Performance of a multi-level TDR system exposed to tropical field conditions - A time-space comparison with tensiometry

Time-domain reflectometry (TDR) is an important technique to obtain series of soil water content measurements in the field. Diode-segmented probes represent an improvement in TDR applicability, allowing measurements of the soil water content profile with a single probe. In this paper we explore an extensive soil water content dataset obtained by tensiometry and TDR from internal drainage experiments in two consecutive years in a tropical soil in Brazil. Comparisons between the variation patterns of the water content estimated by both methods exhibited evidences of deterioration of the TDR system during this two year period at field conditions. The results showed consistency in the variation pattern for the tensiometry data, whereas TDR estimates were inconsistent, with sensitivity decreasing over time. This suggests that difficulties may arise for the long-term use of this TDR system under tropical field conditions. (c) 2008 Elsevier B.V. All rights reserved.

Sound objects in time, space and action

SOUND OBJECTS IN TIME, SPACE AND ACTIONThe term "sound object" describes an auditory experience that is associated with an acoustic event produced by a sound source. At cortical level, sound objects are represented by temporo-spatial activity patterns within distributed neural networks. This investigation concerns temporal, spatial and action aspects as assessed in normal subjects using electrical imaging or measurement of motor activity induced by transcranial magnetic stimulation (TMS).Hearing the same sound again has been shown to facilitate behavioral responses (repetition priming) and to modulate neural activity (repetition suppression). In natural settings the same source is often heard again and again, with variations in spectro-temporal and spatial characteristics. I have investigated how such repeats influence response times in a living vs. non-living categorization task and the associated spatio-temporal patterns of brain activity in humans. Dynamic analysis of distributed source estimations revealed differential sound object representations within the auditory cortex as a function of the temporal history of exposure to these objects. Often heard sounds are coded by a modulation in a bilateral network. Recently heard sounds, independently of the number of previous exposures, are coded by a modulation of a left-sided network.With sound objects which carry spatial information, I have investigated how spatial aspects of the repeats influence neural representations. Dynamics analyses of distributed source estimations revealed an ultra rapid discrimination of sound objects which are characterized by spatial cues. This discrimination involved two temporo-spatially distinct cortical representations, one associated with position-independent and the other with position-linked representations within the auditory ventral/what stream.Action-related sounds were shown to increase the excitability of motoneurons within the primary motor cortex, possibly via an input from the mirror neuron system. The role of motor representations remains unclear. I have investigated repetition priming-induced plasticity of the motor representations of action sounds with the measurement of motor activity induced by TMS pulses applied on the hand motor cortex. TMS delivered to the hand area within the primary motor cortex yielded larger magnetic evoked potentials (MEPs) while the subject was listening to sounds associated with manual than non- manual actions. Repetition suppression was observed at motoneuron level, since during a repeated exposure to the same manual action sound the MEPs were smaller. I discuss these results in terms of specialized neural network involved in sound processing, which is characterized by repetition-induced plasticity.Thus, neural networks which underlie sound object representations are characterized by modulations which keep track of the temporal and spatial history of the sound and, in case of action related sounds, also of the way in which the sound is produced.LES OBJETS SONORES AU TRAVERS DU TEMPS, DE L'ESPACE ET DES ACTIONSLe terme "objet sonore" décrit une expérience auditive associée avec un événement acoustique produit par une source sonore. Au niveau cortical, les objets sonores sont représentés par des patterns d'activités dans des réseaux neuronaux distribués. Ce travail traite les aspects temporels, spatiaux et liés aux actions, évalués à l'aide de l'imagerie électrique ou par des mesures de l'activité motrice induite par stimulation magnétique trans-crânienne (SMT) chez des sujets sains. Entendre le même son de façon répétitive facilite la réponse comportementale (amorçage de répétition) et module l'activité neuronale (suppression liée à la répétition). Dans un cadre naturel, la même source est souvent entendue plusieurs fois, avec des variations spectro-temporelles et de ses caractéristiques spatiales. J'ai étudié la façon dont ces répétitions influencent le temps de réponse lors d'une tâche de catégorisation vivant vs. non-vivant, et les patterns d'activité cérébrale qui lui sont associés. Des analyses dynamiques d'estimations de sources ont révélé des représentations différenciées des objets sonores au niveau du cortex auditif en fonction de l'historique d'exposition à ces objets. Les sons souvent entendus sont codés par des modulations d'un réseau bilatéral. Les sons récemment entendus sont codé par des modulations d'un réseau du côté gauche, indépendamment du nombre d'expositions. Avec des objets sonores véhiculant de l'information spatiale, j'ai étudié la façon dont les aspects spatiaux des sons répétés influencent les représentations neuronales. Des analyses dynamiques d'estimations de sources ont révélé une discrimination ultra rapide des objets sonores caractérisés par des indices spatiaux. Cette discrimination implique deux représentations corticales temporellement et spatialement distinctes, l'une associée à des représentations indépendantes de la position et l'autre à des représentations liées à la position. Ces représentations sont localisées dans la voie auditive ventrale du "quoi".Des sons d'actions augmentent l'excitabilité des motoneurones dans le cortex moteur primaire, possiblement par une afférence du system des neurones miroir. Le rôle des représentations motrices des sons d'actions reste peu clair. J'ai étudié la plasticité des représentations motrices induites par l'amorçage de répétition à l'aide de mesures de potentiels moteurs évoqués (PMEs) induits par des pulsations de SMT sur le cortex moteur de la main. La SMT appliquée sur le cortex moteur primaire de la main produit de plus grands PMEs alors que les sujets écoutent des sons associée à des actions manuelles en comparaison avec des sons d'actions non manuelles. Une suppression liée à la répétition a été observée au niveau des motoneurones, étant donné que lors de l'exposition répétée au son de la même action manuelle les PMEs étaient plus petits. Ces résultats sont discuté en termes de réseaux neuronaux spécialisés impliqués dans le traitement des sons et caractérisés par de la plasticité induite par la répétition. Ainsi, les réseaux neuronaux qui sous-tendent les représentations des objets sonores sont caractérisés par des modulations qui gardent une trace de l'histoire temporelle et spatiale du son ainsi que de la manière dont le son a été produit, en cas de sons d'actions.

