Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

Addressing Sea Surface Salinity retrieval at different spatial resolution. Feasibility study using OCCAM data within SEPS simulator and L2 processor tools

Projecte de recerca elaborat a partir d’una estada a la National Oceanography Centre of Southampton (NOCS), Gran Bretanya, entre maig i juliol del 2006. La possibilitat d’obtenir una estimació precissa de la salinitat marina (SSS) és important per a investigar i predir l’extensió del fenòmen del canvi climàtic. La missió Soil Moisture and Ocean Salinity (SMOS) va ser seleccionada per l’Agència Espacial Europea (ESA) per a obtenir mapes de salinitat de la superfície marina a escala global i amb un temps de revisita petit. Abans del llençament de SMOS es preveu l’anàlisi de la variabilitat horitzontal de la SSS i del potencial de les dades recuperades a partir de mesures de SMOS per a reproduir comportaments oceanogràfics coneguts. L’objectiu de tot plegat és emplenar el buit existent entre les fonts de dades d’entrada/auxiliars fiables i les eines desenvolupades per a simular i processar les dades adquirides segons la configuració de SMOS. El SMOS End-to-end Performance Simulator (SEPS) és un simulador adhoc desenvolupat per la Universitat Politècnica de Catalunya (UPC) per a generar dades segons la configuració de SMOS. Es va utilitzar dades d’entrada a SEPS procedents del projecte Ocean Circulation and Climate Advanced Modeling (OCCAM), utilitzat al NOCS, a diferents resolucions espacials. Modificant SEPS per a poder fer servir com a entrada les dades OCCAM es van obtenir dades de temperatura de brillantor simulades durant un mes amb diferents observacions ascendents que cobrien la zona seleccionada. Les tasques realitzades durant l’estada a NOCS tenien la finalitat de proporcionar una tècnica fiable per a realitzar la calibració externa i per tant cancel•lar el bias, una metodologia per a promitjar temporalment les diferents adquisicions durant les observacions ascendents, i determinar la millor configuració de la funció de cost abans d’explotar i investigar les posibiltats de les dades SEPS/OCCAM per a derivar la SSS recuperada amb patrons d’alta resolució.

Orbit decidability and the conjugacy problem for some extensions of groups

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High-resolution spatial mapping of changes in the neurochemical profile after focal ischemia in mice.

After ischemic stroke, the ischemic damage to brain tissue evolves over time and with an uneven spatial distribution. Early irreversible changes occur in the ischemic core, whereas, in the penumbra, which receives more collateral blood flow, the damage is more mild and delayed. A better characterization of the penumbra, irreversibly damaged and healthy tissues is needed to understand the mechanisms involved in tissue death. MRSI is a powerful tool for this task if the scan time can be decreased whilst maintaining high sensitivity. Therefore, we made improvements to a (1) H MRSI protocol to study middle cerebral artery occlusion in mice. The spatial distribution of changes in the neurochemical profile was investigated, with an effective spatial resolution of 1.4 μL, applying the protocol on a 14.1-T magnet. The acquired maps included the difficult-to-separate glutamate and glutamine resonances and, to our knowledge, the first mapping of metabolites γ-aminobutyric acid and glutathione in vivo, within a metabolite measurement time of 45 min. The maps were in excellent agreement with findings from single-voxel spectroscopy and offer spatial information at a scan time acceptable for most animal models. The metabolites measured differed with respect to the temporal evolution of their concentrations and the localization of these changes. Specifically, lactate and N-acetylaspartate concentration changes largely overlapped with the T(2) -hyperintense region visualized with MRI, whereas changes in cholines and glutathione affected the entire middle cerebral artery territory. Glutamine maps showed elevated levels in the ischemic striatum until 8 h after reperfusion, and until 24 h in cortical tissue, indicating differences in excitotoxic effects and secondary energy failure in these tissue types. Copyright © 2011 John Wiley & Sons, Ltd.

The generic Hanna Neumann conjecture and post correspondence problem

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Choline-PET in prostate cancer management: The point of view of the radiation oncologist.

