Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Official Positions for FRAX® clinical regarding falls and frailty: can falls and frailty be used in FRAX®? From Joint Official Positions Development Conference of the International Society for Clinical Densitometry and International Osteoporosis Foundation on FRAX®.

Risk factors for fracture can be purely skeletal, e.g., bone mass, microarchitecture or geometry, or a combination of bone and falls risk related factors such as age and functional status. The remit of this Task Force was to review the evidence and consider if falls should be incorporated into the FRAX® model or, alternatively, to provide guidance to assist clinicians in clinical decision-making for patients with a falls history. It is clear that falls are a risk factor for fracture. Fracture probability may be underestimated by FRAX® in individuals with a history of frequent falls. The substantial evidence that various interventions are effective in reducing falls risk was reviewed. Targeting falls risk reduction strategies towards frail older people at high risk for indoor falls is appropriate. This Task Force believes that further fracture reduction requires measures to reduce falls risk in addition to bone directed therapy. Clinicians should recognize that patients with frequent falls are at higher fracture risk than currently estimated by FRAX® and include this in decision-making. However, quantitative adjustment of the FRAX® estimated risk based on falls history is not currently possible. In the long term, incorporation of falls as a risk factor in the FRAX® model would be ideal.

Scale Effects in Hydraulic Model Tests of Rock Protected Structures, HR-119, 1970

A laboratory investigation was undertaken to determine the limiting model Reynolds number above which the scour behavior of rock protected structures can be reproduced in hydraulic models scaled according to the Froude criterion. A submerged jet was passed over an initially full scour pocket containing uniform glass spheres and the rate of scour was measured as a function of time. The dimensions of the scour pocket and jet and the particle diameters were varied as needed to maintain strict geometric similarity. For each of two different Froude numbers the Reynolds number was varied over a wide range. The normalized scour rate was found to be practically independent of the Reynolds number, R, (based on the jet velocity and particle diameter) at values of R above about 2.5 x 10^3, and to decrease with Rat smaller values. A grid placed in the jet was found to have a very strong effect on the scour rate. In an attempt to explain the effect of R on the scour behavior, turbulent pressure and velocity fluctuations were measured in air flows and water flows, respectively, over rigid scour pockets having the same geometry as those formed in the scour experiments. The normalized spectra of the fluctuations were found to be nearly independent of R, but the flow pattern was found to be very sensitive to the inlet condition, the jet deflecting upward or downward in a not wholly explainable manner. This indicates that scour behavior can be modeled only if the approach flow is also accurately modeled.

Gravity-driven slug motion in capillary tubes

The velocity of a liquid slug falling in a capillary tube is lower than predicted for Poiseuille flow due to presence of menisci, whose shapes are determined by the complex interplay of capillary, viscous, and gravitational forces. Due to the presence of menisci, a capillary pressure proportional to surface curvature acts on the slug and streamlines are bent close to the interface, resulting in enhanced viscous dissipation at the wedges. To determine the origin of drag-force increase relative to Poiseuille flow, we compute the force resultant acting on the slug by integrating Navier-Stokes equations over the liquid volume. Invoking relationships from differential geometry we demonstrate that the additional drag is due to viscous forces only and that no capillary drag of hydrodynamic origin exists (i.e., due to hydrodynamic deformation of the interface). Requiring that the force resultant is zero, we derive scaling laws for the steady velocity in the limit of small capillary numbers by estimating the leading order viscous dissipation in the different regions of the slug (i.e., the unperturbed Poiseuille-like bulk, the static menisci close to the tube axis and the dynamic regions close to the contact lines). Considering both partial and complete wetting, we find that the relationship between dimensionless velocity and weight is, in general, nonlinear. Whereas the relationship obtained for complete-wetting conditions is found in agreement with the experimental data of Bico and Quere [J. Bico and D. Quere, J. Colloid Interface Sci. 243, 262 (2001)], the scaling law under partial-wetting conditions is validated by numerical simulations performed with the Volume of Fluid method. The simulated steady velocities agree with the behavior predicted by the theoretical scaling laws in presence and in absence of static contact angle hysteresis. The numerical simulations suggest that wedge-flow dissipation alone cannot account for the entire additional drag and that the non-Poiseuille dissipation in the static menisci (not considered in previous studies) has to be considered for large contact angles.

