Empilhamento sísmico pela composição de ondas planas

No presente trabalho de tese é apresentada uma nova técnica de empilhamento de dados sísmicos para a obtenção da seção de incidência normal ou afastamento fonte-receptor nulo, aplicável em meios bidimensionais com variações laterais de velocidade. Esta nova técnica denominada Empilhamento Sísmico pela Composição de Ondas Planas (empilhamento PWC) foi desenvolvida tomando como base os conceitos físicos e matemáticos da decomposição do campo de ondas em ondas planas. Este trabalho pode ser dividido em três partes: Uma primeira parte, onde se apresenta uma revisão da técnica de empilhamento sísmico convencional e do processo de decomposição do campo de ondas produzido a partir de fontes pontuais em suas correspondentes ondas planas. Na segunda parte, é apresentada a formulação matemática e o procedimento de aplicação do método de empilhamento sísmico pela composição de ondas planas. Na terceira parte se apresenta a aplicação desta nova técnica de empilhamento na serie de dados Marmousi e uma analise sobre a atenuação de ruído. A formulação matemática desta nova técnica de empilhamento sísmico foi desenvolvida com base na teoria do espalhamento aplicado a ondas sísmicas sob a restrição do modelo de aproximação de Born. Nesse sentido, inicialmente se apresenta a determinação da solução da equação de onda caustica para a configuração com afastamento fonte-receptor finito, que posteriormente é reduzido para a configuração de afastamento fonte-receptor nulo. Por outra parte, com base nessas soluções, a expressão matemática deste novo processo de empilhamento sísmico é resolvida dentro do contexto do modelo de aproximação de Born. Verificou-se que as soluções encontradas por ambos procedimentos, isto é, por meio da solução da equação da onda e pelo processo de empilhamento proposto, são iguais, mostrando-se assim que o processo de empilhamento pela composição de ondas planas produz uma seção com afastamento fonte-receptor nulo. Esta nova técnica de empilhamento basicamente consiste na aplicação de uma dupla decomposição do campo de ondas em onda planas por meio da aplicação de dois empilhamentos oblíquos (slant stack), isto é um ao longo do arranjo das fontes e outro ao longo do arranjo dos detectores; seguido pelo processo de composição das ondas planas por meio do empilhamento obliquo inverso. Portanto, com base nestas operações e com a ajuda de um exemplo de aplicação nos dados gerados a partir de um modelo simples, são descritos os fundamentos e o procedimento de aplicação (ou algoritmo) desta nova técnica de obtenção da seção de afastamento nulo. Como exemplo de aplicação do empilhamento PWC em dados correspondentes a um meio com variações laterais de velocidade, foi aplicado nos dados Marmousi gerados segundo a técnica de cobertura múltipla a partir de um modelo que representa uma situação geológica real. Por comparação da seção resultante com a similar produzida pelo método de empilhamento convencional, observa-se que a seção de afastamento nulo desta nova técnica apresenta melhor definição e continuidade dos reflectores, como também uma melhor caracterização da ocorrência de difrações. Por último, da atenuação de ruído aleatório realizada nos mesmos dados, observa-se que esta técnica de empilhamento também produz uma atenuação do ruído presente no sinal, a qual implica um aumento na relação sinal ruído.

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An analog implementation of radial basis function network appropriate for transducer linearizer

A circuit for transducer linearizer tasks have been designed and built using discrete components and it implements by: a Radial Basis Function Network (RBFN) with three basis functions. The application in a linearized thermistor showed that the network has good approximation capabilities. The circuit advantages is the amplitude, width and center.

Cadmium Uptake by Lettuce (Lactuca sativa L.) as Basis for Derivation of Risk Limits in Soils

The availability and uptake of Cd by lettuce (Lactuca sativa L.) in two common tropical soils (before and after liming) were studied in order to derive human health-based risk soil concentration. Cadmium concentrations ranging from 1 to 12 mg kg(-1) were added to samples from a clayey Oxisol and a sandy-loam Ultisol under glasshouse conditions. After incubation, a soil sample was taken from each pot, the concentration of Cd in the soil was determined, lettuce was grown during 36 d, and the edible parts were harvested and analyzed for Cd. A positive linear correlation was observed between total soil Cd and the Cd concentration in lettuce. The amount of Cd absorbed by lettuce grown in the Ultisol was about twice the amount absorbed in the Oxisol. Liming increased the soil pH and slightly reduced Cd availability and uptake. CaCl2 extraction was better than DTPA to reflect differences in binding strength of Cd between limed and unlimed soils. Risk Cd concentrations in the Ultisol were lower than in the Oxisol, reflecting the greater degree of uptake from the Ultisol. The derived risk Cd values were dependent on soil type and the exposure scenario.

