86 resultados para Mathematics, Ancient--India

em Université de Lausanne, Switzerland


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The Ajjanahalli gold mine is spatially associated with a Late Archean craton-scale shear zone in the eastern Chitradurga greenstone belt of the Dharwar craton, India. Gold mineralization is hosted by an similar to100-m-wide antiform in a banded iron formation. Original magnetite and siderite are replaced by a peak metamorphic alteration assemblage of chlorite, stilpnomelane, minnesotaite, sericite, ankerite, arsenopyrite, pyrite, pyrrhotite, and gold at ca. 300degrees to 350degreesC. Elements enriched in the banded iron formation include Ca, Mg, C, S, An, As, Bi. Cu, Sb, Zn, Pb, Se, Ag, and Te, whereas in the wall rocks As, Cu, Zn, Bi, Ag, and An are only slightly enriched. Strontium correlates with CaO, MgO, CO2, and As, which indicates cogenetic formation of arsenopyrite and Mg-Ca carbonates. The greater extent of alteration in the Fe-rich banded iron formation layers than in the wall rock reflects the greater reactivity of the banded iron formation layers. The ore fluids, as interpreted from their isotopic composition (delta(18)O = 6.5-8.5parts per thousand; initial Sr-87/Sr-86 = 0.7068-0.7078), formed by metamorphic devolatilization of deeper levels of the Chitradurga greenstone belt. Arsenopyrite, chalcopyrite, and pyrrhotite have delta(34)S values within a narrow range between 2.1 and 2.7 per mil, consistent with a sulfur source in Chitradurga greenstone belt lithologies. Based on spatial and temporal relationships between mineralization, local structure development, and sinistral strike-slip deformation in the shear zone at the eastern contact of the Chitradurga greenstone belt, we suggest that the Ajjanahalli gold mineralization formed by fluid infiltration into a low strain area within the first-order structure. The ore fluids were transported along this shear zone into relatively shallow crustal levels during lateral terrane accretion and a change from thrust to transcurrent tectonics. Based on this model of fluid flow, exploration should focus on similar low strain areas or potentially connected higher order splays of the first-order shear zone.

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The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

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The deep-sea sponge Monorhaphis chuni forms giant basal spicules, which can reach lengths of 3 m; they represent the largest biogenic silica structures on Earth that is formed from an individual metazoan. The spicules offer a unique opportunity to record environmental change of past oceanic and climatic conditions. A giant spicule collected in the East China Sea in a depth of 1110 m was investigated. The oxygen isotopic composition and Mg/Ca ratios determined along center-to-surface segments are used as geochemical proxies for the assessment of seawater paleotemperatures. Calculations are based on the assumption that the calculated temperature near the surface of the spicule is identical with the average ambient temperature of 4 degrees C. A seawater temperature of 1.9 degrees C is inferred for the beginning of the lifespan of the Monorhaphis specimen. The temperature increases smoothly to 2.3 degrees C, to be followed by sharply increased and variable temperatures up to 6-10 degrees C. In the outer part of the spicule, the inferred seawater temperature is about 4 degrees C. The lifespan of the spicule can be estimated to 11,000 +/- 3000 years using the long-term trend of the inferred temperatures fitted to the seawater temperature age relationships since the Last Glacial Maximum. Specimens of Monorhaphis therefore represents one the oldest living animals on Earth. The remarkable temperature spikes of the ambient seawater occurring 9500-3100 years B.P. are explained by discharges of hydrothermal fluids in the neighborhood of the spicule. The irregular lamellar organization of the spicule and the elevated Mn concentrations during the high-temperature growth are consistent with a hydrothermal fluid input. (C) 2012 Elsevier B.V. All rights reserved.