The Effects of Headcut and Knickpoint Propagation on Bridges in Iowa, TR-541, 2008

The overarching goal of the proposed research was to provide a predictive tool for knickpoint propagation within the HCA (Hungry Canyon Alliance) territory. Knickpoints threaten the stability of bridge structures in Western Iowa. The study involved detailed field investigations over two years in order to monitor the upstream migration of a knickpoint on Mud Creek in Mills County, IA and identify the key mechanisms triggering knickpoint propagation. A state-of-the-art laser level system mounted on a movable truss provided continuous measurements of the knickpoint front for different flow conditions. A pressure transducer found in proximity of the truss provided simultaneous measurements of the flow depth. The laser and pressure transducer measurements led to the identification of the conditions at which the knickpoint migration commences. It was suggested that negative pressures developed by the reverse roller flow near the toe of the knickpoint face triggered undercutting of the knickpoint at this location. The pressure differential between the negative pressure and the atmospheric pressure also draws the impinging jet closer to the knickpoint face producing scour. In addition, the pressure differential may induce suction of sediment from the face. Other contributing factors include slump failure, seepage effects, and local fluvial erosion due to the exerted fluid shear. The prevailing flow conditions and soil information along with the channel cross-sectional geometry and gradient were used as inputs to a transcritical, one dimensional, hydraulic/geomorphic numerical model, which was used to map the flow characteristics and shear stress conditions near the knickpoint. Such detailed flow calculations do not exist in the published literature. The coupling of field and modeling work resulted in the development of a blueprint methodology, which can be adopted in different parts of the country for evaluating knickpoint evolution. This information will assist local government agencies in better understanding the principal factors that cause knickpoint propagation and help estimate the needed response time to control the propagation of a knickpoint after one has been identified.

Insights into the Design and Characteristics of the Sedimentation Process at Multi-Barrel Culverts in Iowa, TR-596, 2010

The present study is an integral part of a broader study focused on the design and implementation of self-cleaning culverts, i.e., configurations that prevent the formation of sediment deposits after culvert construction or cleaning. Sediment deposition at culverts is influenced by many factors, including the size and characteristics of material of which the channel is composed, the hydraulic characteristics generated under different hydrology events, the culvert geometry design, channel transition design, and the vegetation around the channel. The multitude of combinations produced by this set of variables makes the investigation of practical situations a complex undertaking. In addition to the considerations above, the field and analytical observations have revealed flow complexities affecting the flow and sediment transport through culverts that further increase the dimensions of the investigation. The flow complexities investigated in this study entail: flow non-uniformity in the areas of transition to and from the culvert, flow unsteadiness due to the flood wave propagation through the channel, and the asynchronous correlation between the flow and sediment hydrographs resulting from storm events. To date, the literature contains no systematic studies on sediment transport through multi-box culverts or investigations on the adverse effects of sediment deposition at culverts. Moreover, there is limited knowledge about the non-uniform, unsteady sediment transport in channels of variable geometry. Furthermore, there are few readily useable (inexpensive and practical) numerical models that can reliably simulate flow and sediment transport in such complex situations. Given the current state of knowledge, the main goal of the present study is to investigate the above flow complexities in order to provide the needed insights for a series of ongoing culvert studies. The research was phased so that field observations were conducted first to understand the culvert behavior in Iowa landscape. Modeling through complementary hydraulic model and numerical experiments was subsequently carried out to gain the practical knowledge for the development of the self-cleaning culvert designs.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

Methionine-321 in the C-terminal alpha-helix of catabolic ornithine carbamoyltransferase from Pseudomonas aeruginosa is important for positive homotropic cooperativity.

Pseudomonas aeruginosa has a pair of distinct ornithine carbamoyltransferases. The anabolic ornithine carbamoyltransferase encoded by the argF gene catalyzes the formation of citrulline from ornithine and carbamoylphosphate. The catabolic ornithine carbamoyltransferase encoded by the arcB gene promotes the reverse reaction in vivo; although this enzyme can be assayed in vitro for citrulline synthesis, its unidirectionality in vivo is determined by its high concentration at half maximum velocity for carbamoylphosphate ([S]0.5) and high cooperativity toward this substrate. We have isolated mutant forms of catabolic ornithine carbamoyltransferase catalyzing the anabolic reaction in vivo. The corresponding arcB mutant alleles on a multicopy plasmid specifically suppressed an argF mutation of P. aeruginosa. Two new mutant enzymes were obtained. When methionine 321 was replaced by isoleucine, the mutant enzyme showed loss of homotropic cooperativity at physiological carbamoylphosphate concentrations. Substitution of glutamate 105 by lysine resulted in a partial loss of the sigmoidal response to increasing carbamoylphosphate concentrations. However, both mutant enzymes were still sensitive to the allosteric activator AMP and to the inhibitor spermidine. These results indicate that at least two residues of catabolic ornithine carbamoyltransferase are critically involved in positive carbamoylphosphate cooperativity: glutamate 105 (previously known to be important) and methionine 321. Mutational changes in either amino acid will affect the geometry of helix H2, which contains several residues required for carbamoylphosphate binding.

