While most statistical applications involve real numbers, some demand complex numbers. Statistical shape analysis is one such area. The complex Bingham distribution is utilized in the shape analysis of landmark data in two dimensions. Previous analysis of data arising from this distribution involved classical statistical techniques. In this report, a full Bayesian inference was carried out on the posterior distribution of the parameter matrix when data arise from a complex Bingham distribution. We utilized a Markov chain Monte Carlo algorithm to sample the posterior distribution of the parameters. A Metropolis-Hastings algorithm sampled the posterior conditional distribution of the eigenvalues while a successive conditional Monte Carlo sampler was used to sample the eigenvectors. The method was successfully verifi ed on simulated data, using both at and informative priors. / text

Thesis (M.S.)--University of Massachusetts Amherst, 2008. / Includes bibliographical references (p. 93-97).

Non-Newtonian fluids are of great scientific interest due to their range of physical properties, which arise from the characteristic shear stress-shear rate relation for each fluid. The applications of non-Newtonian fluids are widespread and occur in many industrial (e.g. lubricants, suspensions, paints, etc.) and environmental (e.g. mud, ice, blood, etc.) problems, often involving multiple fluids. In this study, the novel technique of Incompressible Smoothed Particle Hydrodynamics (ISPH) with shifting (Lind et al., J. Comput. Phys., 231(4):1499-1523, 2012), is extended beyond the state-of-the-art to model non-Newtonian and multi-phase flows. The method is used to investigate important problems of both environmental and industrial interest. The proposed methodology is based on a recent ISPH algorithm with shifting with the introduction of an appropriate stress formulation. The new method is validated both for Newtonian and non-Newtonian fluids, in closed-channel and free-surface flows. Applications in complex moulding flows are conducted and compared to previously published results. Validation includes comparison with other computational techniques such as weakly compressible SPH (WCSPH) and the Control Volume Finite Element method. Importantly, the proposed method offers improved pressure results over state-of-the-art WCSPH methods, while retaining accurate prediction of the flow patterns. Having validated the single-phase non-Newtonian ISPH algorithm, this develops a new extension to multi-phase flows. The method is applied to both Newtonian/Newtonian and Newtonian/non-Newtonian problems. Validations against a novel semi-analytical solution of a two-phase Poiseuille Newtonian/non-Newtonian flow, the Rayleigh-Taylor instability, and a submarine landslide are considered. It is shown that the proposed method can offer improvements in the description of interfaces and in the prediction of the flow fields of demanding multi-phase flows with both environmental and industrial application. Finally, the Lituya Bay landslide and tsunami is examined. The problem is approached initially on the real length-scales and compared with state-of-the-art computational techniques. Moreover, a detailed investigation is carried out aiming at the full reproduction of the experimental findings. With the introduction of a k-ε turbulence model, a simple saturation model and correct experimental initial conditions, significant improvements over the state-of-the-art are shown, managing an accurate representation of both the landslide as well as the wave run-up. The computational method proposed in this thesis is an entirely novel ISPH algorithm capable of modelling highly deforming non-Newtonian and multi-phase flows, and in many cases shows improved accuracy and experimental agreement compared with the current state-of-the-art WCSPH and ISPH methodologies. The variety of problems examined in this work show that the proposed method is robust and can be applied to a wide range of applications with potentially high societal and economical impact.

Nesta tese apresenta-se uma nova formulação mista estabilizada regularizada de elementos finitos nas variáveis primais com interpolação contínua para a velocidade e descontínua para a pressão, para problemas de fluidos viscoplásticos.Esta formulação tem base nos métodos de lagrangeano aumentado-regularização e de estabilização por mínimos quadrados.Discutem-se as dificuldades de resolução dos problemas viscoplásticos especialmente aqueles modelados pela relação de Bingham que prevê uma descontinuidade na forma de restrição de desigualdade. São apresentadas criticamente a teoria de lagrangeano aumentado, os modelos regularizados e o método estabilizado via mínimos quadrados. São feitas análises matemáticas para a nova formulação em termos de estabilidade, existência e unicidade de solução. Ordens de convergência ótimas são obtidas matematicamente, superando os métodos clássicos que também apresentam limitação para o valor de tensão limite. Resultados numéricos são apresentados confirmando a teoria aqui desenvolvida e mostrando a robustez do novo método para resolver problemas onde a tensão limite é muito elevada.

Nesta tese apresenta-se uma nova formulação mista estabilizada regularizada de elementos finitos nas variáveis primais com interpolação contínua para a velocidade e descontínua para a pressão, para problemas de fluidos viscoplásticos. Esta formulação tem base nos métodos de lagrangeano aumentado-regularização e de estabilização por mínimos quadrados. Discutem-se as dificuldades de resolução dos problemas viscoplásticos especialmente aqueles modelados pela relação de Bingham que prevê uma descontinuidade na forma de restrição de desigualdade. São apresentadas criticamente a teoria de lagrangeano aumentado, os modelos regularizados e o método estabilizado via mínimos quadrados. São feitas análises matemáticas para a nova formulação em termos de estabilidade, existência e unicidade de solução. Ordens de convergência ótimas são obtidas matematicamente, superando os métodos clássicos que também apresentam limitação para o valor de tensão limite. Resultados numéricos são apresentados confirmando a teoria aqui desenvolvida e mostrando a robustez do novo método para resolver problemas onde a tensão limite é muito elevada.

