Aplicación de Métodos Meshless al Análisis de Problemas de Autovalores

La presente Tesis Doctoral aborda la aplicación de métodos meshless, o métodos sin malla, a problemas de autovalores, fundamentalmente vibraciones libres y pandeo. En particular, el estudio se centra en aspectos tales como los procedimientos para la resolución numérica del problema de autovalores con estos métodos, el coste computacional y la viabilidad de la utilización de matrices de masa o matrices de rigidez geométrica no consistentes. Además, se acomete en detalle el análisis del error, con el objetivo de determinar sus principales fuentes y obtener claves que permitan la aceleración de la convergencia. Aunque en la actualidad existe una amplia variedad de métodos meshless en apariencia independientes entre sí, se han analizado las diferentes relaciones entre ellos, deduciéndose que el método Element-Free Galerkin Method [Método Galerkin Sin Elementos] (EFGM) es representativo de un amplio grupo de los mismos. Por ello se ha empleado como referencia en este análisis. Muchas de las fuentes de error de un método sin malla provienen de su algoritmo de interpolación o aproximación. En el caso del EFGM ese algoritmo es conocido como Moving Least Squares [Mínimos Cuadrados Móviles] (MLS), caso particular del Generalized Moving Least Squares [Mínimos Cuadrados Móviles Generalizados] (GMLS). La formulación de estos algoritmos indica que la precisión de los mismos se basa en los siguientes factores: orden de la base polinómica p(x), características de la función de peso w(x) y forma y tamaño del soporte de definición de esa función. Se ha analizado la contribución individual de cada factor mediante su reducción a un único parámetro cuantificable, así como las interacciones entre ellos tanto en distribuciones regulares de nodos como en irregulares. El estudio se extiende a una serie de problemas estructurales uni y bidimensionales de referencia, y tiene en cuenta el error no sólo en el cálculo de autovalores (frecuencias propias o carga de pandeo, según el caso), sino también en términos de autovectores. This Doctoral Thesis deals with the application of meshless methods to eigenvalue problems, particularly free vibrations and buckling. The analysis is focused on aspects such as the numerical solving of the problem, computational cost and the feasibility of the use of non-consistent mass or geometric stiffness matrices. Furthermore, the analysis of the error is also considered, with the aim of identifying its main sources and obtaining the key factors that enable a faster convergence of a given problem. Although currently a wide variety of apparently independent meshless methods can be found in the literature, the relationships among them have been analyzed. The outcome of this assessment is that all those methods can be grouped in only a limited amount of categories, and that the Element-Free Galerkin Method (EFGM) is representative of the most important one. Therefore, the EFGM has been selected as a reference for the numerical analyses. Many of the error sources of a meshless method are contributed by its interpolation/approximation algorithm. In the EFGM, such algorithm is known as Moving Least Squares (MLS), a particular case of the Generalized Moving Least Squares (GMLS). The accuracy of the MLS is based on the following factors: order of the polynomial basis p(x), features of the weight function w(x), and shape and size of the support domain of this weight function. The individual contribution of each of these factors, along with the interactions among them, has been studied in both regular and irregular arrangement of nodes, by means of a reduction of each contribution to a one single quantifiable parameter. This assessment is applied to a range of both one- and two-dimensional benchmarking cases, and includes not only the error in terms of eigenvalues (natural frequencies or buckling load), but also of eigenvectors

