Two-layer particle filter for multiple target detection and tracking

This paper deals with the detection and tracking of an unknown number of targets using a Bayesian hierarchical model with target labels. To approximate the posterior probability density function, we develop a two-layer particle filter. One deals with track initiation, and the other with track maintenance. In addition, the parallel partition method is proposed to sample the states of the surviving targets.

Self-consistent resonance absorption with two layer profile steepening

Resonance absorption of p-polarized light, incident at angle 6 on a flowing, stratified plasma, is analyzed; profile steepening within (i) a layer around the turning point, and (ii) a thinner,embedded sublayer at the critical surface is taken into account self-consistently. The entire steepened region is taken as collisionless and isothermal. The structure of the main layer shows a variety of regimes, depending on how the flow crosses a sonic point. The structure of the sublayer is also determined; it is entirely subsonic (with no wave breaking) for a well-defined,broad parameter range. Density changes across both layer and sublayer, and fractional absorption, are given in terms of [(wavelength)2 Xintensity/temperature], and (temperature/mec2). The flow outside the double structure is also analyzed for particular conditions.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

The role of biases in on-line learning of two-layer networks

The influence of biases on the learning dynamics of a two-layer neural network, a normalized soft-committee machine, is studied for on-line gradient descent learning. Within a statistical mechanics framework, numerical studies show that the inclusion of adjustable biases dramatically alters the learning dynamics found previously. The symmetric phase which has often been predominant in the original model all but disappears for a non-degenerate bias task. The extended model furthermore exhibits a much richer dynamical behavior, e.g. attractive suboptimal symmetric phases even for realizable cases and noiseless data.

On-line learning with adaptive back-propagation in two-layer networks

An adaptive back-propagation algorithm parameterized by an inverse temperature 1/T is studied and compared with gradient descent (standard back-propagation) for on-line learning in two-layer neural networks with an arbitrary number of hidden units. Within a statistical mechanics framework, we analyse these learning algorithms in both the symmetric and the convergence phase for finite learning rates in the case of uncorrelated teachers of similar but arbitrary length T. These analyses show that adaptive back-propagation results generally in faster training by breaking the symmetry between hidden units more efficiently and by providing faster convergence to optimal generalization than gradient descent.

Correlations between thermal environment and egg quality of two layer commercial strains

Heat stress limits the productivity of laying hens, as reflected by egg production and egg quality. The present study aimed at showing the correlations between egg quality parameters and environmental variables recorded on the day eggs were laid and on the previous days. Birds were housed in battery cages in a commercial poultry house. Main component analyses were used to verify associations between environmental and production variables, and Pearson's linear correlation tests were used to further investigate those associations. Analyses were carried out separately for to layer strains, Dekalb® White and Hy-Line® w36, and the variables egg weight (g), eggshell weight (g), specific gravity (g/cm³) and eggshell percentage (%) were compared with the environmental variables of the same day of the production, and one, two, three, and four days before egg production. Sound intensity measured inside the houses was positively associated with the quality parameters of eggs produced on the next day. Thermal environmental variables affected the egg quality differently in each strain, particularly air temperature, internal roof tile temperature, relative humidity, and air velocity. Ammonia concentration measured inside the houses was lower than 1ppm, and did not affect production performance.