Rift-related inheritance in orogens: a case study from the Austroalpine nappes in Central Alps (SE-Switzerland and N-Italy)

The Austroalpine nappe systems in SE-Switzerland and N-Italy preserve remnants of the Adriatic rifted margin. Based on new maps and cross-sections, we suggest that the complex structure of the Campo, Grosina/Languard, and Bernina nappes is inherited largely from Jurassic rifting. We propose a classification of the Austroalpine domain into Upper, Middle and Lower Austroalpine nappes that is new because it is based primarily on the rift-related Jurassic structure and paleogeography of these nappes. Based on the Alpine structures and pre-Alpine, rift-related geometry of the Lower (Bernina) and Middle (Campo, Grosina/Languard) Austroalpine nappes, we restore these nappes to their original positions along the former margin, as a means of understanding the formation and emplacement of the nappes during initial reactivation of the Alpine Tethyan margin. The Campo and Grosina/Languard nappes can be interpreted as remnants of a former necking zone that comprised pre-rift upper and middle crust. These nappes were juxtaposed with the Mesozoic cover of the Bernina nappe during Jurassic rifting. We find evidence for low-angle detachment faults and extensional allochthons in the Bernina nappe similar to those previously described in the Err nappe and explain their role during subsequent reactivation. Our observations reveal a strong control of rift-related structures during the subsequent Alpine reactivation on all scales of the former distal margin. Two zones of intense deformation, referred to as the Albula-Zebru and Lunghin-Mortirolo movement zones, have been reactivated during Alpine deformation and cannot be described as simple monophase faults or shear zones. We propose a tectonic model for the Austroalpine nappe systems that link inherited, rift-related structures with present-day Alpine structures. In conclusion, we believe that apart from the direct regional implications, the results of this paper are of general interest in understanding the control of rift structures during reactivation of distal-rifted margins.

Structure and kinematics of the Siviez-Mischabel nappe in the Mattertal (western Alps of Switzerland) = Structure et cinématique de la nappe de Siviez-Mischabel le long de la vallée de Zermatt (Alpes de Suisse occidentale)

