Experiences numeriques sur des billards C1 formes de quatre arcs de cercles     

A. Hayli  Th. Dumont 《Celestial Mechanics and Dynamical Astronomy》1986,38(1):23-66

The paper deals with some properties of the dynamical system with two degrees of freedom defined by the motion of a particle in a certain type of billiard. These properties are studied by means of numerical experiments. Most results are represented in the now classical surface of section. One parameter families of billiards with a C¹ boundary constructed with four arcs of circles are defined; we use the property that the four meeting points of such billiards lie on the same circle. These billiards may be convex or non convex. They generalize the ‘oval’ billiard with two axes of symmetry studied by Benettin and Strelcyn. We call them generalized billiards. We find the following results:

1. The periodic orbit along the small diameter of a billiard is stable or unstable in the linear approximation according to the position of the center of each relevant are with respect to the opposite one. This orbit is always stable if the billiard is symmetric with respect to its large diameter.
2. When the center of an arc lies on the opposite arc two different transition patterns from order to chaos are observed for the same billiard. If the billiard is of the Benettin and Strelcyn type three distinct nested chaotic seas are seen two of which are separated by a pseudo-invariant curve generated by a so called cancellation orbit.
3. The total area of non chaotic regions is greater for symmetric billiards.
4. Peanut shaped billiards always look ergodic. It can happen also that strictly convex asymmetric billiards look ergodic. This is important since no strictly convex billiard is known for which ergodicity has been proven. The conjecture is proposed that a generalized billiard with neither 2-periodic nor 4-periodic stable orbit in the linear approximation is ergodic.
5. Transverse invariant curves such as the one found by Hénon and Wisdom seem common for billiards with two axes of symmetry but probably do not exist for asymmetric billiards.

There are therefore several properties which differentiate symmetric billiards from asymmetric ones. We conclude by emphasizing that C¹ generalized billiards are indeed inadequate models for smooth mappings in general.  相似文献   

Der Stabilitätsbereich des Pyrophyllits unter dem Einfluß von Säuren     

Egon Althaus 《Contributions to Mineralogy and Petrology》1966,13(2):97-107

Zusammenfassung Die in Teil I dargestellten Ergebnisse der experimentellen Untersuchungen über den Einfluß von Säuren auf den Stabilitätsbereich von Pyrophyllit werden in Teil II auf natürliche Paragenesen angewandt. In offenen Systemen ist im allgemeinen mit Assoziationen von zwei festen Phasen (z.B. Quarz + 1 Al-Silikat) zu rechnen, während in geschlossenen Systemen meistens Assoziationen von drei festen Phasen vorliegen werden (z.B. Quarz + 2 Al-Silikate). Mit wesentlich erhöhten Säurekonzentrationen in der fluiden Phase und starker Erniedrigung der Bildungstemperaturen von Pyrophyllit und Andalusit kann nur bei der Kontaktmetamorphose gerechnet werden, insbesondere dann, wenn gleichzeitig eine hydrothermale Tätigkeit stattfand. Bei der Regionalmetamorphose herrschten im allgemeinen wesentlich geringere Aciditäten; daher werden die Bildungstemperaturen von Pyrophyllit und Andalusit weniger stark herabgesetzt. Besondere Bedeutung haben die experimentellen Ergebnisse für die Genese von Pyrophyllit- und Andalusitlagerstätten; aus der Vielzahl der in der Literatur beschriebenen Vorkommen wurden drei ausgewählt und deren Genese mit Hilfe der Ergebnisse der Experimente diskutiert.

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The results of the experimental investigations of the influence of acids on the stability field of pyrophyllite, put forth in the first part of this paper, have been applied here on natural mineral assemblages. In general, assemblages with two solid phases (e.g. quartz and an aluminium silicate) are expected to occur in open systems, whereas in closed systems, usually three solid phases (quartz and two aluminium silicates) would be present. High acidity of the fluid phase, leading to a strong depression of the lower stability limits of pyrophyllite and andalusite, is liable to be encountered in contact metamorphism, especially when a notable hydrothermal activity was taking place simultaneously. In contradiction to that, the regional metamorphism is commonly characterized by an essentially lower acidity of the fluid phase, so that the temperatures of origin of pyrophyllite and andalusite were but slightly depressed. The results of the present experimental investigations are highly important in discussing the genesis of pyrophyllite and andalusite deposits. This has been demonstrated by applying them to three such cases chosen from the literature.