Estabilidad de un buque ultra heavy lift carrier

Se plantea la posible demanda en un futuro del transporte de grandes plataformas petrolíferas semisumergibles de más de 70.000 t de peso, para perforaciones a más de 10.000 pies de profundidad. Estudia la estabilidad de buques Heavy Lift Carrier con mangas atípicas, capaces de transportar estas cargas, y en algunos casos sobresaliendo por sus amuras. Para esto se: 1. Estudia y genera posibles carenas, su compartimentación y lastre para la inmersión o emersión de la cubierta de intemperie, a más de 10 m de profundidad para tomar o dejar la carga, optimizando el proceso. 2. Analiza la estabilidad del buque tanto en inmersión/emersión y navegación, con máximas cargas y con altos centros de gravedad, y establece ábacos de estabilidad límite en función de los parámetros del buque. 3. Plantea la corrección de estabilidad excesiva del buque en condiciones de navegación para evitar las excesivas aceleraciones. Los resultados obtenidos aportan ábacos que permiten, en función de los parámetros carga a transportar (Zg max) - Peso Carga), elegir el buque más adecuado, capaz de efectuar la inmersión, emersión, y navegación, y plantea acciones futuras de investigación. ABSTRACT This work raises the potential demand in the future, to transport large semisubmersible oil rigs over 70,000 tonnes of weight for drilling to 10,000 feet deep. Study vessel stability Heavy Lift Carrier with atypical breadths capable of carrying these burdens, and in some cases standing out for their bows. 1. Examines possible hulls, their partitioning and ballast for immersion or emersion of the weather deck, more than 10 m deep to take –loading (lifting) - or leave (off- loading). 2. Analyzes the stability of the vessel both immersion / emersion and navigation, with maximum loads with high centers of gravity and stability limit states abacus according to the parameters of the ship. 3. Correction raises the stability of the ship over navigation to prevent excessive accelerations. The results allow, in terms of cargo transport parameters (Zg max) - Weight Load), choosing the most suitable vessel capable of carrying out the immersion, emersion, and navigation, and suggests future research activities.

Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

On ergodic least-squares estimators of the generalized diffusion coefficient for fractional Brownian motion

We analyse a class of estimators of the generalized diffusion coefficient for fractional Brownian motion Bt of known Hurst index H, based on weighted functionals of the single time square displacement. We show that for a certain choice of the weight function these functionals possess an ergodic property and thus provide the true, ensemble-averaged, generalized diffusion coefficient to any necessary precision from a single trajectory data, but at expense of a progressively higher experimental resolution. Convergence is fastest around H ? 0.30, a value in the subdiffusive regime.

The design of planar gradient coils. Part ll: A weighted superposition method

In this work a superposition technique for designing gradient coils for the purpose of magnetic resonance imaging is outlined, which uses an optimized weight function superimposed upon an initial winding similar to that obtained from the target field method to generate the final wire winding. This work builds on the preliminary work performed in Part I on designing planar insertable gradient coils for high resolution imaging. The proposed superposition method for designing gradient coils results in coil patterns with relatively low inductances and the gradient coils can be used as inserts into existing magnetic resonance imaging hardware. The new scheme has the capacity to obtain images faster with more detail due to the deliver of greater magnetic held gradients. The proposed method for designing gradient coils is compared with a variant of the state-of-the-art target field method for planar gradient coils designs, and it is shown that the weighted superposition approach outperforms the well-known the classical method.

Sigmoidal cosine series on the interval

We construct a set of functions, say, psi([r])(n) composed of a cosine function and a sigmoidal transformation gamma(r) of order r > 0. The present functions are orthonormal with respect to a proper weight function on the interval [-1, 1]. It is proven that if a function f is continuous and piecewise smooth on [-1, 1] then its series expansion based on psi([r])(n) converges uniformly to f so long as the order of the sigmoidal transformation employed is 0 < r

General bounds on Bayes errors for regression with Gaussian processes

Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

Splines in Numerical Integration

AMS Subj. Classification: 65D07, 65D30.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

Vehicle Routing Problems that Minimize the Completion Time: Heuristics, Worst-Case Analyses, and Computational Results