Résumé Cette étude porte sur le flanc inverse de la nappe de Siviez-Mischabel et sur les unités tectoniques sous jacentes (zone de Stalden supérieur et zone Houillère) dans la vallée menant à Zermatt. L'étude structurale du granite permien de Randa (orthogneiss oeillé) permet de mieux comprendre les effets de la déformation alpine sur les roches de socle. La cartographie détaillée de l'orthogneiss et de son encaissant, ainsi que l'étude lithostratigraphique des terrains sédimentaires associés permettent de proposer un schéma structural et cinématique du flanc inverse de la nappe de Siviez-Mischabel et de mieux comprendre ses relations avec les unités tectoniques sous-jacentes. L'analyse structurale de l'orthogneiss de Randa et de son encaissant révèle la superposition de plusieurs phases de déformation ductile. Cet orthogneiss formé sous des conditions métamorphiques du faciès schiste vert possède une forte schistosité alpine avec au moins deux linéations d'extension. La première, L1, orientée NW-SE est associée à la mise en place de la nappe. La seconde, L2, orientée SW-NE, se corrèle au cisaillement ductile du Simplon. La quantification de la déformation au moyen de la méthode de Fry sur les faciès porphyriques donne des ellipses à rapports axiaux compris entre 1.9 et 5.3, en accord avec les valeurs obtenues par d'autres marqueurs {tourmalines étirées, fibres). Les valeurs mesurées parallèlement à L1 ou L2 sont très semblables. La méthode de Fry a nécessité une étude théorique préalable afin de vérifier son applicabilité aux orthogneiss oeillés. La méthode requiert une distribution spatiale homogène et isotrope des marqueurs utilisés. Les tests statistiques effectués ont révélé que les phénocristaux de feldspath alcalin satisfont à cette condition et qu'ils peuvent être utilisés comme marqueur de la déformation au moyen de la méthode de Fry. Les valeurs obtenues révèlent l'importance du cisaillement ductile du Simplon sur la géométrie de la nappe dans la région d'étude. Le levé cartographique a permis d'améliorer la lithostratigraphie de la base de la nappe de Siviez-Mischabel. Trois formations en position renversée peuvent être observées sous les gneiss formant le coeur de la nappe. Ces trois formations forment le coeur du synclinal de St-Niklaus qui connecte la nappe de Siviez-Mischabel à la zone de Stalden supérieur. La datation par U-Pb de zircons détritiques et magmatiques par LA-ICP-MS permet de contraindre l'âge des formations observées (probablement Carbonifère à Trias précoce). Ces données ont des répercussions importantes sur la structure de la nappe dans la région, prouvant l'existence de plusieurs plis avec des séries normales et renversées bien préservées. La définition et la datation de ces formations, ainsi que leur identification dans la-Zone- Houillère avoisinante permettent de mieux comprendre la géométrie initiale et les relations tectoniques des nappes du Pennique moyen dans la vallée de Zermatt. Summary This study investigates the overturned limb of the Siviez-Mischabel nappe and underlying tectonic units (Upper Stalden zone and Houillère zone) in the Mattertal area. Detailed structural analysis in the Permian Randa granite (augen orthogneiss) allows a better understanding of the Alpine deformation effects on basement rocks. Detailed mapping of this orthogneiss and surrounding rocks, and the study of the lithostratigraphy in the related sedimentary horizons allow the proposition of a structural and kinematic model for the overturned limb of the Siviez-Mischabel and to better understand the relations with the underlying tectonic units. The structural analysis of the Randa orthogneiss and surrounding rocks revealed the superposition of several phases of ductile deformation. This orthogneiss formed under greenschist facies metamorphic conditions displays a strong Alpine foliation with at least two stretching lineations. The first lineation, L1, is oriented NW-SE and is related to the nappe emplacement northward. The second one, L2, is related to the Simplon ductile shear zone. Strain estimation using the Fry method has been performed on porphyritic facies of the Randa orthogneiss. The obtained ellipses have axial ratios varying between 1.9 and 5.3, in agreement with strain estimation obtained from other markers (stretched turmalines, fringes). The strain values are very similar if measured parallel to L1 or to L2. A theoretical approach was necessary to verify the relevant application of the Fry method to augen orthogneiss. This method requires that the distribution of the used markers has to be homogeneous and isotropic. Statistical tests have been done and revealed that K-feldspar phenocrysts satisfy these conditions and can be used as strain markers with the Fry method. The obtained strain measurements revealed the importance of the Simplon ductile shear zone on the geometry of the nappe in the studied area. Mapping has improved the lithostratigraphy at the base of the Siviez-Mischabel nappe. Three overturned formations can be observed below the gneisses forming the core of the nappe. These three formations form the St-Niklaus syncline, which connects the Siviez-Mischabel nappe to the underlying Upper Stalden zone. U-Pb dating of detrital and magmatic zircons by LA-ICPMS allowed the age of the observed formations to be constrained (presumably Carboniferous to Early Triassic). This data has critical implications for nappe structure in the region, composed of few recumbent folds with well preserved normal and overturned limbs. The definition and dating of these formations, as well as their identification in the adjacent "Houillère Zone" improve the understanding of the geometry and tectonic relations of the Middle Penninic nappes in the Mattertal.

Initial results on in vivo human coronary MR angiography at 7 T.

Seven tesla (T) MR imaging is potentially promising for the morphologic evaluation of coronary arteries because of the increased signal-to-noise ratio compared to lower field strengths, in turn allowing improved spatial resolution, improved temporal resolution, or reduced scanning times. However, there are a large number of technical challenges, including the commercial 7 T systems not being equipped with homogeneous body radiofrequency coils, conservative specific absorption rate constraints, and magnified sample-induced amplitude of radiofrequency field inhomogeneity. In the present study, an initial attempt was made to address these challenges and to implement coronary MR angiography at 7 T. A single-element radiofrequency transmit and receive coil was designed and a 7 T specific imaging protocol was implemented, including significant changes in scout scanning, contrast generation, and navigator geometry compared to current protocols at 3 T. With this methodology, the first human coronary MR images were successfully obtained at 7 T, with both qualitative and quantitative findings being presented.