Time-resolved evolution of coherent structures in turbulent channels

El objetivo de esta tesis es estudiar la dinámica de la capa logarítmica de flujos turbulentos de pared. En concreto, proponemos un nuevo modelo estructural utilizando diferentes tipos de estructuras coherentes: sweeps, eyecciones, grupos de vorticidad y streaks. La herramienta utilizada es la simulación numérica directa de canales turbulentos. Desde los primeros trabajos de Theodorsen (1952), las estructuras coherentes han jugado un papel fundamental para entender la organización y dinámica de los flujos turbulentos. A día de hoy, datos procedentes de simulaciones numéricas directas obtenidas en instantes no contiguos permiten estudiar las propiedades fundamentales de las estructuras coherentes tridimensionales desde un punto de vista estadístico. Sin embargo, la dinámica no puede ser entendida en detalle utilizando sólo instantes aislados en el tiempo, sino que es necesario seguir de forma continua las estructuras. Aunque existen algunos estudios sobre la evolución temporal de las estructuras más pequeñas a números de Reynolds moderados, por ejemplo Robinson (1991), todavía no se ha realizado un estudio completo a altos números de Reynolds y para todas las escalas presentes de la capa logarítmica. El objetivo de esta tesis es llevar a cabo dicho análisis. Los problemas más interesantes los encontramos en la región logarítmica, donde residen las cascadas de vorticidad, energía y momento. Existen varios modelos que intentan explicar la organización de los flujos turbulentos en dicha región. Uno de los más extendidos fue propuesto por Adrian et al. (2000) a través de observaciones experimentales y considerando como elemento fundamental paquetes de vórtices con forma de horquilla que actúan de forma cooperativa para generar rampas de bajo momento. Un modelo alternativo fué ideado por del Álamo & Jiménez (2006) utilizando datos numéricos. Basado también en grupos de vorticidad, planteaba un escenario mucho más desorganizado y con estructuras sin forma de horquilla. Aunque los dos modelos son cinemáticamente similares, no lo son desde el punto de vista dinámico, en concreto en lo que se refiere a la importancia que juega la pared en la creación y vida de las estructuras. Otro punto importante aún sin resolver se refiere al modelo de cascada turbulenta propuesto por Kolmogorov (1941b), y su relación con estructuras coherentes medibles en el flujo. Para dar respuesta a las preguntas anteriores, hemos desarrollado un nuevo método que permite seguir estructuras coherentes en el tiempo y lo hemos aplicado a simulaciones numéricas de canales turbulentos con números de Reynolds lo suficientemente altos como para tener un rango de escalas no trivial y con dominios computacionales lo suficientemente grandes como para representar de forma correcta la dinámica de la capa logarítmica. Nuestros esfuerzos se han desarrollado en cuatro pasos. En primer lugar, hemos realizado una campaña de simulaciones numéricas directas a diferentes números de Reynolds y tamaños de cajas para evaluar el efecto del dominio computacional en las estadísticas de primer orden y el espectro. A partir de los resultados obtenidos, hemos concluido que simulaciones con cajas de longitud 2vr y ancho vr veces la semi-altura del canal son lo suficientemente grandes para reproducir correctamente las interacciones entre estructuras coherentes de la capa logarítmica y el resto de escalas. Estas simulaciones son utilizadas como punto de partida en los siguientes análisis. En segundo lugar, las estructuras coherentes correspondientes a regiones con esfuerzos de Reynolds tangenciales intensos (Qs) en un canal turbulento han sido estudiadas extendiendo a tres dimensiones el análisis de cuadrantes, con especial énfasis en la capa logarítmica y la región exterior. Las estructuras coherentes han sido identificadas como regiones contiguas del espacio donde los esfuerzos de Reynolds tangenciales son más intensos que un cierto nivel. Los resultados muestran que los Qs separados de la pared están orientados de forma isótropa y su contribución neta al esfuerzo de Reynolds medio es nula. La mayor contribución la realiza una familia de estructuras de mayor tamaño y autosemejantes cuya parte inferior está muy cerca de la pared (ligada a la pared), con una geometría compleja y dimensión fractal « 2. Estas estructuras tienen una forma similar a una ‘esponja de placas’, en comparación con los grupos de vorticidad que tienen forma de ‘esponja de cuerdas’. Aunque el número de objetos decae al alejarnos de la pared, la fracción de esfuerzos de Reynolds que contienen es independiente de su altura, y gran parte reside en unas pocas estructuras que se extienden más allá del centro del canal, como en las grandes estructuras propuestas por otros autores. Las estructuras dominantes en la capa logarítmica son parejas de sweeps y eyecciones uno al lado del otro y con grupos de vorticidad asociados que comparten las dimensiones y esfuerzos con los remolinos ligados a la pared propuestos por Townsend. En tercer lugar, hemos estudiado la evolución temporal de Qs y grupos de vorticidad usando las simulaciones numéricas directas presentadas anteriormente hasta números de Reynolds ReT = 4200 (Reynolds de fricción). Las estructuras fueron identificadas siguiendo el proceso descrito en el párrafo anterior y después seguidas en el tiempo. A