Modeling of fireside deposit formation in two industrial furnaces

Fireside deposits can be found in many types of utility and industrial furnaces. The deposits in furnaces are problematic because they can reduce heat transfer, block gas paths and cause corrosion. To tackle these problems, it is vital to estimate the influence of deposits on heat transfer, to minimize deposit formation and to optimize deposit removal. It is beneficial to have a good understanding of the mechanisms of fireside deposit formation. Numerical modeling is a powerful tool for investigating the heat transfer in furnaces, and it can provide valuable information for understanding the mechanisms of deposit formation. In addition, a sub-model of deposit formation is generally an essential part of a comprehensive furnace model. This work investigates two specific processes of fireside deposit formation in two industrial furnaces. The first process is the slagging wall found in furnaces with molten deposits running on the wall. A slagging wall model is developed to take into account the two-layer structure of the deposits. With the slagging wall model, the thickness and the surface temperature of the molten deposit layer can be calculated. The slagging wall model is used to predict the surface temperature and the heat transfer to a specific section of a super-heater tube panel with the boundary condition obtained from a Kraft recovery furnace model. The slagging wall model is also incorporated into the computational fluid dynamics (CFD)-based Kraft recovery furnace model and applied on the lower furnace walls. The implementation of the slagging wall model includes a grid simplification scheme. The wall surface temperature calculated with the slagging wall model is used as the heat transfer boundary condition. Simulation of a Kraft recovery furnace is performed, and it is compared with two other cases and measurements. In the two other cases, a uniform wall surface temperature and a wall surface temperature calculated with a char bed burning model are used as the heat transfer boundary conditions. In this particular furnace, the wall surface temperatures from the three cases are similar and are in the correct range of the measurements. Nevertheless, the wall surface temperature profiles with the slagging wall model and the char bed burning model are different because the deposits are represented differently in the two models. In addition, the slagging wall model is proven to be computationally efficient. The second process is deposit formation due to thermophoresis of fine particles to the heat transfer surface. This process is considered in the simulation of a heat recovery boiler of the flash smelting process. In order to determine if the small dust particles stay on the wall, a criterion based on the analysis of forces acting on the particle is applied. Time-dependent simulation of deposit formation in the heat recovery boiler is carried out and the influence of deposits on heat transfer is investigated. The locations prone to deposit formation are also identified in the heat recovery boiler. Modeling of the two processes in the two industrial furnaces enhances the overall understanding of the processes. The sub-models developed in this work can be applied in other similar deposit formation processes with carefully-defined boundary conditions.

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

Instabilities in two-liquid layers subject to a horizontal temperature gradient

We study theoretically the stability of two superposed fluid layers heated laterally. The fluids are supposed to be immiscible, the interface undeformable and of infinite horizontal extension. Combined thermocapillary and buoyancy forces give rise to a basic flow when a temperature difference is applied. The calculations are performed for a melt of GaAs under a layer of molten B2 O3 , a configuration of considerable technological importance. Four dif- ferent flow patterns and five temperature configurations are found for the basic state in this system. A linear stability analysis shows that the basic state may be destabilized by oscilla- tory motions leading to the so-called hydrothermal waves. Depending on the relative height of the two layers these hydrothermal waves propagate parallel or perpendicular to the temperature gradient. This analysis reveals that these perturbations can alter significantly the liquid flow in the liquid-encapsulated crystal growth techniques.

A two-fluid model for tissue growth within a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89). The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a chanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population.

Air Entrainment in the Turbulent Ship Hull Boundary Layer

Turbulent fluctuations in the vicinity of the water free surface along a flat, vertically oriented surface-piercing plate are studied experimentally using a laboratory-scale experiment. In this experiment, a meter-wide stainless steel belt travels horizontally in a loop around two rollers with vertically oriented axes, which are separated by 7.5 meters. This belt device is mounted inside a large water tank with the water level set just below the top edge of the belt. The belt, rollers, and supporting frame are contained within a sheet metal box to keep the device dry except for one 6-meter-long straight test section between rollers. The belt is launched from rest with an acceleration of up to 3-g in order to quickly reach steady state velocity. This creates a temporally evolving boundary layer analogous to the spatially evolving boundary layer created along a flat-sided ship moving at the same velocity, with a length equivalent to the length of belt that has passed the measurement region since the belt motion began. Surface profile measurements in planes normal to the belt surface are conducted using cinematic Laser Induced Fluorescence and quantitative surface profiles are extracted at each instant in time. Using these measurements, free surface fluctuations are examined and the propagation behavior of these free surface ripples is studied. It is found that free surface fluctuations are generated in a region close to the belt surface, where sub-surface velocity fluctuations influence the behavior of these free surface features. These rapidly-changing surface features close to the belt appear to lead to the generation of freely-propagating waves far from the belt, outside the influence of the boundary layer. Sub-surface PIV measurements are performed in order to study the modification of the boundary layer flow field due to the effects of the water free surface. Cinematic planar PIV measurements are performed in horizontal planes parallel to the free surface by imaging the flow from underneath the tank, providing streamwise and wall-normal velocity fields. Additional planar PIV experiments are performed in vertical planes parallel to the belt surface in order to study the bahvior of streamwise and vertical velocity fields. It is found that the boundary layer grows rapidly near the free surface, leading to an overall thicker boundary layer close to the surface. This rapid boundary layer growth appears to be linked to a process of free surface bursting, the sudden onset of free surface fluctuations. Cinematic white light movies are recorded from beneath the water surface in order to determine the onset location of air entrainment. In addition, qualitative observations of these processes are made in order to determine the mechanisms leading to air entrainment present in this flow.