Impingement jet cooling of end windings in a high-speed electric machine

The rotational speed of high-speed electric machines is over 15 000 rpm. These machines are compact in size when compared to the power rate. As a consequence, the heat fluxes are at a high level and the adequacy of cooling becomes an important design criterion. In the high-speed machines, the air gap between the stator and rotor is a narrow flow channel. The cooling air is produced with a fan and the flow is then directed to the air gap. The flow in the gap does not provide sufficient cooling for the stator end windings, and therefore additional cooling is required. This study investigates the heat transfer and flow fields around the coil end windings when cooling jets are used. As a result, an innovative and new assembly is introduced for the cooling jets, with the benefits of a reduced amount of hot spots, a lower pressure drop, and hence a lower power need for the cooling fan. The gained information can also be applied to improve the cooling of electric machines through geometry modifications. The objective of the research is to determine the locations of the hot spots and to find out induced pressure losses with different jet alternatives. Several possibilities to arrange the extra cooling are considered. In the suggested approach cooling is provided by using a row of air jets. The air jets have three main tasks: to cool the coils effectively by direct impingement jets, to increase and cool down the flow that enters the coil end space through the air gap, and to ensure the correct distribution of the flow by forming an air curtain with additional jets. One important aim of this study is the arrangement of cooling jets in such manner that hot spots can be avoided to wide extent. This enables higher power density in high-speed motors. This cooling system can also be applied to the ordinary electric machines when efficient cooling is needed. The numerical calculations have been performed using a commercial Computational Fluid Dynamics software. Two geometries have been generated: cylindrical for the studied machine and Cartesian for the experimental model. The main parameters include the positions, arrangements and number of jets, the jet diameters, and the jet velocities. The investigated cases have been tested with two widely used turbulence models and using a computational grid of over 500 000 cells. The experimental tests have been made by using a simplified model for the end winding space with cooling jets. In the experiments, an emphasis has been given to flow visualisation. The computational analysis shows good agreement with the experimental results. Modelling of the cooling jet arrangement enables also a better understanding of the complex system of heat transfer at end winding space.

Computational and Experimental Analysis of Flow Field in the Diffusers of Centrifugal Compressors

Centrifugal compressors are widely used for example in process industry, oil and gas industry, in small gas turbines and turbochargers. In order to achieve lower consumption of energy and operation costs the efficiency of the compressor needs to be improve. In the present work different pinches and low solidity vaned diffusers were utilized in order to improve the efficiency of a medium size centrifugal compressor. In this study, pinch means the decrement of the diffuser flow passage height. First different geometries were analyzed using computational fluid dynamics. The flow solver Finflo was used to solve the flow field. Finflo is a Navier-Stokes solver. The solver is capable to solve compressible, incompressible, steady and unsteady flow fields. Chien's k-e turbulence model was used. One of the numerically investigated pinched diffuser and one low solidity vaned diffuser were studied experimentally. The overall performance of the compressor and the static pressure distribution before and after the diffuser were measured. The flow entering and leaving the diffuser was measured using a three-hole Cobra-probe and Kiel-probes. The pinch and the low solidity vaned diffuser increased the efficiency of the compressor. Highest isentropic efficiency increment obtained was 3\% of the design isentropic efficiency of the original geometry. It was noticed in the numerical results that the pinch made to the hub and the shroud wall was most beneficial to the operation of the compressor. Also the pinch made to the hub was better than the pinchmade to the shroud. The pinch did not affect the operation range of the compressor, but the low solidity vaned diffuser slightly decreased the operation range.The unsteady phenomena in the vaneless diffuser were studied experimentally andnumerically. The unsteady static pressure was measured at the diffuser inlet and outlet, and time-accurate numerical simulation was conducted. The unsteady static pressure showed that most of the pressure variations lay at the passing frequency of every second blade. The pressure variations did not vanish in the diffuser and were visible at the diffuser outlet. However, the amplitude of the pressure variations decreased in the diffuser. The time-accurate calculations showed quite a good agreement with the measured data. Agreement was very good at the design operation point, even though the computational grid was not dense enough inthe volute and in the exit cone. The time-accurate calculation over-predicted the amplitude of the pressure variations at high flow.

Growth mechanisms and timing of emplacement of a vertically layered mafic intrusion in the feeder zone of an ocean island volcano (Fuerteventura, Canary islands)