través de la interseción geométrica de estructuras pertenecientes a instantes de tiempo contiguos, hemos creado gratos de conexiones temporales entre todos los objetos y, a partir de ahí, definido ramas primarias y secundarias, de tal forma que cada rama representa la evolución temporal de una estructura coherente. Una vez que las evoluciones están adecuadamente organizadas, proporcionan toda la información necesaria para caracterizar la historia de las estructuras desde su nacimiento hasta su muerte. Los resultados muestran que las estructuras nacen a todas las distancias de la pared, pero con mayor probabilidad cerca de ella, donde la cortadura es más intensa. La mayoría mantienen tamaños pequeños y no viven mucho tiempo, sin embargo, existe una familia de estructuras que crecen lo suficiente como para ligarse a la pared y extenderse a lo largo de la capa logarítmica convirtiéndose en las estructuras observas anteriormente y descritas por Townsend. Estas estructuras son geométricamente autosemejantes con tiempos de vida proporcionales a su tamaño. La mayoría alcanzan tamaños por encima de la escala de Corrsin, y por ello, su dinámica está controlada por la cortadura media. Los resultados también muestran que las eyecciones se alejan de la pared con velocidad media uT (velocidad de fricción) y su base se liga a la pared muy rápidamente al inicio de sus vidas. Por el contrario, los sweeps se mueven hacia la pared con velocidad -uT y se ligan a ella más tarde. En ambos casos, los objetos permanecen ligados a la pared durante 2/3 de sus vidas. En la dirección de la corriente, las estructuras se desplazan a velocidades cercanas a la convección media del flujo y son deformadas por la cortadura. Finalmente, hemos interpretado la cascada turbulenta, no sólo como una forma conceptual de organizar el flujo, sino como un proceso físico en el cual las estructuras coherentes se unen y se rompen. El volumen de una estructura cambia de forma suave, cuando no se une ni rompe, o lo hace de forma repentina en caso contrario. Los procesos de unión y rotura pueden entenderse como una cascada directa (roturas) o inversa (uniones), siguiendo el concepto de cascada de remolinos ideado por Richardson (1920) y Obukhov (1941). El análisis de los datos muestra que las estructuras con tamaños menores a 30η (unidades de Kolmogorov) nunca se unen ni rompen, es decir, no experimentan el proceso de cascada. Por el contrario, aquellas mayores a 100η siempre se rompen o unen al menos una vez en su vida. En estos casos, el volumen total ganado y perdido es una fracción importante del volumen medio de la estructura implicada, con una tendencia ligeramente mayor a romperse (cascada directa) que a unirse (cascade inversa). La mayor parte de interacciones entre ramas se debe a roturas o uniones de fragmentos muy pequeños en la escala de Kolmogorov con estructuras más grandes, aunque el efecto de fragmentos de mayor tamaño no es despreciable. También hemos encontrado que las roturas tienen a ocurrir al final de la vida de la estructura y las uniones al principio. Aunque los resultados para la cascada directa e inversa no son idénticos, son muy simétricos, lo que sugiere un alto grado de reversibilidad en el proceso de cascada. ABSTRACT The purpose of the present thesis is to study the dynamics of the logarithmic layer of wall-bounded turbulent flows. Specifically, to propose a new structural model based on four different coherent structures: sweeps, ejections, clusters of vortices and velocity streaks. The tool used is the direct numerical simulation of time-resolved turbulent channels. Since the first work by Theodorsen (1952), coherent structures have played an important role in the understanding of turbulence organization and its dynamics. Nowadays, data from individual snapshots of direct numerical simulations allow to study the threedimensional statistical properties of those objects, but their dynamics can only be fully understood by tracking them in time. Although the temporal evolution has already been studied for small structures at moderate Reynolds numbers, e.g., Robinson (1991), a temporal analysis of three-dimensional structures spanning from the smallest to the largest scales across the logarithmic layer has yet to be performed and is the goal of the present thesis. The most interesting problems lie in the logarithmic region, which is the seat of cascades of vorticity, energy, and momentum. Different models involving coherent structures have been proposed to represent the organization of wall-bounded turbulent flows in the logarithmic layer. One of the most extended ones was conceived by Adrian et al. (2000) and built on packets of hairpins that grow from the wall and work cooperatively to gen- ´ erate low-momentum ramps. A different view was presented by del Alamo & Jim´enez (2006), who extracted coherent vortical structures from DNSs and proposed a less organized scenario. Although the two models are kinematically fairly similar, they have important dynamical differences, mostly regarding the relevance of the wall. Another open question is whether such a model can be used to explain the cascade process proposed by Kolmogorov (1941b) in terms of coherent structures. The challenge would be to identify coherent structures undergoing a turbulent cascade that can be quantified. To gain a better insight into the previous questions, we have developed