Analytical solution and numerical model for the interface in a stratified long wave system

For a two layered long wave propagation, linearized governing equations, which were derived earlier from the Euler equations of mass and momentum assuming negligible friction and interfacial mixing are solved analytically using Fourier transform. For the solution, variations of upper layer water level is assumed to be sinosoidal having known amplitude and variations of interface level is solved. As the governing equations are too complex to solve it analytically, density of upper layer fluid is assumed as very close to the density of lower layer fluid to simplify the lower layer equation. A numerical model is developed using the staggered leap-forg scheme for computation of water level and discharge in one dimensional propagation having known amplitude for the variations of upper layer water level and interface level to be solved. For the numerical model, water levels (upper layer and interface) at both the boundaries are assumed to be known from analytical solution. Results of numerical model are verified by comparing with the analytical solutions for different time period. Good agreements between analytical solution and numerical model are found for the stated boundary condition. The reliability of the developed numerical model is discussed, using it for different a (ratio of density of fluid in the upper layer to that in the lower layer) and p (ratio of water depth in the lower layer to that in the upper layer) values. It is found that as ‘CX’ increases amplification of interface also increases for same upper layer amplitude. Again for a constant lower layer depth, as ‘p’ increases amplification of interface. also increases for same upper layer amplitude.

Actively shielded multi-layer gradient coil designs with improved cooling properties

In standard cylindrical gradient coils consisting of a single layer of wires, a limiting factor in achieving very large magnetic field gradients is the rapid increase in coil resistance with efficiency. This is a particular problem in small-bore scanners, such as those used for MR microscopy. By adopting a multi-layer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favourable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. Previously this approach has been applied to the design of unshielded, longitudinal, and transverse gradient coils. Here, the multi-layer approach has been extended to allow the design of actively shielded multi-layer gradient coils, and also to produce coils exhibiting enhanced cooling characteristics. An iterative approach to modelling the steady-state temperature distribution within the coil has also been developed. Results indicate that a good level of screening can be achieved in multi-layer coils, that small versions of such coils can yield higher efficiencies at fixed resistance than conventional two-layer (primary and screen) coils, and that performance improves as the number of layers of increases. Simulations show that by optimising multi-layer coils for cooling it is possible to achieve significantly higher gradient strengths at a fixed maximum operating temperature. A four-layer coil of 8 mm inner diameter has been constructed and used to test the steady-state temperature model. (C) 2003 Elsevier Inc. All rights reserved.