Résumé pour le grand public L'île de Fuerteventura (Canaries) offre l'occasion rare d'observer les racines d'un volcan océanique édifié il y a 25 à 30 millions d'années et complètement érodé. On y voit de nombreux petits plutons de forme et composition variées, témoignant d'autant d'épisodes de l'activité magmatique. L'un de ces plutons, appelé PX1, présente une structure inhabituelle formée d'une alternance de bandes verticales d'épaisseur métrique à hectométrique de roches sombres de composition pyroxénilique ou gabbroïque. Les pyroxénites résultent clairement de l'accumulation de cristaux de pyroxènes et non de la simple solidification d'un magma? Se pose dès lors la question de la nature du processus qui a conduit à l'accumulation verticale de niveaux concentrés en pyroxènes. En effet, les litages pyroxénitiques classiques sont subhorizontaux, car ils résultent de l'accumulation gravitaire des cristaux séparés du magma dont ils cristalli¬sent par sédimentation. Cette étude vise à identifier et comprendre les mécanismes qui ont engendré ce Iitage minéralogique vertical et l'im¬portant volume de ces faciès cumulatifs. Nous nous sommes également intéressés aux conditions de pression et de température régnant au moment de la mise en place du pluton, ainsi qu'à sa durée de vie et à sa vitesse de refroidis¬sement. Enfin une approche géochimique nous a permis de préciser la nature de la source mantellique des magmas liés à cette activité magmatique. PX1 est en réalité un complexe filonien formé à des conditions de pression et de température de 1-2 kbar et 1050- 1100°C; sa construction a nécessité au moins 150 km3 de magma. L'alternance d'horizons gabbroïques et pyroxéniti¬ques représente des injections successives de magma sous la forme de filons verticaux, mis en place dans un contexte régional en extension. L'étude des orientations des minéraux dans ces faciès révèle que les horizons gabbroïques enregistrent l'extension régionale, alors que les pyroxénites sont générées par une compaction au sein du pluton. Ceci suggère que le régime des contraintes, qui était extensif lors de l'initiation de la mise en place de PX1, est pério¬diquement devenu compressif au sein même du pluton. Cette compression serait liée à des cycles de mise en place où la vitesse de croissance du pluton dépassait celle de l'extension régionale. La différenciation observée au sein de chaque horizon, depuis des pyroxénites riches en olivine jusqu'à des pyroxé¬nites à plagioclase interstitiel et des gabbros, ainsi que la composition géochimique des minéraux qui les constituent suggèrent que chaque filon vertical s'est mis en place à partir d'un magma de composition identique, puis a évolué indépendamment des autres en fonction du régime thermique et du régime des contraintes local. Lorsque le magma en train de cristalliser s'est trouvé en compression, le liquide résiduel a été séparé des cristaux déjà formés et extrait du système, laissant derrière lui une accumulation de cristaux dont la nature et les proportions dépendaient du stade de cristallisation atteint par le magma au moment de l'extraction. Ainsi, les niveaux de pyroxénites à olivine (premier minéral à cristalliser) ont été formés lorsque le magma correspondant était encore peu cristallisé; à l'inverse, les py¬roxénites riches en plagioclase (minéral plus tardif dans la séquence de cristallisation) et certains gabbros à caractère cumulatif résultent d'une compression tardive dans le processus de cristallisation du filon concerné. Les liquides résiduels extraits des niveaux pyroxénitiques sont rarement observés dans PX1, certaines poches et filonets de com¬position anorthositique pourraient en être les témoins. L'essentiel de ces liquides a probablement gagné des niveaux supérieurs du pluton, voire la surface du volcan. L'origine du régime compressif périodique affectant les filons en voie de cristallisation est attribuée aux injections suivantes de magma au sein du pluton, qui se sont succédées à un rythme plus rapide que la vitesse de consolidation des filons. Des datations U/Pb de haute précision sur des cristaux de zircon et de baddeleyite ainsi que40Ar/39Ar sur des cris¬taux d'amphibole révèlent une initiation de la mise en place de PX1 il y a 22.1 ± 0,7 Ma; celle-ci a duré quelque 0,48 ± 0,22 à 0,52 ± 0,29 Ma. Ce laps de temps est compatible avec celui nécessaire à la cristallisation des filons individuels, qui va de moins d'une année lors de l'initiation du magmatisme à 5 ans lors du maximum d'activité de PX1. La présence de cristaux résorbés enregistrant une cristallisation complexe suggère l'existence d'une chambre mag¬matique convective sous-jacente à PX1 et périodiquement rechargée. Les compositions isotopiques des roches étu¬diées révèlent une source mantellique profonde de type point chaud avec une contribution du manteau lithosphéri- que métasomatisé présent sous les îles Canaries. Résumé L'intrusion mafique Miocène PX1 fait partie du soubassement superficiel (0.15-0.2 GPa, 1100 °Q d'un volcan d'île océanique. La particularité de ce pluton est l'existence d'alternances d'unités de gabbros et de pyroxénites qui met¬tent en