a novel method to track coherent structures in time, and used it to characterize the temporal evolutions of eddies in turbulent channels with Reynolds numbers high enough to include a non-trivial range of length scales, and computational domains sufficiently long and wide to reproduce correctly the dynamics of the logarithmic layer. Our efforts have followed four steps. First, we have conducted a campaign of direct numerical simulations of turbulent channels at different Reynolds numbers and box sizes, and assessed the effect of the computational domain in the one-point statistics and spectra. From the results, we have concluded that computational domains with streamwise and spanwise sizes 2vr and vr times the half-height of the channel, respectively, are large enough to accurately capture the dynamical interactions between structures in the logarithmic layer and the rest of the scales. These simulations are used in the subsequent chapters. Second, the three-dimensional structures of intense tangential Reynolds stress in plane turbulent channels (Qs) have been studied by extending the classical quadrant analysis to three dimensions, with emphasis on the logarithmic and outer layers. The eddies are identified as connected regions of intense tangential Reynolds stress. Qs are then classified according to their streamwise and wall-normal fluctuating velocities as inward interactions, outward interactions, sweeps and ejections. It is found that wall-detached Qs are isotropically oriented background stress fluctuations, common to most turbulent flows, and do not contribute to the mean stress. Most of the stress is carried by a selfsimilar family of larger wall-attached Qs, increasingly complex away from the wall, with fractal dimensions « 2. They have shapes similar to ‘sponges of flakes’, while vortex clusters resemble ‘sponges of strings’. Although their number decays away from the wall, the fraction of the stress that they carry is independent of their heights, and a substantial part resides in a few objects extending beyond the centerline, reminiscent of the very large scale motions of several authors. The predominant logarithmic-layer structures are sideby- side pairs of sweeps and ejections, with an associated vortex cluster, and dimensions and stresses similar to Townsend’s conjectured wall-attached eddies. Third, the temporal evolution of Qs and vortex clusters are studied using time-resolved DNS data up to ReT = 4200 (friction Reynolds number). The eddies are identified following the procedure presented above, and then tracked in time. From the geometric intersection of structures in consecutive fields, we have built temporal connection graphs of all the objects, and defined main and secondary branches in a way that each branch represents the temporal evolution of one coherent structure. Once these evolutions are properly organized, they provide the necessary information to characterize eddies from birth to death. The results show that the eddies are born at all distances from the wall, although with higher probability near it, where the shear is strongest. Most of them stay small and do not last for long times. However, there is a family of eddies that become large enough to attach to the wall while they reach into the logarithmic layer, and become the wall-attached structures previously observed in instantaneous flow fields. They are geometrically self-similar, with sizes and lifetimes proportional to their distance from the wall. Most of them achieve lengths well above the Corrsin’ scale, and hence, their dynamics are controlled by the mean shear. Eddies associated with ejections move away from the wall with an average velocity uT (friction velocity), and their base attaches very fast at the beginning of their lives. Conversely, sweeps move towards the wall at -uT, and attach later. In both cases, they remain attached for 2/3 of their lives. In the streamwise direction, eddies are advected and deformed by the local mean velocity. Finally, we interpret the turbulent cascade not only as a way to conceptualize the flow, but as an actual physical process in which coherent structures merge and split. The volume of an eddy can change either smoothly, when they are not merging or splitting, or through sudden changes. The processes of merging and splitting can be thought of as a direct (when splitting) or an inverse (when merging) cascade, following the ideas envisioned by Richardson (1920) and Obukhov (1941). It is observed that there is a minimum length of 30η (Kolmogorov units) above which mergers and splits begin to be important. Moreover, all eddies above 100η split and merge at least once in their lives. In those cases, the total volume gained and lost is a substantial fraction of the average volume of the structure involved, with slightly more splits (direct cascade) than mergers. Most branch interactions are found to be the shedding or absorption of Kolmogorov-scale fragments by larger structures, but more balanced splits or mergers spanning a wide range of scales are also found to be important. The results show that splits are more probable at the end of the life of the eddy, while mergers take place at the beginning of the life. Although the results for the direct and the inverse cascades are not identical, they are found to be very symmetric, which suggests a high degree of reversibility of the cascade process.