Molecular basis for the diagnosis and treatment of acute promyelocytic leukemia

Acute promyelocytic leukemia is characterized by gene rearrangements that always involve the retinoic acid receptor alpha on chromosome 15. In the majority of patients t(15;17) is detected, which generates the promyelocytic leukemia gene/retinoic acid receptor alpha rearrangement. This rearrangement interacts with several proteins, including the native promyelocytic leukemia gene, thus causing its delocalization from the nuclear bodies, impairing its function. The immunofluorescence staining technique using the anti-PML antibody may be used to provide a rapid diagnosis and to immediately start therapy using all-trans retinoic acid. The experience of the International Consortium on Acute Promyelocytic Leukemia has demonstrated that early mortality was significantly reduced by adopting the immunofluorescence technique. All-trans retinoic acid combined with chemotherapy is the standard therapy; this promotes complete remission rates greater than 90% and cure rates of nearly 80%. However, early mortality is still an important limitation and hematologists must be aware of the importance of treating newly diagnosed acute promyelocytic leukemia as a medical emergency.

Reduced-order modelling, circuit-level design and SOI fabrication of microelectromechanical resonators

This thesis deals with two important research aspects concerning radio frequency (RF) microresonators and switches. First, a new approach for compact modeling and simulation of these devices is presented. Then, a combined process flow for their simultaneous fabrication on a SOI substrate is proposed. Compact models for microresonators and switches are extracted by applying mathematical model order reduction (MOR) to the devices finite element (FE) description in ANSYS c° . The behaviour of these devices includes forms of nonlinearities. However, an approximation in the creation of the FE model is introduced, which enables the use of linear model order reduction. Microresonators are modeled with the introduction of transducer elements, which allow for direct coupling of the electrical and mechanical domain. The coupled system element matrices are linearized around an operating point and reduced. The resulting macromodel is valid for small signal analysis around the bias point, such as harmonic pre-stressed analysis. This is extremely useful for characterizing the frequency response of resonators. Compact modelling of switches preserves the nonlinearity of the device behaviour. Nonlinear reduced order models are obtained by reducing the number of nonlinearities in the system and handling them as input to the system. In this way, the system can be reduced using linear MOR techniques and nonlinearities are introduced directly in the reduced order model. The reduction of the number of system nonlinearities implies the approximation of all distributed forces in the model with lumped forces. Both for microresonators and switches, a procedure for matrices extraction has been developed so that reduced order models include the effects of electrical and mechanical pre-stress. The extraction process is fast and can be done automatically from ANSYS binary files. The method has been applied for the simulation of several devices both at devices and circuit level. Simulation results have been compared with full model simulations, and, when available, experimental data. Reduced order models have proven to conserve the accuracy of finite element method and to give a good description of the overall device behaviour, despite the introduced approximations. In addition, simulation is very fast, both at device and circuit level. A combined process-flow for the integrated fabrication of microresonators and switches has been defined. For this purpose, two processes that are optimized for the independent fabrication of these devices are merged. The major advantage of this process is the possibility to create on-chip circuit blocks that include both microresonators and switches. An application is, for example, aswitched filter bank for wireless transceiver. The process for microresonators fabrication is characterized by the use of silicon on insulator (SOI) wafers and on a deep reactive ion etching (DRIE) step for the creation of the vibrating structures in single-crystal silicon and the use of a sacrificial oxide layer for the definition of resonator to electrode distance. The fabrication of switches is characterized by the use of two different conductive layers for the definition of the actuation electrodes and by the use of a photoresist as a sacrificial layer for the creation of the suspended structure. Both processes have a gold electroplating step, for the creation of the resonators electrodes, transmission lines and suspended structures. The combined process flow is designed such that it conserves the basic properties of the original processes. Neither the performance of the resonators nor the performance of the switches results affected by the simultaneous fabrication. Moreover, common fabrication steps are shared, which allows for cheaper and faster fabrication.