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A gradual increase in Earth's surface temperatures marking the transition from the late Paleocene to early Eocene (55.8±0.2Ma), represents an extraordinary warming event known as Paleocene-Eocene Thermal Maximum (PETM). Both marine and continental sedimentary records during this period reveal evidences for the massive injection of isotopically light carbon. The carbon dioxide injection from multiple potential sources may have triggered the global warming. The importance of the PETM studies is due to the fact that the PETM bears some striking resemblances to the human-caused climate change unfolding today. Most notably, the culprit behind it was a massive injection of heat-trapping greenhouse gases into the atmosphere and oceans, comparable in volume to what our persistent burning of fossil fuels could deliver in coming centuries. The exact knowledge of what went on during the PETM could help us to foresee the future climate change. The response of the oceanic and continental environments to the PETM is different. Many factors might control the response of the environments to the PETM such as paleogeography, paleotopography, paleoenvironment, and paleodepth. To better understand the mechanisms triggering PETM events, two different environments were studied: 1) shallow marine to inner shelf environment (Wadi Nukhul, Sinai; and the Dababiya GSSP, Luxor, Egypt), and 2) terrestrial environments (northwestern India lignite mines) representing wetland, and fluvial environments (Esplugafreda, Spain) both highlighting the climatic changes observed in continental conditions. In the marine realm, the PETM is characterized by negative ö13Ccar and ô13Corg excursions and shifts in Ô15N to ~0%o values above the P/E boundary and persisting along the interval suggesting a bloom and high production of atmospheric N2-fixers. Decrease in carbonate contents could be due to dissolution and/or dilution by increasing detrital input. High Ti, K and Zr and decreased Si contents at the P/E boundary indicate high weathering index (CIA), which coincides with significant kaolinite input and suggests intense chemical weathering under humid conditions at the beginning of the PETM. Two anoxic intervals are observed along the PETM. The lower one may be linked to methane released from the continental shelf with no change in the redox proxies, where the upper anoxic to euxinic conditions are revealed by increasing U, Mo, V, Fe and the presence of small size pyrite framboids (2-5fim). Productivity sensitive elements (Cu, Ni, and Cd) show their maximum concentrated within the upper anoxic interval suggesting high productivity in surface water. The obtained data highlight that intense weathering and subsequent nutrient inputs are crucial parameters in the chain of the PETM events, triggering productivity during the recovery phase. In the terrestrial environments, the establishment of wetland conditions and consequence continental climatic shift towards more humid conditions led to migration of modern mammals northward following the extension of the tropical belts. Relative ages of this mammal event based on bio-chemo- and paleomagnetic stratigraphy support a migration path originating from Asia into Europe and North America, followed by later migration from Asia into India and suggests a barrier to migration that is likely linked to the timing of the India-Asia collision. In contrast, at Esplugafereda, northeastern Spain, the terrestrial environment reacted differently. Two significant S13C shifts with the lower one linked to the PETM and the upper corresponding to the Early Eocene Thermal Maximum (ETM2); 180/160 paleothermometry performed on two different soil carbonate nodule reveal a temperature increase of around 8°C during the PETM. The prominent increase in kaolinite content within the PETM is linked to increased runoff and/or weathering of adjacent and coeval soils. These results demonstrate that the PETM coincides globally with extreme climatic fluctuations and that terrestrial environments are very likely to record such climatic changes. - La transition Paléocène-Eocène (55,8±0,2 Ma) est marquée par un réchauffement extraordinaire communément appelé « Paleocene-Eocene Thermal Maximum » (PETM). Les données géochimiques caractérisant les sédiments marins et continentaux de cette période indiquent que ce réchauffement a été déclenché par une augmentation massive de CO2 lié à la déstabilisation des hydrates de méthane stockés le long des marges océaniques. L'étude des événements PETM constitue donc un bon analogue avec le réchauffement actuel. Le volume de CO2 émis durant le PETM est comparable avec le CO2 lié à l'activité actuelle humaine. La compréhension des causes du réchauffement du PETM peut être cruciale pour prévoir et évaluer les conséquences du réchauffement anthropogénique, en particulier les répercussions d'un tel réchauffement sur les domaines continentaux et océaniques. De nombreux facteurs entrent en ligne de compte dans le cas du PETM, tels que la paléogéographie, la paléotopographie et les paléoenvironnement. Pour mieux comprendre les réponses environnementales aux événements du PETM, 2 types d'environnements ont été choisis : (1) le domaine marin ouvert mais relativement peu profond (Wadi Nukhul. Sinai, Dababiya, Luxor, Egypte), (2) le milieu continental marécageux humide (mines de lignite, Inde) et fluviatile, semi-aride (Esplugafreda, Pyrénées espagnoles). Dans le domaine marin, le PETM est caractérisé par des excursions négatives du ô13Ccar et ô13Corg et un shift persistant des valeurs de 815N à ~ 0 %o indiquant une forte activité des organismes (bactéries) fixant l'azote. La diminution des carbonates observée durant le PETM peut-être due à des phénomènes de dissolution ou une augmentation des apports terrigènes. Des taux élevés en Ti, K et Zr et une diminution des montants de Si, reflétés par des valeurs des indices d'altération (CIA) qui coïncident avec une augmentation significative des apports de kaolinite impliquent une altération chimique accrue, du fait de conditions plus humides au début du PETM. Deux événements anoxiques globaux ont été mis en évidence durant le PETM. Le premier, situé dans la partie inférieur du PETM, serait lié à la libération des hydrates de méthane stockés le long des talus continentaux et ne correspond pas à des variations significatives des éléments sensibles aux changements de conditions redox. Le second est caractérisé par une augmentation des éléments U, Mo, V et Fe et la présence de petit framboids de pyrite dont la taille varie entre 2 et 5pm. Le second épisode anoxique est caractérisé par une forte augmentation des éléments sensibles aux changements de la productivité (Cu, Ni et Co), indiquant une augmentation de la productivité dans les eaux de surface. Les données obtenues mettent en évidence le rôle crucial joué par l'altération et les apports en nutriments qui en découlent. Ces paramètres sont cruciaux pour la succession des événements qui ont conduit au PETM, et plus particulièrement l'augmentation de la productivité dans la phase de récupération. Durant le PETM, le milieu continental est caractérisé par l'établissement de conditions humides qui ont facilité voir provoqué la migration des mammifères modernes qui ont suivi le déplacement de ces ceintures climatiques. L'âge de cette migration est basé sur des arguments chimiostratigraphiques (isotopes stables), biostratigraphiques et paléomagnétiques. Les données bibliographiques ainsi que celles que nous avons récoltées en Inde, montrent que les mammifères modernes ont d'abord migré depuis l'Asie vers l'Europe, puis dans le continent Nord américain. Ces derniers ne sont arrivés en Inde que plus tardivement, suggérant que le temps de leur migration est lié à la collision Inde-Asie. Dans le Nord-Est de l'Espagne (Esplugafreda), la réponse du milieu continental aux événements PETM est assez différente. Comme en Inde, deux excursions signicatives en ô13C ont été observées. La première correspond au PETM et la seconde est corrélée avec l'optimum thermique de l'Eocène précoce (ETM2). Les isotopes stables de l'oxygène mesurés 2 différents types de nodules calcaires provenant de paléosols suggère une augmentation de 10°C pendant le PETM. Une augmentation simultanée des taux de kaolinite indique une intensification de l'altération chimique et/ou de l'érosion de sols adjacents. Ces résultats démontrent que le PETM coïncide globalement avec des variations climatiques extrêmes qui sont très aisément reconnaissables dans les dépôts continentaux.