Fluid-rock interaction during late stages of the Alpine exhumation

Résumé de la thèseLa fracturation des roches au cours de phases compressives ou extensives est un souvent évoquée pour expliquer la circulation de fluide au sein des roches cristallines. Dans le cadre de cette thèse, la circulation des fluides lors de l'exhumation tardive des Alpes a été étudiée en utilisant deux approches différentes: analyses structurales de la déformation fragile d'une part et analyses géochimiques des roches et des minéraux (isotopes stables, datations U/Pb, thermochronologie (U-Th)/He) d'autre part. Cette approche combinée a permis de mieux comprendre l'interaction existante entre les fluides métamorphiques et les fluides météoriques, ainsi que leur interaction avec les roches encaissantes. Le travail a été effectué dans la zone Pennique du Valais suisse.La première partie était focalisée sur la déformation fragile, le but étant de définir les différents types de déformations existantes et de déterminer l'âge relatif des différentes familles de failles. Dans la région d'étude, quatre domaines ont été distingués. Chacun d'eux comportent deux types de structures fragiles, certaines sont minéralisées alors que d'autre non. Au sein de chaque domaine, la direction principale des structures minéralisées correspond à l'orientation des accidents tectoniques majeurs de la région (Aosta- Ranzola Line au Sud, Rhône Line au Nord et Simplon Fault Zone à l'Est), alors que les structures non- minéralisées montrent des orientations plus variables. Ainsi, le premier type de structure est interprété comme résultant d'une dislocation tectonique alors que le deuxième type de structure résulterait d'une dislocation gravitaire locale. Il n'est néanmoins pas possible de classer chronologiquement la formation de ces deux types de structure ni d'attribuer un âge relatif aux changements d'orientation des contraintes majeures.La deuxième étude a été effectuée dans la région de la zone de faille du Simplon. Dans cette zone, la composition isotopique des minéraux ayant cristallisé à l'intérieur des fractures tardives permet de distinguer différents types de circulation de fluide. Les valeurs δ180 du quartz de la roche encaissante ainsi que ceux des veines tardives du bloque inférieur de la faille sont comparables. Ces valeurs indiquent un rééquilibrage et un tamponnage isotopique des fluides tardifs au contact de la roche encaissante lors de la fracturation de cette dernière et de la cristallisation des veines tardives. La même situation est observée dans la partie nord du bloque supérieur ainsi que dans sa partie sud. Ceci n'est néanmoins pas le cas pour la partie centrale du bloque supérieur où les valeurs isotopiques des minéraux dans les veines tardives sont approximativement 3 %o plus basses (avec des valeurs extrêmes négatifs), indiquant une contribution d'eau météorique aux fluides circulant dans les veines. Ces données suggèrent qu'une infiltration d'eau météorique a pu avoir lieu dans le bloque supérieur, où la fracturation des roches est plus intensive car le déplacement relatif le long de la faille y fut plus important, et la température maximale du métamorphisme plus basse. La troisième contribution traite de la géo-thermochronologie de la zone de contact entre la klippe de la Dent Blanche et la nappe de Tsaté. De petits zircons euhédraux ont été trouvés dans un plan de faille minéralisé (parallèle à la Faille du Rhône, voir première partie de l'étude), riche en hématite et quartz, de la zone d'étude. Les analyses U/Pb donnent des âges radiométriques autour de 270 - 280 Ma aux zircons extraits de la minéralisation ainsi que ceux extraits de la roche encaissante, ce qui correspond à l'âge de la nappe de la Dent Blanche et non celui de la nappe du Tsaté qui est elle-même classiquement interprétée comme une ophiolite Jurassique de l'Océan Liguro-Piémontais. Ces données suggèrent que les zircons contenus dans la veine ont été hérités de la roche encaissante. Les résultats (U-Th)/He indiquent un âge de refroidissement différent pour la roche encaissante (25.5 ± 2.0 Ma) que celui de la minéralisation (17.7 ±1.4 Ma). Le thermomètre isotopique quartz-hématite indique une température d'équilibre, et donc de mise en place de la minéralisation, d'environ 170 °C, température très proche de la température de -180 °C de fermeture du zircon pour le système (U-Th)/He. Ceci suggère que l'âge de refroidissement des zircons de la minéralisation correspond aussi à l'âge de formation de la faille.Thesis