Among PET radiotracers, FDG seems to be quite accepted as an accurate oncology diagnostic tool, frequently helpful also in the evaluation of treatment response and in radiation therapy treatment planning for several cancer sites. To the contrary, the reliability of Choline as a tracer for prostate cancer (PC) still remains an object of debate for clinicians, including radiation oncologists. This review focuses on the available data about the potential impact of Choline-PET in the daily clinical practice of radiation oncologists managing PC patients. In summary, routine Choline-PET is not indicated for initial local T staging, but it seems better than conventional imaging for nodal staging and for all patients with suspected metastases. In these settings, Choline-PET showed the potential to change patient management. A critical limit remains spatial resolution, limiting the accuracy and reliability for small lesions. After a PSA rise, the problem of the trigger PSA value remains crucial. Indeed, the overall detection rate of Choline-PET is significantly increased when the trigger PSA, or the doubling time, increases, but higher PSA levels are often a sign of metastatic spread, a contraindication for potentially curable local treatments such as radiation therapy. Even if several published data seem to be promising, the current role of PET in treatment planning in PC patients to be irradiated still remains under investigation. Based on available literature data, all these issues are addressed and discussed in this review.

Urban image classification with semisupervised multiscale cluster kernels

This paper presents a semisupervised support vector machine (SVM) that integrates the information of both labeled and unlabeled pixels efficiently. Method's performance is illustrated in the relevant problem of very high resolution image classification of urban areas. The SVM is trained with the linear combination of two kernels: a base kernel working only with labeled examples is deformed by a likelihood kernel encoding similarities between labeled and unlabeled examples. Results obtained on very high resolution (VHR) multispectral and hyperspectral images show the relevance of the method in the context of urban image classification. Also, its simplicity and the few parameters involved make the method versatile and workable by unexperienced users.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Improved temporal resolution for functional studies with reduced number of segments with three-dimensional echo planar imaging.

PURPOSE: To introduce a new k-space traversal strategy for segmented three-dimensional echo planar imaging (3D EPI) that encodes two partitions per radiofrequency excitation, effectively reducing the number excitations used to acquire a 3D EPI dataset by half. METHODS: The strategy was evaluated in the context of functional MRI applications for: image quality compared with segmented 3D EPI, temporal signal-to-noise ratio (tSNR) (the ability to detect resting state networks compared with multislice two-dimensional (2D) EPI and segmented 3D EPI, and temporal resolution (the ability to separate cardiac- and respiration-related fluctuations from the desired blood oxygen level-dependent signal of interest). RESULTS: Whole brain images with a nominal voxel size of 2 mm isotropic could be acquired with a temporal resolution under half a second using traditional parallel imaging acceleration up to 4× in the partition-encode direction and using novel data acquisition speed-up of 2× with a 32-channel coil. With 8× data acquisition speed-up in the partition-encode direction, 3D reduced excitations (RE)-EPI produced acceptable image quality without introduction of noticeable additional artifacts. Due to increased tSNR and better characterization of physiological fluctuations, the new strategy allowed detection of more resting state networks compared with multislice 2D-EPI and segmented 3D EPI. CONCLUSION: 3D RE-EPI resulted in significant increases in temporal resolution for whole brain acquisitions and in improved physiological noise characterization compared with 2D-EPI and segmented 3D EPI. Magn Reson Med 72:786-792, 2014. © 2013 Wiley Periodicals, Inc.

An Empirical Examination of the R&D Boundaries of the Firm - A Problem-Solving Perspective

We consider, both theoretically and empirically, how different organization modes are aligned to govern the efficient solving of technological problems. The data set is a sample from the Chinese consumer electronics industry. Following mainly the problem solving perspective (PSP) within the knowledge based view (KBV), we develop and test several PSP and KBV hypotheses, in conjunction with competing transaction cost economics (TCE) alternatives, in an examination of the determinants of the R&D organization mode. The results show that a firm’s existing knowledge base is the single most important explanatory variable. Problem complexity and decomposability are also found to be important, consistent with the theoretical predictions of the PSP, but it is suggested that these two dimensions need to be treated as separate variables. TCE hypotheses also receive some support, but the estimation results seem more supportive of the PSP and the KBV than the TCE.

Tractable valuations under uncertainty

I put forward a concise and intuitive formula for the calculation of the valuation for a good in the presence of the expectation that further, related, goods will soon become available. This valuation is tractable in the sense that it does not require the explicit resolution of the consumerís life-time problem.

Symmetry for a Dirichlet-Neumann problem arising in water waves

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