Time-dependent evolution of tissue markers by MALDI-MS imaging

We have used MALDI-MS imaging (MALDI-MSI) to monitor the time dependent appearance and loss of signals when tissue slices are brought rapidly to room temperature for short to medium periods of time. Sections from mouse brain were cut in a cryostat microtome, placed on a MALDI target and allowed to warm to room temperature for 30 s to 3 h. Sections were then refrozen, fixed by ethanol treatment and analysed by MALDI-MSI. The intensity of a range of markers were seen to vary across the time course, both increasing and decreasing, with the intensity of some markers changing significantly within 30 s and markers also showed tissue location specific evolution. The markers resulting from this autolysis were compared directly to those that evolved in a comparable 16 h on-tissue trypsin digest, and the markers that evolved in the two studies were seen to be substantially different. These changes offer an important additional level of location-dependent information for mapping changes and seeking disease-dependent biomarkers in the tissue. They also indicate that considerable care is required to allow comparison of biomarkers between MALDI-MSI experiments and also has implications for the standard practice of thaw-mounting multiple tissue sections onto MALDI-MS targets.

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.

Consumerism in urban Russia in the 1880s and 90s: Exploring conceptions of time, space, and modernity through bicycle and watch advertisements

This paper discusses the urban consumer culture in Moscow and Petersburg during the 1880s and 1890s and uses the consumption of bicycles and watches as a lens through which to explore changing perceptions of time and space within the experience of modernity at the end of the nineteenth century. Specifically, I argue that the way in which consumers and merchants constructed a dialogue of meaning around particular objects; the way in which objects are consumed by a culture gives insight into the values, morals, and tenure of that culture. The paper preferences newspaper ads and photographs as the mouthpieces of merchants and consumers respectively as they constructed a dialogue in the language of consumerism, and explores the ways in which both parties sought to assign meaning to objects during the experience of modernity. I am particularly interested in the way consumers perform elements of cultural modernity in photographs and how these instances of performance relate to their negotiation of modernity. The paper takes as its focus large section of the urban Russian population, much of whom can traditionally be called “middle class” but whose diversity has led me to the adoption of the term “consumer community,” and whose makeup is described in detail. The paper contributes to the continuing scholarly discourse on the makeup of the middle class in Russia and the social boundaries of late tsarist society. It speaks to the the developing sensibilities and values of a generation struggling to define itself in a rapidly changing world, to the ways in which conceptualizations of public and private space, as well as feminine and masculine space were redefined, and to the developing visual culture of the Russian consumer society, largely predicated on the display of objects to signify socially desirable traits. Whereas other explorations of consumer culture and advertisements have portrayed the relationship between merchants and consumers as a one-sided monologue in which merchants convince consumers that certain objects have cultural value, I emphasis the dialogue between merchants and consumers, and their mutual negotiation of cultural meaning through objects.

Dinâmica da paisagem no litoral oriental do Rio Grande do Norte: geocartografia e padrões espaciais dos campos de dunas móveis