abstractFluid circulation in fractured rocks is a common process in geology, and it is generally the consequence of faulting and fracturing during both tectonic compression and extension. This thesis is focused on fluid circulation during late stages of the Alpine exhumation. After a structural analysis of the late brittle deformation of the studied samples, several analytical methods (stable isotope investigations, U/Pb radiometric dating, (U-Th)/He thermochronology) have been applied to understand the interaction of metamorphic and meteoric fluids with one another as well as with the host rock. This thesis is articulated around three study directions. All studies were conducted in the Penninic Zone of the Valais, Switzerland. The first study deals with late, brittle deformation and focuses on the different deformation styles and on the relative age of the different families of fractures. In order to do this, late brittle structures observed in four different domains have been subdivided as a function of the existence (or not) and type of mineralization. Comparisons between mineralized and non-mineralized strike directions for all four domains show that mineralized structures follow the strike orientation of major tectonic movements indicated in the Penninic Zone of the Valais (Aosta-Ranzola Line to the S, Rhône Line to the Ν and Simplon Fault Zone to the E), whereas non-mineralized fractures have a more variable strike orientation. This difference could be interpreted as indicative of tectonic-related faulting (mineralized structures) vs. local, collapse-related faulting (non-mineralized fractures), but it is not strong enough to indicate a relative age of the late brittle structures, and/or a change in the orientation of the strain field in post-Miocene times. The second studied area is focused on the Simplon Fault Zone (SFZ). Stable isotope analyses of minerals filling these late fractures indicate that there are two different fluid circulation systems in the footwall and hanging wall of the SFZ. In the footwall, δ180 values of quartz from both the host rock and the late veins range from +10 %o to +12 %o. This is consistent with buffering of circulating fluids by the host rock during fracturing and vein precipitation. In the hanging wall, δΙ80 values for quartz crystals from the host rock and the late veins are similar in both the northern and southern parts of the detachment that are both affected by the same degree of metamorphism (greenschist to the Ν and amphibolite to the S). This is not the case in the central part of the SFZ, where there is a jump from amphibolite facies in the footwall to greenschist facies in the hanging wall. δ,80 values for quartz from the hanging wall late veins are approximately 3.0 %o lower (down to negative values in some cases) than the values observed in the footwall These data suggest that infiltration of meteoric water may have occurred in the most fractured parts of the hanging wall, where relative displacement on the SFZ was the greatest and the peak temperature lower. In the less fractured footwall the δ180 values reflect a host rock-buffered system.The third study is focused on geo-thermochronology at the contact between the Dent Blanche nappe and the Tsaté nappe where small, euhedral zircons were found in a hematite- and quartz-rich mineralization on a late normal fault plane parallel to the Rhône Line (see first part of the study). U/Pb analysis indicates that the zircons - both in the late mineralization and in the host rock - have absolute radiometric ages clustering around 270 - 280 Ma, which is the accepted age for intrusive rocks from the Austroalpine Dent Blanche units but not for the Tsaté nappe. The latter is classically interpreted as an ophiolitic remnant of the Jurassic Liguro-Piemontais Ocean. U/Pb analyses suggest that zircons in late mineralization are all inherited from the host rock; however, results of (U-Th)/He analyses indicate that cooling ages for the host rocks are different to the cooling ages for the zircons in late mineralization. Indeed, the calculated cooling age for the Arolla gneiss is 25.5 ± 2.0 Ma, whilst the cooling age for the associated mineralized fault plane is 17.7 ±1.4 Ma. Oxygen stable isotope fractionation between quartz and hematite in the same late mineralization corresponds to temperatures of about 170 °C. The proximity of the calculated emplacement temperature for the mineralization and the lower accepted closure temperature for zircon in the (U-Th)/He system (-180 °C) imply