Amphiphile Kern-Schale-my-Netzwerke auf der Basis von Polyorganosiloxanen

Die Synthese funktionalisierter Polyorganosiloxan-µ-Netzwerke (Rh = 5 – 30 nm) gelingt durch Polycokondensation von Alkoxysilanen. Die entstehenden sphärischen Teilchen sind in unpolaren organischen Lösungsmitteln partikulär dispergierbar. Durch die sequentielle Zugabe der Silanmonomere können Kern-Schale-Partikel mit unterschiedlichen Teilchenarchitekturen realisiert werden. In der vorliegenden Arbeit wird p-Chlormethylphenyltrimethoxysilan als funktionalisiertes Monomer verwendet, um den µ-Netzwerken durch eine anschließende Quaternisierung der Chlorbenzylgruppen mit Dimethylaminoethanol amphiphile Eigenschaften zu verleihen. Durch den Kern-Schale-Aufbau der Partikel sind die hydrophilen Bereiche im Kugelinneren von der hydrophoben äußeren Schale separiert, was unerläßlich für die Verwendung der Partikel zur Verkapselung wasserlöslicher Substanzen ist.So können in den amphiphilen µ-Netzwerken beispielsweise wasserlösliche Farbstoffe verkapselt werden. Diese diffundieren sowohl aus Lösung als auch aus dem Festkörper in das geladene Partikelinnere und werden dort angereichert. Es wird eine Abhängigkeit der Farbstoffbeladung vom Quaternisierungsgrad gefunden, wobei die Anzahl an verkapselten Farbstoffmolekülen mit dem Quaternisierungsgrad zunimmt.Weiterhin können amphiphile µ-Gelpartikel auch als molekulare Nanoreaktoren zur Synthese von Edelmetallkolloiden verwendet werden, die in den Netzwerken topologisch gefangen sind. Hierzu werden zuerst Metallionen im Kugelinneren verkapselt und anschließend reduziert, wobei das Kolloidwachstum durch den wohldefinierten Reaktionsraum gesteuert wird. Neben Gold- und Palladiumkolloiden können auf diese Weise beispielsweise auch Silberkolloide in den Kernen von µ-Netzwerken hergestellt werden.

Der Austausch von Carbonylsulfid (COS) zwischen Vegetation und Atmosphäre unter erhöhter CO 2-Umgebungskonzentration

The responses of photosynthetic plant gas exchange, COS uptake and carbonic anhydrase (CA) activity were studied on Quercus ilex (Holm oak), and beech Fagus sylvatica L

Reinforcement Lernen mit Regularisierungsnetzwerken

Die Arbeit behandelt das Problem der Skalierbarkeit von Reinforcement Lernen auf hochdimensionale und komplexe Aufgabenstellungen. Unter Reinforcement Lernen versteht man dabei eine auf approximativem Dynamischen Programmieren basierende Klasse von Lernverfahren, die speziell Anwendung in der Künstlichen Intelligenz findet und zur autonomen Steuerung simulierter Agenten oder realer Hardwareroboter in dynamischen und unwägbaren Umwelten genutzt werden kann. Dazu wird mittels Regression aus Stichproben eine Funktion bestimmt, die die Lösung einer "Optimalitätsgleichung" (Bellman) ist und aus der sich näherungsweise optimale Entscheidungen ableiten lassen. Eine große Hürde stellt dabei die Dimensionalität des Zustandsraums dar, die häufig hoch und daher traditionellen gitterbasierten Approximationsverfahren wenig zugänglich ist. Das Ziel dieser Arbeit ist es, Reinforcement Lernen durch nichtparametrisierte Funktionsapproximation (genauer, Regularisierungsnetze) auf -- im Prinzip beliebig -- hochdimensionale Probleme anwendbar zu machen. Regularisierungsnetze sind eine Verallgemeinerung von gewöhnlichen Basisfunktionsnetzen, die die gesuchte Lösung durch die Daten parametrisieren, wodurch die explizite Wahl von Knoten/Basisfunktionen entfällt und so bei hochdimensionalen Eingaben der "Fluch der Dimension" umgangen werden kann. Gleichzeitig sind Regularisierungsnetze aber auch lineare Approximatoren, die technisch einfach handhabbar sind und für die die bestehenden Konvergenzaussagen von Reinforcement Lernen Gültigkeit behalten (anders als etwa bei Feed-Forward Neuronalen Netzen). Allen diesen theoretischen Vorteilen gegenüber steht allerdings ein sehr praktisches Problem: der Rechenaufwand bei der Verwendung von Regularisierungsnetzen skaliert von Natur aus wie O(n**3), wobei n die Anzahl der Daten ist. Das ist besonders deswegen problematisch, weil bei Reinforcement Lernen der Lernprozeß online erfolgt -- die Stichproben werden von einem Agenten/Roboter erzeugt, während er mit der Umwelt interagiert. Anpassungen an der Lösung müssen daher sofort und mit wenig Rechenaufwand vorgenommen werden. Der Beitrag dieser Arbeit gliedert sich daher in zwei Teile: Im ersten Teil der Arbeit formulieren wir für Regularisierungsnetze einen effizienten Lernalgorithmus zum Lösen allgemeiner Regressionsaufgaben, der speziell auf die Anforderungen von Online-Lernen zugeschnitten ist. Unser Ansatz basiert auf der Vorgehensweise von Recursive Least-Squares, kann aber mit konstantem Zeitaufwand nicht nur neue Daten sondern auch neue Basisfunktionen in das bestehende Modell einfügen. Ermöglicht wird das durch die "Subset of Regressors" Approximation, wodurch der Kern durch eine stark reduzierte Auswahl von Trainingsdaten approximiert wird, und einer gierigen Auswahlwahlprozedur, die diese Basiselemente direkt aus dem Datenstrom zur Laufzeit selektiert. Im zweiten Teil übertragen wir diesen Algorithmus auf approximative Politik-Evaluation mittels Least-Squares basiertem Temporal-Difference Lernen, und integrieren diesen Baustein in ein Gesamtsystem zum autonomen Lernen von optimalem Verhalten. Insgesamt entwickeln wir ein in hohem Maße dateneffizientes Verfahren, das insbesondere für Lernprobleme aus der Robotik mit kontinuierlichen und hochdimensionalen Zustandsräumen sowie stochastischen Zustandsübergängen geeignet ist. Dabei sind wir nicht auf ein Modell der Umwelt angewiesen, arbeiten weitestgehend unabhängig von der Dimension des Zustandsraums, erzielen Konvergenz bereits mit relativ wenigen Agent-Umwelt Interaktionen, und können dank des effizienten Online-Algorithmus auch im Kontext zeitkritischer Echtzeitanwendungen operieren. Wir demonstrieren die Leistungsfähigkeit unseres Ansatzes anhand von zwei realistischen und komplexen Anwendungsbeispielen: dem Problem RoboCup-Keepaway, sowie der Steuerung eines (simulierten) Oktopus-Tentakels.