This study shows the results of a research developed in the coastal regions of the Maxaranguape and Touros municipalities, more specific in the mobile dune fields of the Rio Grande do Norte's eastern coast. Although the coastal zones, represent a small percentage of the earth's surface it concentrates a great part of the world's population. The Rio Grande do Norte's state coastal landscape mosaic composed by the dune fields suggest a dynamic scene of changes in the spatial and temporal arranges, with significant changes in the geometry of the sedimentary cover. Following this perspective this research has the objective to map the emerged coastal zone of the Rio Grande do Norte's eastern coast under the perspective of the time-space evolution of the mobile dune fields using geoprocessing techniques, which includes remote sensing, digital images processing and geographic information system (GIS). The results imply the issue of thematic maps: Geologic map; multitemporal evolution map of the mobile dune fields; quantification of the mobile dune fields differences map; temporal evolution of the mobile dune fields surrounds map. The El Niño episodes have directly affected the atmospheric circulation, what have enhanced the sedimentary input in the sand dune, what can justify the relative area growth between the years of 1993 and 2001. The dynamic of the landscape transition were higher than the stability of the spatial pattern of the dune and it's surrounds, as a result the Rio Grande do Norte eastern coast dune fields, specially the mobile dunes from Touros, Zumbi and Maracajau have shown a decrease on the sedimentary cover without vegetation area from 1970 to 2007. Therefore, the data acquired and the techniques used, can be, eventually applied to the mobile dune fields monitoring in order to preserve the dune ecosystems in the Rio Grande do Norte coast

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Petrology and chemistry of the Chalten Plutonic Complex and implications on the magmatic and tectonic evolution of the Southernmost Andes (Patagonia) during the Miocene