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Herrn Professor Dr. H. G. F. Winkler danke ich für sein Interesse and dieser Arbeit, für wertvolle Kritik und nützliche Ratschläge sowie für die Erlaubnis, die Experimente in Apparaturen durchzuführen, die ihm von der Deutschen Forschungsgemeinschaft zur Verfügung gestellt wurden.

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I. Mitteilung: Diese Zeitschrift 13, 31–50 (1966).  相似文献   

Structure and physics of solar faculae     

J. -C. Pecker  S. Dumont  Z. Mouradian 《Solar physics》1992,138(2):213-222

Taking into account the effect of roughness (or local departures from sphericity) of the emitting layers in the chromosphere-corona transition zone (CCT) allows one to determine the optical depths of layers responsible for resolved structures in Cii, Ciii, Oiv, and Ovi lines. The result, at the top of the irregularities, is of the order of respectively ₁ 3.5,2.0, 1.6,0.5, and for the bottom of these irregularities, ₂ = 0.7, 0.4, 0.3, 0.25. The characteristic angle of these irregularities is, respectively, of the order of 35 °, 33 °, 35 °, and 41 °. For unresolved structures of Civ and Ovi (already analyzed in the spherical symmetry hypothesis in Paper III), one finds ₁ 0.6; 0.9 and ₂ 0.12; 0.2 in the case of quiet areas; in the case of active areas, the range is broader for Civ and Ovi, from 1.0 to 1.7 for ₁ and from 0.2 to 0.9 for ₂. The values obtained from Ovi are in reasonable agreement with each other for resolved and unresolved structures. And the obtained values of ₁ and ₂ correspond not too badly with the determinations made in Paper III, by methods not exceedingly influenced by the spherical symmetry hypothesis.  相似文献   

Alkaline fluid circulation in ultramafic rocks and formation of nucleotide constituents: a hypothesis     

Nils G Holm  Marion Dumont  Magnus Ivarsson  Cécile Konn 《Geochemical transactions》2006,7(1):7-7

Seawater is constantly circulating through oceanic basement as a low-temperature hydrothermal fluid (<150°C). In cases when ultramafic rocks are exposed to the fluids, for instance during the initial phase of subduction, ferromagnesian minerals are altered in contact with the water, leading to high pH and formation of secondary magnesium hydroxide, among other – brucite, that may scavenge borate and phosphate from seawater. The high pH may promote abiotic formation of pentoses, particularly ribose. Pentoses are stabilized by borate, since cyclic pentoses form a less reactive complex with borate. Analyses have shown that borate occupies the 2' and 3' positions of ribose, thus leaving the 5' position available for reactions like phosphorylation. The purine coding elements (adenine, in particular) of RNA may be formed in the same general hydrothermal environments of the seafloor.  相似文献   

Fan beheading and drainage diversion as evidence of a 3200-2800 BP earthquake event in the Esmeraldas-Tumaco seismic zone: A case study for the effects of great subduction earthquakes   总被引：1，自引：0，他引：1  

J.F. Dumont  E. Santana  F. Valdez  J.P. Tihay  P. Usselmann  D. Iturralde  E. Navarette 《Geomorphology》2006,74(1-4):100-123

The San Lorenzo area belongs to the Esmeraldas–Tumaco seismic zone where some of the strongest earthquakes of South America occurred during the 20th century. This paper provides evidence for a succession of geomorphic changes characterized by the disruption of the Quaternary drainage network and the reshaping of the Cayapas–Santiago estuary. The rise of the La Boca uplift bordered by the La Boca and San Lorenzo faults is responsible for the southward diversion of the Palabi, Tululbi, Bogotá and Carolina rivers toward the Santiago and Cayapas rivers. The increase of the discharge directed to the Cayapas River generated the change of the channel pattern downstream from the confluence, and the avulsion of a new estuary through the coastal plain. According to the dating of beach ridges the avulsion occurred in the period 3200–2800 BP. This period corresponds also to a faster accretion of the beach ridge margin, interpreted as a response to a small uplift of the shore. The coherency of the three morphologic evidences—diversion of drainage network, avulsion and increase of coastal accretion—suggest a unique morphotectonic event, in relation with the activity of the Esmaraldas–Tumaco seismic zone. The opening of a direct communication through the mangrove margin may have brought favorable conditions for the development of the La Tolita archaeological site after 3000 BP.  相似文献   