that the age of 17.7 ± 1.4 Ma can also be interpreted as the formation age of this late brittle fault.Résumé grand publicLa circulation des fluides dans les roches fracturées est typique de nombreux processus géologiques, et très souvent est la conséquence de la fracturation des roches. Cette thèse aborde la question de la circulation des fluides pendant les dernières phases du soulèvement des Alpes. Après une analyse structurale de la fracturation directement sur le terrain, plusieurs méthodes géochimiques ont été appliquées pour comprendre l'interaction entre les différents fluides circulants, et avec leur propre roche mère. L'étude, concentrée sur trois directions principales, a été conduite dans la zone Pennique du Valais suisse. La première partie traite de la déformation cassante dans le secteur cité. L'analyse détaillée des fractures a permis de les subdiviser en structures minéralisées et non-minéralisées, sur quatre domaines différents. La comparaison entre les directions des structures minéralisées et non-minéralisées a permis de montrer que les premières suivent l'orientation des accidents tectoniques majeurs de la région, alors que les structures non- minéralisées ont une orientation plus variable. Cette différence pourrait être interprétée comme indication d'une dislocation tectonique (structures minéralisées) contre une dislocation gravitaire locale (structures non-minéralisées), mais elle n'est pas assez forte pour indiquer un âge relatif des structures tardives et/ou un changement de l'orientation des contraintes après -20 Ma vers le présent.A partir de ces observations, la deuxième étude est concentrée dans la région de la faille du Simplon. Les analyses géochimiques sur les minéraux remplissant les structures tardives indiquent qu'il y a deux différents systèmes de circulation des fluides dans les deux parties (toit et mur) de la faille. Dans le mur, les valeurs isotopiques des minéraux cristallisés à partir d'un fluide tardif sont les mêmes de ceux de la roche mère, donc il y a eu rééquilibration chimique entre fluide et roche pendant la fracturation de cette dernière et la précipitation des minéraux. Dans le toit, les valeurs isotopiques dans la roche mère et dans les minéraux des veines tardives sont comparables dans les parties Ν et S de la faille, où les roches du toit et du mur ont atteint une température maximale - pendant phase prograde de la formation des Alpes - comparable. Au contraire, dans la partie centrale, où le mur a atteint des températures maximales plus élevées par rapport au toit, les valeurs géochimiques des minéralisations tardives du toit sont parfois plus basses que les valeurs observées dans le mur. Ces données suggèrent que l'infiltration de l'eau de surface aurait pu se produire dans la partie plus fracturée du toit, où le déplacement relatif le long de la faille était majeur et les températures maximales mineures. Au contraire, les données géochimiques du mur de la partie centrale indiquent un système isotopique équilibré par la roche mère.La troisième partie de ce travail se base sur l'étude géochimique intégrée des isotopes stables d'Oxygène et radioactifs du Plomb, Uranium, Thorium et Hélium, auprès d'une faille normale minéralisée et des roches de la région à cheval entre deux nappes, la nappe de la Dent Blanche et la nappe de Tsaté. Ici, des petits zircons ont été trouvés dans la minéralisation citée, riche en hématite et quartz. L'analyse radiométrique Uranium/Plomb a montré que les zircons dans la minéralisation et dans les roches autour ont des âges comparables (autour 280 Ma). Cela signifie que les zircons dans la minéralisation tardive ont été hérités de la roche mère pendant la fracturation et la circulation des fluides tardives. De l'autre coté, les résultats des analyses Uranium-Thorium/Hélium indiquent que les âges de refroidissement pour les roches mères sont différents comparés aux âges de refroidissement pour les zircons dans la minéralisation tardive: ces derniers sont plus jeunes d'environ 8 Ma (autour 25 Ma et autour 17 Ma respectivement). Les analyses des isotopes de l'oxygène sur quartz et hématite dans la même minéralisation donnent une température de mise en place de cette dernière d'environ 170° C. La température de fermeture du système chimique des zircons dans le système (Uranium-Thorium)/Hélium est d'environ 180 °C: la proximité de ces deux températures implique que l'âge de refroidissement de la minéralisation tardive peut également être interprété comme âge de formation de la faille.