Résumé Scientific:Pétrologie et Géochimie du Complexe Plutonique de Chaltén et les conséquences pour l'évolution magmatique et tectonique du Andes du Sud (Patagonia) pendant le MiocèneLe sujet de cette thèse est le Complexe Plutonique de Chaltén (CHPC), situé à la frontière entre le Chili et l'Argentine, en Patagonie (49°15'S). Ce complexe s'est mis en place au début du Miocène, dans un contexte de changements tectoniques importants. La géométrie et la vitesse de migration des plaques en Patagonie a été modifiée suite l'ouverture de la plaque Farallon il y a 25Ma (Pardo-Casas and Molnar 1987) et la subduction de la ride active du Chili sous la plaque sud-américaine il y a 14Ma (Cande and Leslie 1986). Les effets de cette reconfiguration tectonique sur la morphologie et le magmatisme de la plaque supérieure sont encore sujets à discussion. Dans ce contexte, un groupe d'intrusions miocènes - telle que le CHPC - est particulièrement intriguant, car en position transitionnelle entre le batholithe patagonien et l'arc volcanique cénozoïque et récent à l'ouest, et les laves de plateau de Patagonie à l'est (Fig. 1). A cause de leur position tectonique transitoire, ces plutons isolés hors du batholithe représentent un endroit clé pour comprendre les interactions entre la tectonique à large échelle et le magmatisme en Patagonie. Ici, je présente de nouvelles données de terrain, petrologiques, géochimiques et géochronologiques dans le but de caractériser la nature du CHPC, qui était largement inconnu avant cette étude, dans le but de tester l'hypothèse de migration de l'arc et erosion par subduction.Les résultats de l'investigation géochimique (chapitre 2) montrent que le CHPC n'est qu'un exemple parmi les plutons isolés d'arrière arc ave une composition calco-alcaline caractéristique, c-à-d une signature d'arc. La plupart de ces plutons isolés ont une composition alcaline. Le CHPC, contrairement, a une signature calco-alcaline avec Κ intermédiaire, tel que le batholithe patagonien et la plupart des roches volcaniques quaternaires liées à l'arc le long des Andes.De nouvelles données géochronologiques U-Pb de haute précision sur des zircons, acquis par TIMS, sur le CHPC donnent des âges entre 17.0 et 16.4Ma. Les âges absolus sont en accord avec la séquence intrusive déduite des relations de terrain (chapitre 1). Ces données sont les premières contraintes d'âge U-Pb sur le CHPC. Elles montrent clairement que l'histoire magmatique du CHPC n'a pas de lien direct avec la subduction de la ride à cette latitude (Cande and Leslie 1986), car le complexe est au moins 6Ma plus ancien.Une comparaison en profondeur avec les autres intrusions d'âge Miocène en Patagonie révèlent - pour la première fois - une évolution temporelle intéressante. Il y a une tendance E-W distincte au magmatisme calco-alcalin entre 20-16Ma avec une diminution de l'âge vers l'est - le CHPC est l'expression la plus orientale de cette tendance. Je suggère que la relation espace-temps reflète une migration vers l'est (vers le continent) de l'arc magmatique. Je propose que le facteur principal contrôlant cette migration est la subduction rapide suite à la reconfiguration de la vitesse des plaques tectoniques après l'ouverture la plaque Farallon (à ~26Ma) qui résulterait en une déformation importante ainsi qu'à des taux élevés d'érosion dans la fosse de subduction.Les rapports d'isotopes radiogéniques (Pb, Sr, Nd) élevés, une signature 6018 basse et un rapport Th/La élevé sont des paramètres distinctifs pour les roches mafiques du CHPC. Le modèle isotopique présenté (chapitre 2) suggère que cette signature reflète une contamination de la source, dans le coin de manteau, plutôt qu'une contamination crustale. La signature des éléments en trace du CHPC indiquent que le coin de manteau a été contaminé par des composés terrigènes, le plus vraisemblablement par des sédiments paléozoïques.Les travaux de terrain, la pétrographie et la géothermobarométrie ont été utilisés dans le but de comprendre l'histoire interne du CHPC (chapitre 3). Ces données suggèrent deux niveaux distincts de cristallisation : l'un dans la croûte moyenne (6 à 4.5kbar) et l'autre à un niveau peu profond (3.5 à 2kbar). La modélisation isotopique AFC de la contamination crustale indique des taux variables d'assimilation, qui ne sont pas corrélés avec le degré de différenciation. Cela suggère que différents volumes de magma se sont différenciés en profondeur, de façon indépendante. Cela implique que le CHPC se serait formés en plusieurs puises de magmas provenant d'au moins trois sources différentes. Les textures des granodiorites et des granites indiquent des teneurs élevées en cristaux avant la mise en place et, par conséquent, des températures d'emplacement faibles. Les observations de terrain montrent que les roches mafiques sont déformées, alors que ce n'est pas le cas pour les granodiorites et granites (plus jeunes). La déformation des roches mafiques est encore sujet de recherche, afin de savoir si elle est liée à la déformation régionale en régime compressif ou à l'emplacement lui-même. Cependant, la mise en place de grand volume de magma felsique riche en cristaux suggère un régime d'extension.Scientific Abstract:Petrology and chemistry of the Chaltén Plutonic Complex and implications on the magmatic and tectonic evolution of the Southernmost Andes (Patagonia) during the MioceneThe subject of this thesis is the Chaltén Plutonic Complex (CHPC) located at the frontier between Chile and Argentina in Patagonia (at 49° 15 'Southern latitude). This complex intruded during early Miocene in a context of major tectonics changes. The plate geometry of Patagonia has been modified by changes in the plate motions after the break up of the Farallôn plate at 25Ma (Pardo-Casas and Molnar 1987) and by the subduction of the Chile spreading Ridge beneath South-America at 14 Ma (Cande and Leslie 1986). The effects of this tectonic setting on the morphology and the magmatism of the overriding plate are a matter of on-going discussion. Particularly intriguing in this context is a group of isolated Miocene intrusions - like the CHPC - which are located in a transitional position between the Patagonian Batholith and the Cenozoic and Recent volcanic arc in the West, and the Patagonian plateau lavas in the East (Fig. 1). Due to their transient tectonic position these isolated plutons outside the batholith represent a key to understanding the interaction between global-scale tectonics and magmatism in Patagonia. Here, I present new field, penological, geochemical and geochronological data to characterize the nature of the CHPC, which was largely unknown before this study, in order to test the hypothesis of time- transgressive magmatism.The results of the geochemical investigation (Chapter 2) show that the CHPC is only one among these isolated back-arc plutons with a characteristic calc-alkaline composition, i.e. arc signature. Most of these isolated intrusives have an alkaline character. The CHPC, in contrast, has a medium Κ calc-alkaline signature, like the Patagonian batholith and most