Morphological and microtectonic analysis of Quaternary deformation from Puná and Santa Clara Islands, Gulf of Guayaquil, Ecuador (South America)     

J.F. Dumont  E. Santana  W. Vilema  K. Pedoja  M. Ordez  M. Cruz  N. Jimnez  I. Zambrano 《Tectonophysics》2005,399(1-4):331

This paper presents the neotectonic study of Santa Clara and Puná Islands sited in the Gulf of Guayaquil eastern part. Both islands are located on the south-western segment of the fault zone bounding to the east the North Andean Block. Fault motion and morphostructural analysis were carried out from Pleistocene age terrain. A two step deformation characterises the South Puná tectonics. The first step involves the Zambapala Cordillera uplift that post-dates Pleistocene sediments and pre-dates a marine terrace correlated with the M.I.S. 11 or 13 (440–550 ka). The second step is the formation of a pull-apart that shows evidence of 2.9 km dextral offset since the M.I.S. 11 or 13, giving an offset mean rate of 5.3 to 6.6 mm/yr. This rate is higher than the one calculated on the Pallatanga Fault northeast of the study area, in the Western Andean Cordillera, suggesting that deformation is split in different fault segments from the Gulf of Guayaquil to the continent. The Zambapala Cordillera uplift and transpression deformation requires a compressive event that may have been induced by the subduction process during the early Pleistocene.  相似文献   

Biomarkers in sedimentary sulfides of precambrian age     

Bernd Mycke  Walter Michaelis  Egon T. Degens 《Organic Geochemistry》1988,13(4-6)

Samples of the Mt Isa formation (Australia, c, 1.5 Ga), and the Shungit formation (U.S.S.R., c. 2.3 Ga) were studied by organic geochemical means. All samples were freed of any low-molecular-weight solvent soluble organic material in order to insure the authenticity of the analysed material. The isolation of biochemical compounds entrapped in sulfides was the major goal of this work.Organic compounds that were entrapped during the early stages of sulfide formation may obviously survive extended periods of time and can be released by a mild hydrogenation of the sulfides. Preliminary investigations of the hydrocarbon fraction indicate n-alkanes, monomethylalkanes, cycloalkanes, and an unknown series of branched alkanes as major constituents. Their distribution patterns show great selectivity with respect to structures and chain lengths of individual compounds. Differences between the hydrogenation reaction product and the sample extract may arise from the release of a different kind of lipid material through dissolution of the sulfides.  相似文献   

Effects of CO₂-H₂O and oblique collision on orogenesis—the european hercynides as an example     

How Kin Wong  Egon T. Degens 《Tectonophysics》1983,95(3-4)

The European Hercynides are considered the collisional result of Baltica and the microcontinents of Southern Europe, after subduction destroyed the intervening Rheic Ocean during the early Paleozoic. Their geotectonic development is assumed to consist of four overlapping stages:

1. (1) lithospheric thinning, upwelling of hot asthenospheric material, subsidence along listric faults, and basinal and geosynclinal development on the opposing shelves of the Rheic Ocean starting in pre-Devonian time;

2. (2) intermittent subduction of the Rheic Ocean interspersed with episodes of fracturing, volcanism, local uplift and subsidence, and basement reactivation as a result of compression with dextral megashear, particularly since the earliest Devonian;

3. (3) several phases of folding with a northward vergence, and thrusting and overthrusting along listric surfaces, the true orogenic stage;

4. (4) post-orogenic stage of massive granite intrusions and subsequent volcanism in the Permo-Triassic