In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles to deliver the demands of all customers such that the total distance traveled by the fleet is minimized. In this dissertation, we study variants of the VRP that minimize the completion time, i.e., we minimize the distance of the longest route. We call it the min-max objective function. In applications such as disaster relief efforts and military operations, the objective is often to finish the delivery or the task as soon as possible, not to plan routes with the minimum total distance. Even in commercial package delivery nowadays, companies are investing in new technologies to speed up delivery instead of focusing merely on the min-sum objective. In this dissertation, we compare the min-max and the standard (min-sum) objective functions in a worst-case analysis to show that the optimal solution with respect to one objective function can be very poor with respect to the other. The results motivate the design of algorithms specifically for the min-max objective. We study variants of min-max VRPs including one problem from the literature (the min-max Multi-Depot VRP) and two new problems (the min-max Split Delivery Multi-Depot VRP with Minimum Service Requirement and the min-max Close-Enough VRP). We develop heuristics to solve these three problems. We compare the results produced by our heuristics to the best-known solutions in the literature and find that our algorithms are effective. In the case where benchmark instances are not available, we generate instances whose near-optimal solutions can be estimated based on geometry. We formulate the Vehicle Routing Problem with Drones and carry out a theoretical analysis to show the maximum benefit from using drones in addition to trucks to reduce delivery time. The speed-up ratio depends on the number of drones loaded onto one truck and the speed of the drone relative to the speed of the truck.

The Influence Of Body Weight On Sexual Function And Quality Of Life In Women With Polycystic Ovary Syndrome.

To assess sexual function (SF) and quality of life (QOL) in women with polycystic ovary syndrome (PCOS). A cross-sectional study was conducted to assess 56 women with PCOS and 102 control women with regular menstrual cycles. To assess SF and QOL in Brazilian women with PCOS with Female Sexual Function Index (FSFI) and the WHOQOL-bref questionnaires. Women with PCOS had a worse evaluation to arousal, lubrication, satisfaction, pain and total FSFI, and there was no difference in sexual desire and orgasm. Besides, they had a worse evaluation concerning health status than controls. The body mass index was inversely correlated to the QOL, especially to the physical, psychological, environment aspects and self-assessment of QOL, but it did not show correlation to the SF. Women with PCOS had a worse sexual function and self-assessment of health condition in comparison to controls. The body weight as isolated symptom was correlated to the worsening in quality of life, but not with the worsening of sexual function.

Improvement in coronary circulatory function in morbidly obese individuals after gastric bypass-induced weight loss: relation to alterations in endocannabinoids and adipocytokines.

AIMS: To investigate the effect of surgical gastric bypass-induced weight loss and related alterations in endocannabinoids (ECs) and adipocytokine plasma levels on coronary circulatory dysfunction in morbidly obese (MOB) individuals. METHODS AND RESULTS: Myocardial blood flow (MBF) responses to cold pressor test (CPT) from rest (ΔMBF) and during pharmacologically induced hyperaemia were measured with &supl;³N-ammonia PET/CT in 18 MOB individuals with a body mass index (BMI) > 40 kg/m² at baseline and after a median follow-up period of 22 months. Gastric bypass intervention decreased BMI from a median of 44.8 (inter-quartile range: 43.3, 48.2) to 30.8 (27.3, 34.7) kg/m² (P < 0.0001). This decrease in BMI was accompanied by a marked improvement in endothelium-related ΔMBF to CPT and hyperaemic MBFs, respectively [0.34 (0.18, 0.41) from 0.03 (-0.08, 0.15) mL/g/min, P = 0.002; and 2.51 (2.17, 2.64) from 1.53 (1.39, 2.18) mL/g/min, P < 0.001]. There was an inverse correlation between decreases in plasma concentrations of the EC anandamide and improvement in ΔMBF to CPT (r = -0.59, P = 0.009), while increases in adiponectin plasma levels correlated positively with hyperaemic MBFs (r = 0.60, P = 0.050). Conversely, decreases in leptin plasma concentrations were not observed to correlate with the improvement in coronary circulatory function (r = 0.22, P = 0.400, and r = -0.31, P = 0.250). CONCLUSIONS: Gastric bypass-related reduction of BMI in MOB individuals beneficially affects coronary circulatory dysfunction. The dysbalance between ECs and adipocytokines appears to be an important determinant of coronary circulatory function in obesity.

Low-molecular-weight or unfractionated heparin in venous thromboembolism: the influence of renal function.