of the Quaternary arc-related volcanic rocks along the Andes.New high precision TIMS U-Pb zircon dating of the CHPC yield ages between 17.0 to 16.4 Ma. The absolute ages support the sequence of intrusion relations established in the field (Chapter 1). These data are the first U-Pb age constraints on the CHPC, and clearly show that the magmatic history of CHPC has no direct link to the subduction of the ridge, since this complex is at least 6 Ma older than the time of collision of the Chile ridge at this latitude (Cande and Leslie 1986).An in-depth comparison with other intrusion of Miocene age in Patagonia reveals - for the first time - an interesting temporal pattern. There is a distinct E-W trend of calc-alkaline magmatism between 20-16 Ma with the younging of ages in the East - the CHPC is the easternmost expression of this trend. I suggest that this time-space relation reflects an eastward (landward) migration of the magmatic arc. I propose that main factor controlling this migration is the fast rates of subduction after the major reconfigurations of the plate tectonic motions after the break up of the Farallôn Plate (at -26 ) resulting in strong deformation and high rates of subduction erosion.High radiogenic isotope ratios (Pb, Sr, Nd) ratios, low 5018 signature and high Th/La ratios in mafic rocks are distinctive features of the CHPC. The presented isotopic models (Chapter 2) suggest that this signature reflects source contamination of the mantle wedge rather than crustal contamination. The trace element signature of the CHPC indicates that the mantle wedge was contaminated with a terrigenous component, most likely from Paleozoic sediments.Fieldwork, petrography and geothermobarometry were used to further unravel the internal history of the CHPC (Chapter 3). These data suggest two main levels of crystallization: one a mid crustal levels (6 to 4.5 kbar) and other a shallow level (3.5 to 2 kbar). Isotopic AFC modeling of crustal contamination indicate variable rates of assimilation, which are not correlated with the degree of differentiation. This suggests that different batches of magma differentiate independently at depths. This implies that the CHPC would have formed by several pulses of magmas from at least 3 different sources. Textures of granodiorites and granites indicate a high content of crystals previous to the emplacement and consequently low emplacement temperatures. Field observations show that the mafic rocks are deformed, whereas the (younger) granodiorites and granites are not. It is still subject of investigation whether the deformation of the mafic rocks is related to regional deformation during a compressional regime or to the emplacement it self. However, the emplacement of huge amount of crystal rich felsic magmas suggests an extensional regime.Résumé Grand PublicPétrologie et Géochimie du Complexe Plutonique de Chaltén et les conséquences pour l'évolution magmatique et tectonique du Andes du Sud (Patagonia) pendant le MiocèneLe Complexe Plutonique de Chaltén (CHPC) est un massif montagneux situé à 49°S à la frontière entre le Chili et l'Argentine, en Patagonie (région la plus au sud de l'Amérique du Sud). Il est composé de montagnes qui peuvent atteindre plus de 3000 mètres d'altitude, telles que le Cerro Fitz Roy (3400m) et le Cerro Torre (3100m). Ces montagnes sont composées de roches plutoniques, c.-à-d. des magmas qui se sont refroidis et ont cristallisés sous la surface terrestre.La composition chimique de ces roches montre que les magmas, qui ont formé ce complexe plutonique, font partie d'un volcanisme d'arc. Celui-ci se forme lorsqu'une plaque océanique plonge sous une plaque continentale. Les géologues appellent ce processus « subduction ». Dans un tel scénario, le manteau terrestre, qui se fait prendre entre ces deux plaques, fond pour former ainsi du magma. Ce magma remonte à travers la plaque continentale vers la surface. Si celui-ci atteint la surface, il forme les roches volcaniques, comme par exemple des laves. S'il n'atteint pas la surface, le magma se refroidit pour former finalement les roches plutoniques.Le long de la marge ouest d'Amérique du Sud, la plaque Nazca - qui se situe au sud-est de la plaque océanique pacifique - passe en dessous de la plaque d'Amérique du Sud. La bordure ouest du sud de la plaque sud-américaine a également été affectée par d'autres processus tectoniques, tels que des changements dramatiques dans les déplacements de plaques (il y a 25Ma) et la collision de la ride du Chili (depuis 15 Ma jusqu'à aujourd'hui). Ces caractéristiques tectoniques et magmatiques font de cette région un haut lieu pour les géologues. La plaque Nazca, s'est formée suite à l'ouverture d'une plaque océanique plus ancienne, il y a 25Ma. Cette ouverture est liée aux vitesses de subduction les plus rapides jamais connues. La ride du Chili est l'endroit où le sol de l'Océan Pacifique s'ouvre, formant deux plaques océaniques : les plaques Nazca et Antarctique. La ride du Chili subducte sous la plaque sud-américaine depuis 15Ma, en association avec la formation de grands volumes de magma ainsi que des changements morphologiques importants. La question de savoir lequel de ces changements tectoniques globaux affecte la géologie et la géographie de Patagonie a été, et est encore, discutée pendant de nombreuses années. De nombreux chercheurs suggèrent que la plupart des caractéristiques morphologiques et magmatiques en Patagonie sont liés à la subduction de la ride du Chili, mais cette suggestion est encore débattue comme le montre notre étude.Le batholithe de Patagonie du sud (SPB) est un énorme massif composé de roches plutoniques et il s'étend tout au long de la côte ouest de Patagonie (au sud de 47°S). Ces roches correspondent certainement aux racines d'un ancien arc volcanique, qui a été soulevé et érodé. Le CHPC, ainsi que d'autres petites intrusions dans la région, se situe dans une position exotique, à 100km à l'est du SPB. Certains chercheurs suggèrent que ces intrusions pourraient être liées à la subduction de la ride du Chili.Afin de débattre de cette problématique, nous avons utilisé différentes méthodes géochronologiques pour déterminer l'âge du CHPC et le comparer (a) à l'âge des roches intrusives similaires du SPB et (b) à l'âge de la collision de la ride du Chili. Dans ce travail, nous prouvons que le CHPC s'est formé au moins 7Ma avant la collision avec la ride du Chili. Sur la base des âges du CHPC et de la composition chimique de ses roches et minéraux, nous proposons que le CHPC fait partie d'un arc volcanique ancien. La migration de l'arc volcanique plus profondément dans le continent résulte de la grande vitesse de subduction entre 25 et lOMa. Des caractéristiques évidentes pour un tel processus - telles qu'une déformation importante et une vitesse d'érosion élevée - peuvent être rencontrées tout au long de la bordure ouest de l'Amérique du sud.

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay

Space, time, and deity, the Gifford lectures at Glasgow, 1916-1918,

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