.The high clastic content (as opposed to carbonates) of the sedimentary sequences involved in the subduction and folding processes and the consequent release of large amounts of meteoric water are held responsible for the synorogenic and post-orogenic magma rise, and for the wide zone of anatectic granites and migmatites. The dominant dextral megashear, the constant re-adjustment of the microcontinents of Southern Europe (oblique collision) and the scarcity of back-arc basins, oceanic plateaus and microcontinents led to the poor preservation of ophiolites and ultrabasic rocks, and to a wide (over 1500 km) Hercynian Foldbelt.During the Paleozoic, the depositional center of the Rhenish Massif shifted from south polar latitudes in the early Ordovician to tropical positions within a period of about 100 m.y. The sediment facies reflects this paleogeographic development.  相似文献   

Methodische Schwierigkeiten bei der Untersuchung Litoraler Sedimente     

Groba  Egon 《International Journal of Earth Sciences》1958,47(1):24-28

Zusammenfassung Die Untersuchung rezenter Sedimentationsverhältnisse im Litoral erfordert synchrone Probenentnahme und Messungen aller hydrographischen und meteorologischen Daten über größere Zeiträume hinweg. Die Auswertung der Meß- und Analysenergebnisse soll statistisch erfolgen. Für die kartenmäßige Darstellung der Korngemische ist die Methode von G.Ludwig (1955) zweckmäßig.  相似文献   

Lake Kivu: structure,chemistry and biology of an East African rift lake     

Egon T. Degens  Richard P. von Herzen  How-Kin Wong  Werner G. Deuser  Holger W. Jannasch 《International Journal of Earth Sciences》1973,62(1):245-277

Geophysical, geochemical and biological data are integrated to unravel the origin and evolution of an unusual rift lake. The northern basin of Lake Kivu contains about 0.5 km of sediments which overlie a basement believed to be crystalline rocks of Precambrian age. Volcanic rocks at the northern end of the lake have created large magnetic anomalies of up to 300. Heat flow varies from 0.4 to 4 hfu. The extreme variability may be due in part to sedimentation or recent changes in the temperature of the bottom water. Sharp boundaries in the vertical temperature and salinity structure of the water across the lake can best be explained as separate convecting layers. Such convecting cells are the result of the increase in both temperature and salinity with depth.Concentrations of the major dissolved gases in the deep water, CO₂ and CH₄, approach saturation but do not exceed it at any depth. The salts are supplied mainly by hydrothermal discharges at the bottom of the lake which we calculate to have a salinity of 4 which is about 60% higher than the salinity of the bottom water. The annual discharge at the present time is about 0.5 km³. Zinc anomalies in the water are explained by the accumulation of sphalerite-containing globules at certain depths.Stratigraphic correlation of sediments is possible across the entire lake, based on physical, geochemical and paleontological criteria. Sedimentation rates are of the order of 30 cm/1000 years implying a Pliocene age for the deepest part of the lake. Periods of hydrothermal activities and heightened volcanism, as recorded in the sediments, appear to have coincided with pluvial times.Enrichment of the surface waters of Lake Kivu by nutrients has led to explosive speciation in the diatom genusNitzschia. Several new types of methane oxidizing and-producing bacteria were isolated. Bacterial degradation of recent plankton appears insufficient to explain the amount of methane in the lake, and some of it is derived diagenetically.