BACKGROUND: In patients with acute venous thromboembolism and renal insufficiency, initial therapy with unfractionated heparin may have some advantages over low-molecular-weight heparin. METHODS: We used the Registro Informatizado de la Enfermedad TromboEmbólica (RIETE) Registry data to evaluate the 15-day outcome in 38,531 recruited patients. We used propensity score matching to compare patients treated with unfractionated heparin with those treated with low-molecular-weight heparin in 3 groups stratified by creatinine clearance levels at baseline: >60 mL/min, 30 to 60 mL/min, or <30 mL/min. RESULTS: Patients initially receiving unfractionated heparin therapy (n = 2167) more likely had underlying diseases than those receiving low-molecular-weight heparin (n = 34,665). Propensity score-matched groups of patients with creatinine clearance levels >60 mL/min (n = 1598 matched pairs), 30 to 60 mL/min (n = 277 matched pairs), and <30 mL/min (n = 210 matched pairs) showed an increased 15-day mortality for unfractionated heparin compared with low-molecular-weight heparin (4.5% vs 2.4% [P = .001], 5.4% vs 5.8% [P = not significant], and 15% vs 8.1% [P = .02], respectively), an increased rate of fatal pulmonary embolism (2.8% vs 1.2% [P = .001], 3.2% vs 2.5% [P = not significant], and 5.7% vs 2.4% [P = .02], respectively), and a similar rate of fatal bleeding (0.3% vs 0.3%, 0.7% vs 0.7%, and 0.5% vs 0.0%, respectively). Multivariate analysis confirmed that patients treated with unfractionated heparin were at increased risk for all-cause death (odds ratio, 1.8; 95% confidence interval, 1.3-2.4) and fatal pulmonary embolism (odds ratio, 2.3; 95% confidence interval, 1.5-3.6). CONCLUSIONS: In comparison with low-molecular-weight heparin, initial therapy with unfractionated heparin was associated with a higher mortality and higher rate of fatal pulmonary embolism in patients with creatinine clearance levels >60 mL/min or <30 mL/min, but not in those with levels between 30 and 60 mL/min.

Effects of Obesity and Weight Loss Following Bariatric Surgery on Brain Function, Structural Integrity and Metabolism

Obesity is one of the key challenges to health care system worldwide and its prevalence is estimated to rise to pandemic proportions. Numerous adverse health effects follow with increasing body weight, including increased risk of hypertension, diabetes, hypercholesterolemia, musculoskeletal pain and cancer. Current evidence suggests that obesity is associated with altered cerebral reward circuit functioning and decreased inhibitory control over appetitive food cues. Furthermore, obesity causes adverse shifts in metabolism and loss of structural integrity within the brain. Prior cross-sectional studies do not allow delineating which of these cerebral changes are recoverable after weight loss. We compared morbidly obese subjects with healthy controls to unravel brain changes associated with obesity. Bariatric surgery was used as an intervention to study which cerebral changes are recoverable after weight loss. In Study I we employed functional magnetic resonance imaging (fMRI) to detect the brain basis of volitional appetite control and its alterations in obesity. In Studies II-III we used diffusion tensor imaging (DTI) and voxel-based morphometry (VBM) to quantify the effects of obesity and the effects of weight loss on structural integrity of the brain. In study IV we used positron emission tomography (PET) with [18F]-FDG in fasting state and during euglycemic hyperinsulinemia to quantify effects of obesity and weight loss on brain glucose uptake. The fMRI experiment revealed that a fronto-parietal network is involved in volitional appetite control. Obese subjects had lower medial frontal and dorsal striatal brain activity during cognitive appetite control and increased functional connectivity within the appetite control circuit. Obese subjects had initially lower grey matter and white matter densities than healthy controls in VBM analysis and loss of integrity in white matter tracts as measured by DTI. They also had initially elevated glucose metabolism under insulin stimulation but not in fasting state. After the weight loss following bariatric surgery, obese individuals’ brain volumes recovered and the insulin-induced increase in glucose metabolism was attenuated. In conclusion, obesity is associated with altered brain function, coupled with loss of structural integrity and elevated glucose metabolism, which are likely signs of adverse health effects to the brain. These changes are reversed by weight loss after bariatric surgery, implicating that weight loss has a causal role on these adverse cerebral changes. Altogether these findings suggest that weight loss also promotes brain health.Key words: brain, obesity, bariatric surgery, appetite control, structural magnetic resonance