Molecular basis of Osteoarthritis and aspects of cellular senescence in disease

The aim of this study is to investigate on some molecular mechanisms contributing to the pathogenesis of osteoarthritis (OA) and in particular to the senescence of articular chondrocytes. It is focused on understanding molecular events downstream GSK3β inactivation or dependent on the activity of IKKα, a kinase that does not belong to the phenotype of healthy articular chondrocytes. Moreover, the potential of some nutraceuticals on scavenging ROS thus reducing oxidative stress, DNA damage, and chondrocyte senescence has been evaluated in vitro. The in vitro LiCl-mediated GSK3β inactivation resulted in increased mitochondrial ROS production, that impacted on cellular proliferation, with S-phase transient arrest, increased SA-β gal and PAS staining, cell size and granularity. ROS are also responsible for the of increased expression of two major oxidative lesions, i.e. 1) double strand breaks, tagged by γH2AX, that associates with activation of GADD45β and p21, and 2) 8-oxo-dG adducts, that associate with increased IKKα and MMP-10 expression. The pattern observed in vitro was confirmed on cartilage from OA patients. IKKa dramatically affects the intensity of the DNA damage response induced by oxidative stress (H2O2 exposure) in chondrocytes, as evidenced by silencing strategies. At early time point an higher percentage of γH2AX positive cells and more foci in IKKa-KD cells are observed, but IKKa KD cells proved to almost completely recover after 24 hours respect to their controls. Telomere attrition is also reduced in IKKaKD. Finally MSH6 and MLH1 genes are up-regulated in IKKαKD cells but not in control cells. Hydroxytyrosol and Spermidine have a great ROS scavenging capacity in vitro. Both treatments revert the H2O2 dependent increase of cell death and γH2AX-foci formation and senescence, suggesting the ability of increasing cell homeostasis. These data indicate that nutraceuticals represent a great challenge in OA management, for both therapeutical and preventive purposes.