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Zusammenfassung Geophysikalische, geochemische und biologische Daten werden vorgelegt und miteinander in Beziehung gebracht, um einen besseren Einblick in Entstehung und Evolution eines ungewöhnlichen Sees zu gewinnen. Das nördliche Becken des Kivu-Sees enthält Sedimente von etwa 0,5 km Mächtigkeit, die dem präkambrischen kristallinen Grundgebirge überlagert sind. Die im Norden des Sees vorliegenden vulkanischen Gesteine erklären die hohen magnetischen Anomalien, die bis zu 300 betragen. Der Wärmefluß schwankt zwischen 0,4 und 4 cal/cm²/sec. Diese Schwankungsbreite erklärt sich zum Teil aus den Sedimentationsverhältnissen oder den lokalen Temperaturveränderungen im Tiefenwasser. Scharfe Grenzflächen in der vertikalen Temperatur- und Salinitätsstruktur des Wassers über den Gesamtsee sind das Ergebnis von Konvektion, die zu übereinanderliegenden Konvektionszellen führt, in denen jeweils Temperatur und Salinität konstant sind. Die Bildung, Anzahl und Stabilität solcher Zellen hängt von dem Verhältnis der durch Temperatur und Salzgehalt hervorgerufenen Dichteveränderungen ab.Die Konzentrationen der im Tiefenwasser gelösten Gase, d. h. von Kohlendioxyd und Methan, liegen für alle Tiefen unterhalb der Löslichkeit. Die vorliegenden Salze entstammen weitgehend hydrothermalen Lösungen, die dem Seeboden entweichen und deren Salinität etwa 4 beträgt; der Vergleichswert für das Tiefenwasser beträgt 2,5 Diese hydrothermalen Ausschüttungen haben eine Größe von etwa 0,5 km³ pro Jahr, was etwa ein Tausendstel des Gesamtseevolumens ausmacht. Zinkanomalien im Wasser sind ebenfalls hydrothermal bedingt.Physikalische, geochemische und paläontologische Indikatoren erlauben eine stratigraphische Korrelation aller Sedimentkerne. Die Sedimentationsraten liegen bei 30 cm/ 1000 Jahren, und ein pliozänes Alter errechnet sich daraus für das tiefe nördliche Becken. Perioden hydrothermaler Aktivitäten und verstärkter vulkanischer Tätigkeit, die sich in den Sedimenten nachweisen lassen, scheinen mit Pluvialzeiten zu koinzidieren.Die Anreicherung der Oberflächenwässer vom Kivusee durch Mineralstoffe führte zu einer explosionsartigen Spezisierung in der GattungNitzschia. Verschiedene neue Arten von Methan-oxidierenden und -produzierenden Bakterien wurden isoliert. Das Auftreten von Methan ist zum Teil bakteriell und zum Teil diagenetisch bedingt.

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Résumé Des données géophysiques, géochimiques et biologiques sont présentées et collationnées pour donner une vue meilleure sur l'origine et l'évolution d'un lac particulier de la «Rift valley». La baie septentrionale du lac Kivu contient environ 500 mètres de sédiments qui recouvrent le socle cristallin d'âge précambrien. Des épanchements volcaniques au Nord du lac expliquent les fortes anomalies magnétiques qui atteignent 300. Les valeurs du flux thermique varient entre 0.4 et 4 cal/cm²/sec. Cette importante variation s'explique en partie par la sédimentation ou par des changements locaux de la température de l'eau de fond. Des surfaces-limites brusques dans la structure verticale de la répartition de la température et de la salinité de l'eau dans l'étendue du lac sont dûs à la convection; celle-ci conduit à la superposition de cellules de convection dans lesquelles la température et la salinité sont constantes. La formation, le nombre et la stabilité de telles cellules dépendent du rapport des variations de densité dues à la température et à la teneur en sels.Les concentrations des gaz dissouts dans l'eau profonde, en l'occurrence CO₂ et CH₄, sont, à toute profondeur, inférieures à la saturation. Les sels minéraux proviennent surtout de solutions hydrothermales qui émanent du fond du lac, et dont la salinité est voisine de 4; la valeur comparative pour l'eau profonde est de 2,5. L'apport annuel de ces sources est de l'ordre de 0,5 km³, soit 1/1000 du volume total du lac. Les teneurs anormales en Zn sont dues également à ce caractère hydrothermal.Des données physiques, géochemiques et paléontologiques permettent la corrélation stratigraphique des sédiments. Les vitesses de sédimentation sont de l'ordre de 30 cm/1000 ans, donnant ainsi un âge pliocène pour la partie profonde de la baie septentrionale. Les périodes d'activité hydrothermale et de renforcement de la vulcanicité qui se manifestent dans les sédiments, semblent coïncider avec les périodes pluviales.L'enrichissement des eaux de surface du lac Kivu en substances minérales a entraîné un développement explosif des diatomées, en particulier du genreNitzchia. Différentes espèces nouvelles de bactéries oxydant et produisant CH₄ ont été isolées. La présence de méthane est due en partie à la destruction du plancton par les bactéries et en partie à une transformation diagénétique.

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, , . Kivu 0,5 , . , 300 . 0,4 4 (²) . , . . , , , . , . . _{2 4} . , 4%. 2,5%. 0,5 ³, , 1/1000 . ., . 30 /1000 , . . . , , , . Kivu Nitzschia. , . , — .

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