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An exceptional, tectonically remarkably unaffected, nearly 200 m-thick continuous section of hemipelagic and turbiditic sediments, covering most of the Triassic is described from the Batain Complex of north-eastern Oman. According to conodont and radiolarian data the sequence spans the late Scythian to the early Norian, a time period of nearly 30 M. Coupled with a high resolution stratigraphy, the lithostratigraphy, sedimentology, as well as sequence and isotope stratigraphy of the section are documented. For the Triassic of the Batain Plain we propose the new name Sal Formation, which replaces the formerly used Matbat Formation, and subdivide it into three new members. The Sal Formation was deposited on the proximal continental margin of northeastern Arabia and records various depositional environments. The lower member is interpreted as the distal part of a homoclinal ramp which evolves to a distally steepened ramp during time of deposition of the middle member. The upper member displays a toe of slope position which is indicated by an increase of proximal turbidites. These sediments form part of a segment of the Neo-Tethyan embayment between Arabia and India. The stratigraphic analysis indicates highly varying sedimentation rates from a minimum of 2 m/M gamma around the Anisian/Ladinian boundary up to 15 m/M gamma during the Lower and Upper Triassic. Sequence-stratigraphically, the Sal section is subdivided into six third order cycles which are biochronologically well integrated into the global Triassic cycle chart. The mixed siliciclastic-calcareous upper member of the Sal Formation typically shows highstand related carbonate shedding. It is, therefore, an important test case for sequence-stratigraphic controlled carbonate export to mixed basin fills. The well developed sequence stratigraphic cycles are mirrored in the isotope patterns. Additionally, the carbon and oxygen isotope data from the Sal Formation record the same chemostratigraphic marker at the Spathian/Anisian boundary known from other Tethyan sections.