Diastolic dysfunction in human cardiac allografts is related with reduced SERCA2a gene expression

Previous studies demonstrated that impaired left ventricular (LV) relaxation in cardiac allografts limits exercise tolerance post-transplant despite preserved systolic ejection fraction (EF). This study tested in human cardiac allografts whether the isovolumic relaxation time (IVRT), which provides the basis for most of diastolic LV filling, relates with gene expression of regulatory proteins of calcium homeostasis or cardiac matrix proteins. Gene expression was studied in 31 heart transplant recipients (25 male, 6 female) 13-83 months post-transplant with LVEF >50%, LV end-diastolic pressure <20 mmHg, normal LV mass index and without allograft rejection or significant cardiac pathology. IVRT related with the other diastolic parameters e-wave velocity (r = -0.46; p = 0.01), e/a-wave ratio (r = -0.5; p < 0.01) but not with heart frequency (r = -0.16; p = 0.4). No relation of IVRT was observed for immunosuppression, mean rejection grade or other medication. IVRT was not related with gene expression of desmin, collagen I, phospholamban, the Na+-Ca2+ exchanger, the ryanodine receptor or interstitial fibrosis but correlated inversely with SERCA2a (r = -0.48; p = 0.02). Prolonged IVRT is associated with decreased SERCA2a expression in cardiac allografts without significant other pathology. Similar observations in non-transplanted patients with diastolic failure suggest that decreased SERCA2a expression is an important common pathomechanism.

Reduced beta-cell mass and altered glucose sensing impair insulin-secretory function in betaIRKO mice

Pancreatic beta-cell-restricted knockout of the insulin receptor results in hyperglycemia due to impaired insulin secretion, suggesting that this cell is an important target of insulin action. The present studies were undertaken in beta-cell insulin receptor knockout (betaIRKO) mice to define the mechanisms underlying the defect in insulin secretion. On the basis of responses to intraperitoneal glucose, approximately 7-mo-old betaIRKO mice were either diabetic (25%) or normally glucose tolerant (75%). Total insulin content was profoundly reduced in pancreata of mutant mice compared with controls. Both groups also exhibited reduced beta-cell mass and islet number. However, insulin mRNA and protein were similar in islets of diabetic and normoglycemic betaIRKO mice compared with controls. Insulin secretion in response to insulin secretagogues from the isolated perfused pancreas was markedly reduced in the diabetic betaIRKOs and to a lesser degree in the nondiabetic betaIRKO group. Pancreatic islets of nondiabetic betaIRKO animals also exhibited defects in glyceraldehyde- and KCl-stimulated insulin release that were milder than in the diabetic animals. Gene expression analysis of islets revealed a modest reduction of GLUT2 and glucokinase gene expression in both the nondiabetic and diabetic mutants. Taken together, these data indicate that loss of functional receptors for insulin in beta-cells leads primarily to profound defects in postnatal beta-cell growth. In addition, altered glucose sensing may also contribute to defective insulin secretion in mutant animals that develop diabetes.

Brain electric correlates of strong belief in paranormal phenomena: intracerebral EEG source and regional Omega complexity analyses

The neurocognitive processes underlying the formation and maintenance of paranormal beliefs are important for understanding schizotypal ideation. Behavioral studies indicated that both schizotypal and paranormal ideation are based on an overreliance on the right hemisphere, whose coarse rather than focussed semantic processing may favor the emergence of 'loose' and 'uncommon' associations. To elucidate the electrophysiological basis of these behavioral observations, 35-channel resting EEG was recorded in pre-screened female strong believers and disbelievers during resting baseline. EEG data were subjected to FFT-Dipole-Approximation analysis, a reference-free frequency-domain dipole source modeling, and Regional (hemispheric) Omega Complexity analysis, a linear approach estimating the complexity of the trajectories of momentary EEG map series in state space. Compared to disbelievers, believers showed: more right-located sources of the beta2 band (18.5-21 Hz, excitatory activity); reduced interhemispheric differences in Omega complexity values; higher scores on the Magical Ideation scale; more general negative affect; and more hypnagogic-like reveries after a 4-min eyes-closed resting period. Thus, subjects differing in their declared paranormal belief displayed different active, cerebral neural populations during resting, task-free conditions. As hypothesized, believers showed relatively higher right hemispheric activation and reduced hemispheric asymmetry of functional complexity. These markers may constitute the neurophysiological basis for paranormal and schizotypal ideation.

A loss-of-function variant of PTPN22 is associated with reduced risk of systemic lupus erythematosus.

A gain-of-function R620W polymorphism in the PTPN22 gene, encoding the lymphoid tyrosine phosphatase LYP, has recently emerged as an important risk factor for human autoimmunity. Here we report that another missense substitution (R263Q) within the catalytic domain of LYP leads to reduced phosphatase activity. High-resolution structural analysis revealed the molecular basis for this loss of function. Furthermore, the Q263 variant conferred protection against human systemic lupus erythematosus, reinforcing the proposal that inhibition of LYP activity could be beneficial in human autoimmunity.