évidence un litage magmatique vertical (NNE-SSW). Les horizons gabbroiques et pyroxénitiques sont constitués d'unités de différenciation métriques qui suggèrent tine mise en place par injections périodiques de filons verticaux de magma formant un complexe filonien. Chaque filon vertical a subi une différenciation parallèle à un front de solidification sub-vertical parallèle aux bords du filon. Les pyroxénites résultent du fractionnement et de l'accumulation d'olivine ± clinopyroxene ± plagioclase à partir d'un magma basaltique faiblement alcalin et sont interprétées comme étant des imités de différenciation tronquées dont le liquide interstitiel a été extrait par compaction. L'orientation préférentielle des clinopyroxènes dans ces pyroxe- nites (obtenues par analyse EBSD et micro-tomographique) révèle une composante de cisaillement simple dans la genèse de ces roches, ce qui confirme cette interprétation. La compaction des pyroxénites est probablement causée par a mise en place de filons de magma suivants. Le liquide interstitiel expulsé est probablement par ces derniers. Les clinopyroxènes des gabbros, montrent une composante de cisaillement pure suggérant qu'ils sont affectés par une déformation syn-magmatique parallèle aux zones de cisaillement NNE-SSW observées autour de PX1 et liées au contexte tectonique Miocène d'extension régionale. Ceci suggère que les gabbros sont liés à des taux de mise en place faibles à la fin de cycles d'activité magmatique et sont peu ou pas affectés par la compaction. L'initiation et la géométrie de PX1 sont donc contrôlées par le contexte tectonique régional d'extension alors que les taux et les volumes de magma dépendent de facteurs liés à la source. Des taux d'injection élevés résultent probable¬ment en une croissance du pluton supérieure à la place crée par cette extension. Dans ce cas de figure, la propagation des nouveaux dykes et l'inaptitude du magma à circuler à travers les anciens dykes cristallisés pourrait causer une augmentation de la pression non-lithostatique sur ces derniers, exprimée par un cisaillement simple et l'expulsion du liquide interstitiel qu'ils contiennent (documenté par les zones de collecte anorthositiques). Les compositions en éléments majeurs et traces des gabbros et pyroxenites de PX1 sont globalement homogènes et dépendent de la nature cumulative des échantillons. Cependant, de petites variations des concentrations en éléments traces ainsi que les teneurs en éléments traces des bordures de clinopyroxenes suggèrent que ces derniers ont subi un processus de rééquilibrage et de cristallisation in situ. L'homogénéité des compositions chimiques des échantillons, ainsi que la présence de grains de clinopyroxene résorbés suggère que le complexe filonien PX1 s'est mis en place au dessus d'une chambre magmatique périodiquement rechargée dans laquelle la convection est efficace. Chaque filon est donc issu d'un même magma, mais a subi une différenciation par cristallisation in situ (jusqu'à 70% de fraction¬nement) indépendamment des autres. Dans ces filons cristallisés, les minéraux cumulatifs subissent un rééquilibrage partiel avec les liquide interstitiel avant que ce dernier ne soit expulsé lors de la compaction (mettant ainsi un terme à la différenciation). Ce modèle de mise en place signifie qu'un minimum de 150Km3 de magma est nécessaire à la genèse de PX1, une partie de ce volume ayant été émis par le 'Central Volcanic Complex' de Fuerteventura. Les rapports isotopiques radiogéniques mesurés révèlent la contribution de trois pôles mantelliques dans la genèse du magma formant PX1. Le mélange de ces pôles HIMU, DMM et EM1 refléterai l'interaction du point chaud Cana¬rien avec un manteau lithosphérique hétérogène métasomatisé. Les petites variations de ces rapports et des teneurs en éléments traces au sein des faciès pourrait refléter des taux de fusion partielle variable de la source, résultant en un échantillonnage variable du manteau lithosphérique métasomatisé lors de son interaction avec le point chaud. Des datations U/Pb de haute précision (TIMS) sur des cristaux de zircon et de baddeleyite extraits de gabbros de PX1 révèlent que l'initiation de la cristallisation du magma a eu lieu il y a 22.10±0.07 Ma et que l'activité magmatique a duré un minimum de 0.48 à 0.52 Ma. Des âges 40Ar/39Ar obtenus sur amphibole sont de 21.9 ± 0.6 à 21.8 ± 0.3 Ma, identiques aux âges U/Pb. La combinaison de ces méthodes de datations, suggère que le temps maximum nécessaire à PX1 pour se refroidir en dessous de la température de fermeture de l'amphibole est de 0.8Ma. Ceci signifie que la durée de vie de PX1 est de 520 000 à 800 000 ans. La coexistence de cristaux de baddeleyite et de zircon dans un gabbro est attribuée à son interaction avec un fluide riche en C02 relâché par les carbonatites encaissantes lors du métamorphisme de contact généré par la mise en place de PX1 environ 160 000 ans après le début de sa mise en place. Les durées de vie obtenue sont en accord avec le modèle de mise en place suggérant une durée de cristallisation poux chaque filon allant de 1 an à 5 ans. Abstract The Miocene PX1 gabbro-pyroxenite