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Stratigraphic and petrographic analysis of the Cretaceous to Eocene Tibetan sedimentary succession has allowed us to reinterpret in detail the sequence of events which led to closure of Neotethys and continental collision in the NW Himalaya. During the Early Cretaceous, the Indian passive margin recorded basaltic magmatic activity. Albian volcanic arenites, probably related to a major extensional tectonic event, are unconformably overlain by an Upper Cretaceous to Paleocene carbonate sequence, with a major quartzarenite episode triggered by the global eustatic sea-level fall at the Cretaceous/Tertiary boundary. At the same time, Neotethyan oceanic crust was being subducted beneath Asia, as testified by calc-alkalic volcanism and forearc basin sedimentation in the Transhimalayan belt. Onset of collision and obduction of the Asian accretionary wedge onto the Indian continental rise was recorded by shoaling of the outer shelf at the Paleocene/Eocene boundary, related to flexural uplift of the passive margin. A few My later, foreland basin volcanic arenites derived from the uplifted Asian subduction complex onlapped onto the Indian continental terrace. All along the Himalaya, marine facies were rapidly replaced by continental redbeds in collisional basins on both sides of the ophiolitic suture. Next, foreland basin sedimentation was interrupted by fold-thrust deformation and final ophiolite emplacement. The observed sequence of events compares favourably with theoretical models of rifted margin to overthrust belt transition and shows that initial phases of continental collision and obduction were completed within 10 to 15 My, with formation of a proto-Himalayan chain by the end of the middle Eocene.

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The Upper Lahul region in the NW Himalaya is located in the transition zone between the High Himalayan Crystalline (HHC) to the SW and the Tethyan Zone sedimentary series to the NE. The tectonic evolution of these domains during the Himalayan Orogeny is the consequence of a succession of five deformation events. An early D1 phase corresponds to synmetamorphic, NE verging folding. This deformation created the Tandi Syncline, which consists of Permian to Jurassic Tethyan metasediments cropping out in the core of a large-scale synformal fold within the HHC paragneiss. This tectonic event is interpreted as related to a NE directed nappe stacking (Shikar Beh Nappe), probably during the late Eocene to the early Oligocene. A subsequent D2a phase caused SW verging folding in the HHC. This deformation is interpreted as contemporaneous with late Oligocene to early Miocene SW directed thrusting along the Main Central Thrust. In the Tethyan Zone, a D2b phase is marked by a decollement thrust, a system of reverse faults, and gentle folds, associated with SW directed tectonic movements. This deformation is related to an imbricate structure, characteristic of a shallow structural level, and developed in the frontal part of a nappe affecting the Tethyan Zone units of SE Zanskar (Nyimaling-Tsarap Nappe). A later D3 phase generated the Chandra Dextral Shear Zone (CDSZ), a large-scale, ductile, dextral strike-slip shear zone, located in the transition zone between the HHC and the Tethyan Himalaya. The CDSZ most likely represents a part of a system of early Miocene extensional and/or dextral, strike-slip shear zones-observed at the HHC-Tethyan Zone contact along the entire Himalaya. A final D4 phase induced large-scale doming and NE:verging back folding.