanic crust (tholeiite), oceanic sediments and/or tectonic fragments of sialic crust is envisaged.     

Deformation and patterns of sedimentation,South San Clemente Basin,California Borderland

Seismic reflection profiling in the South San Clemente Basin and the southern portion of the San Diego Trough has revealed at least six sedimentary units exhibiting varying stages of deformation. Four of the units are interpreted to be marine turbidites supplied by adjacent submarine canyons. Sediments comprising the Descanso Plain and correlative material within the South San Clemente Basin are attributed to a southerly source (Banda Canyon), while the more recent Quaternary turbidites from Coronado Canyon filled the southern San Diego Trough and then spilled over into South San Clemente Basin. The relatively high but intermittent rates of sedimentation, together with shifting sources and areas of deposition, have resulted in sedimentary units that were emplaced in comparatively short episodes but which were subjected to relatively continuous tectonic activity. Consequently, the sedimentary layers of each unit appear uniformly affected by deformation which increases in successively older units.     

Reverse flow in turbidity currents: the role of internal solitons

Pickering & Hiscott, (1985) have demonstrated amply the presence of reverse-flow units within the thick-bedded calcareous wacke (TCW) beds of the turbiditic Cloridorme Formation (Middle Ordovician, Gaspé Peninsula, Quebec, Canada). These reverse-flow units are underlain and overlain by units which reveal flow in the primary (obverse) direction. In this paper, a model is proposed for this reverse flow, based on the probable nature of the primary turbidity flow. It appears that the initial flow was highly elongated (thickness h? length L), with h～ 500 m, velocity U～ 2 m s^-1 and sediment concentration C～ 1·25%_o. The rate of momentum loss of the flow is estimated by means of a useful parameter which we call the ‘drag distance’, symbol d_D, defined by where h and L are the thickness and length of the flow, respectively; _cC_d is a combined drag coefficient representing friction on the bottom and at the upper interface; and _fC_d is a form-drag coefficient related to the shape and size of the head. d_D is the distance travelled by a current of constant h and L, flowing over a horizontal bottom and obeying a quadratic friction law, for an e-fold reduction in velocity. Simple considerations, confirmed by our own experiments (described in this paper), show that such an elongated turbidity current cannot be reflected as a whole from an adverse slope: when the nose of the current reaches the slope, it forms a hump, which surges backwards and sooner or later breaks up into a series of internal solitons. The latter, probably numbering 4–7, will cause reverse flow at a given point as they pass by, provided that the residual velocity in the tail is not too great. Flow in the original (obverse) direction will be re-established after the passage of the solitons. Quiescent periods in front of, between and behind the solitons, when soliton-associated currents cancelled out the residual obverse flow, would allow the deposition of thin mud-drapes. Additional flow reversals observed in a few of the TCW beds cannot be explained readily by the re-passage of solitons, since wave breaking at the ends of the basin would cause massive energy loss; internal seiches are the preferred explanation for these later reversals.