intrusion (Fuerteventura, Canary Islands), is interpreted as the shallow-level feeder-zone (0.15-0.2 GPa and 1100-1120°C), to an ocean island volcano. The particularity of PX1 is that it displays a NNE-SSW trending vertical magmatic banding expressed by alternating gabbro and pyroxeriite sequences. The gabbro and pyroxenite sequences consist of metre-thick differentiation units, which suggest emplacement by pe¬riodic injection of magma pulses as vertical dykes that amalgamated, similarly to a sub-volcanic sheeted dyke com¬plex. Individual dykes underwent internal differentiation following a solidification front (favoured by a significant lateral/horizontal thermal gradient) parallel to the dyke edges. Pyroxenitic layers result from the fractionation and accumulation of clinopyroxene ± olivine ± plagioclase crystals from a mildly alkaline basaltic liquid and are interpre¬ted as truncated differentiation sequences, from which residual melts were extracted by compaction. Clinopyroxene mineral orientation in pyroxenites (evidenced by EBSD and micro X-ray tomography analysis) display a marked pure shear component, supporting this interpretation. Compaction and squeezing of the crystal mush is ascribed to the incoming and inflating magma pulses. The resulting expelled interstitial liquid was likely collected and erupted along with the magma flowing through the newly injected dykes. Gabbro sequences represent crystallised coalesced magma batches, emplaced at lower rates at the end of eruptive cycles, and underwent minor melt extraction as evi¬denced by clinopyroxene orientations that record a simple shear component suggesting syn-magmatic deformation parallel to observed NNF.-SSW trending shear-zones induced by the regional tensional Miocene stress-field. The initiation and geometry of PX1 is controlled by the regional extensional tectonic regime whereas rates and vo¬lumes of magma depend on source-related factors. High injection rates are likely to induce intrusion growth rates larger than could be accommodated by the regional extension. In this case, dyke tip geometry and the inability of magma to circulate through previously emplaced and crystallised dykes could result in an increase of non-lithostatic pressure on previously emplaced mushy dyke walls; generating strong pure-shear compaction and interstitial melt expulsion within the feeder-zone as recorded by the cumulitic pyroxenite bands and anorthositic collection zones. The whole-rock major and trace-element chemistry of PX1 gabbros and pyroxenites is globally homogeneous and controlled by the cumulate nature of the samples (i.e. on the modal proportions of olivine, pyroxene, plagioclase and oxides). However, small variations of whole-rock trace-element contents as well as trace-element contents of clinopyroxene rims suggest that in-situ re-equilibration and crystallisation has occurred. Additionally, the global homogeneity and presence of complex zoning of rare resorbed clinopyroxene crystals suggest that the PX1 feeder- zone overlies a periodically replenished and efficiently mixed magma chamber. Each individual dyke of magma thus originated from a compositionally constant mildly alkaline magma and differentiated independently from the others reaching up to 70% fractionation. Following dyke arrest these are affected by interaction with the trapped interstitial liquid prior to its compaction-linked expulsion (thus stopping the differentiation process). This emplacement model implies that minimum amount of approximately 150 km3 of magma is needed to generate PX1, part of it having been erupted through the overlying Central Volcanic Complex of Fuerteventura. The radiogenic isotope ratios of PX1 samples reveal the contribution on three end-members during magma genesis. This mixing of the H1MU, EMI and DMM end-members could reflect the interaction of the deep-seated Canarian mantle plume with a heterogeneous metasomatic and sepentininsed lithospheric mantle. Additionally, the observed trace-element and isotopic variations within the same fades groups could reflect varying degrees of partial melting of the source region, thus tapping more or less large areas of the metasomatised lithospheric mantle during interac¬tion with the plume. High precision ID-TIMS U/Pb zircon and baddeleyite ages from the PX1 gabbro samples, indicate initiation of magma crystallisation at 22.10 ± 0.07 Ma. The magmatic activity lasted a minimum of 0.48 to 0.52 Ma. 40Ar/39Ar amphibole ages are of 21.9 ± 0.6 to 21.8 ± 0.3, identical within errors to the U/Pb ages. The combination of the 40Ar/39Ar and U/Pb datasets imply that the maximum amount of time PX1 took to cool below amphibole Tc is 0.8 Ma, suggesting PX1 lifetime of 520 000 to 800 000 years. On top of this, the coexistence of baddeleyite and zircon in a single sample is ascribed to the interaction of PX1 with C02-rich carbonatite-derived fluids released from the host-rock carbonatites during contact metamorphism 160 000 years after PX1 initiation. These ages are in agreement with the emplacement model, implying a crystallisation time of less than 1 to 5 years for individual dykes.