Reduced order models for industrial thermo-fluid problems

A new method is presented to generate reduced order models (ROMs) in Fluid Dynamics problems of industrial interest. The method is based on the expansion of the flow variables in a Proper Orthogonal Decomposition (POD) basis, calculated from a limited number of snapshots, which are obtained via Computational Fluid Dynamics (CFD). Then, the POD-mode amplitudes are calculated as minimizers of a properly defined overall residual of the equations and boundary conditions. The method includes various ingredients that are new in this field. The residual can be calculated using only a limited number of points in the flow field, which can be scattered either all over the whole computational domain or over a smaller projection window. The resulting ROM is both computationally efficient(reconstructed flow fields require, in cases that do not present shock waves, less than 1 % of the time needed to compute a full CFD solution) and flexible(the projection window can avoid regions of large localized CFD errors).Also, for problems related with aerodynamics, POD modes are obtained from a set of snapshots calculated by a CFD method based on the compressible Navier Stokes equations and a turbulence model (which further more includes some unphysical stabilizing terms that are included for purely numerical reasons), but projection onto the POD manifold is made using the inviscid Euler equations, which makes the method independent of the CFD scheme. In addition, shock waves are treated specifically in the POD description, to avoid the need of using a too large number of snapshots. Various definitions of the residual are also discussed, along with the number and distribution of snapshots, the number of retained modes, and the effect of CFD errors. The method is checked and discussed on several test problems that describe (i) heat transfer in the recirculation region downstream of a backwards facing step, (ii) the flow past a two-dimensional airfoil in both the subsonic and transonic regimes, and (iii) the flow past a three-dimensional horizontal tail plane. The method is both efficient and numerically robust in the sense that the computational effort is quite small compared to CFD and results are both reasonably accurate and largely insensitive to the definition of the residual, to CFD errors, and to the CFD method itself, which may contain artificial stabilizing terms. Thus, the method is amenable for practical engineering applications. Resumen Se presenta un nuevo método para generar modelos de orden reducido (ROMs) aplicado a problemas fluidodinámicos de interés industrial. El nuevo método se basa en la expansión de las variables fluidas en una base POD, calculada a partir de un cierto número de snapshots, los cuales se han obtenido gracias a simulaciones numéricas (CFD). A continuación, las amplitudes de los modos POD se calculan minimizando un residual global adecuadamente definido que combina las ecuaciones y las condiciones de contorno. El método incluye varios ingredientes que son nuevos en este campo de estudio. El residual puede calcularse utilizando únicamente un número limitado de puntos del campo fluido. Estos puntos puede encontrarse dispersos a lo largo del dominio computacional completo o sobre una ventana de proyección. El modelo ROM obtenido es tanto computacionalmente eficiente (en aquellos casos que no presentan ondas de choque reconstruir los campos fluidos requiere menos del 1% del tiempo necesario para calcular una solución CFD) como flexible (la ventana de proyección puede escogerse de forma que evite contener regiones con errores en la solución CFD localizados y grandes). Además, en problemas aerodinámicos, los modos POD se obtienen de un conjunto de snapshots calculados utilizando un código CFD basado en la versión compresible de las ecuaciones de Navier Stokes y un modelo de turbulencia (el cual puede incluir algunos términos estabilizadores sin sentido físico que se añaden por razones puramente numéricas), aunque la proyección en la variedad POD se hace utilizando las ecuaciones de Euler, lo que hace al método independiente del esquema utilizado en el código CFD. Además, las ondas de choque se tratan específicamente en la descripción POD para evitar la necesidad de utilizar un número demasiado grande de snapshots. Varias definiciones del residual se discuten, así como el número y distribución de los snapshots,el número de modos retenidos y el efecto de los errores debidos al CFD. El método se comprueba y discute para varios problemas de evaluación que describen (i) la transferencia de calor en la región de recirculación aguas abajo de un escalón, (ii) el flujo alrededor de un perfil bidimensional en regímenes subsónico y transónico y (iii) el flujo alrededor de un estabilizador horizontal tridimensional. El método es tanto eficiente como numéricamente robusto en el sentido de que el esfuerzo computacional es muy pequeño comparado con el requerido por el CFD y los resultados son razonablemente precisos y muy insensibles a la definición del residual, los errores debidos al CFD y al método CFD en sí mismo, el cual puede contener términos estabilizadores artificiales. Por lo tanto, el método puede utilizarse en aplicaciones prácticas de ingeniería.