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier–Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

Dans cette thèse, nous nous intéressons au problème de tester en grande dimension l'uniformité sur la sphère-unité $S^{p_n-1}$ (la dimension des observations, $p_n$, dépend de leur nombre, $n$, et être en grande dimension signifie que $p_n$ tend vers l'infini en même temps que $n$). Nous nous restreignons dans un premier temps à des contre-hypothèses ``monotones'' de densité croissante le long d'une direction ${\pmb \theta}_n\in S^{p_n-1}$ et dépendant d'un paramètre de concentration $\kappa_n>0$. Nous commençons par identifier le taux $\kappa_n$ auquel ces contre-hypothèses sont contiguës à l'uniformité ;nous montrons ensuite grâce à des résultats de normalité locale asymptotique, que le test d'uniformité le plus classique, le test de Rayleigh, n'est pas optimal quand ${\pmb \theta}_n$ est connu mais qu'il le devient à $p$ fixé et dans le cas FvML en grande dimension quand ${\pmb \theta}_n$ est inconnu.Dans un second temps, nous considérons des contre-hypothèses ``axiales'', attribuant la même probabilité à des points diamétralement opposés. Elles dépendent aussi d'un paramètre de position ${\pmb \theta}_n\in S^{p_n-1}$ et d'un paramètre de concentration $\kappa_n\in\R$. Le taux de contiguïté s'avère ici plus élevé et suggère un problème plus difficile que dans le cas monotone. En effet, le test de Bingham, le test classique dans le cas axial, n'est pas optimal à ${\pmb \theta}_n$ inconnu et $p$ fixé, et ne détecte pas les contre-hypothèses contiguës en grande dimension. C'est pourquoi nous nous tournons vers des tests basés sur les plus grande et plus petite valeurs propres de la matrice de variance-covariance et nous déterminons leurs distributions asymptotiques sous les contre-hypothèses contiguës à $p$ fixé.Enfin, à l'aide d'un théorème central limite pour martingales, nous montrons que sous certaines conditions et après standardisation, les statistiques de Rayleigh et de Bingham sont asymptotiquement normales sous l'hypothèse d'invariance par rotation des observations. Ce résultat permet non seulement d'identifier le taux auquel le test de Bingham détecte des contre-hypothèses axiales mais aussi celui auquel il détecte des contre-hypothèses monotones. / In this thesis we are interested in testing uniformity in high dimensions on the unit sphere $S^{p_n-1}$ (the dimension of the observations, $p_n$, depends on their number, and high-dimensional data are such that $p_n$ diverges to infinity with $n$).We consider first ``monotone'' alternatives whose density increases along an axis ${\pmb \theta}_n\in S^{p_n-1}$ and depends on a concentration parameter $\kappa_n>0$. We start by identifying the rate at which these alternatives are contiguous to uniformity; then we show thanks to local asymptotic normality results that the most classical test of uniformity, the Rayleigh test, is not optimal when ${\pmb \theta}_n$ is specified but becomes optimal when $p$ is fixed and in the high-dimensional FvML case when ${\pmb \theta}_n$ is unspecified.We consider next ``axial'' alternatives, assigning the same probability to antipodal points. They also depend on a location parameter ${\pmb \theta}_n\in S^{p_n-1}$ and a concentration parameter $\kappa_n\in\R$. The contiguity rate proves to be higher in that case and implies that the problem is more difficult than in the monotone case. Indeed, the Bingham test, the classical test when dealing with axial data, is not optimal when $p$ is fixed and ${\pmb \theta}_n$ is not specified, and is blind to the contiguous alternatives in high dimensions. This is why we turn to tests based on the extreme eigenvalues of the covariance matrix and establish their fixed-$p$ asymptotic distributions under contiguous alternatives.Finally, thanks to a martingale central limit theorem, we show that, under some assumptions and after standardisation, the Rayleigh and Bingham test statistics are asymptotically normal under general rotationally symmetric distributions. It enables us to identify the rate at which the Bingham test detects axial alternatives and also monotone alternatives. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Function optimization---finding the minimum or maximum of a given function---is an extremely challenging problem with applications in physics, economics, machine learning, engineering, and many other fields. While optimization is an active area of research, only a portion of this work acknowledges parallel computation, which is now widely available. Today, anyone with a modest budget can buy a cluster with hundreds of cores, pay for access to a supercomputer with thousands of processors, or at least purchase a laptop with 8 cores. Thus, an algorithm that works well in serial but cannot be parallelized is needlessly inefficient in real-life computationalenvironments.We address these issues in three connected threads of development: a high-level programming framework that makes it possible to create flexible and efficient implementations of optimization algorithms; improvements to an existing algorithm, Particle Swarm Optimization, to make it take better advantage of parallel resources; and a statistical model designed to efficiently use available information in parallel optimization by inferring search directions. Each of these is an essential step toward effective parallel optimization. First, without a suitable high-level programming model, expediency leads to purely serial development with parallel issues only an afterthought. Second, PSO has proven effective for optimization and is an excellent candidate to consider for efficient parallel implementations. Third, a model for inference of search directions is useful for understanding communication in the context of parallel optimization and provides a flexible base for continuing optimization research.

The Bingham porphyry Cu-Au-Mo deposit, Utah, may only be world-class because of substantial contributions of sulfur and metals from mafic alkaline magma to an otherwise unremarkable calc-alkaline system. Volcanic mafic alkaline rocks in the district are enriched in Cr, Ni, and Ba as well as ore-related constituents of Cu, Au, platinum group elements (PGE) and S. The bulk of the volcanic section that is comagmatic with ore-related porphyries is dacitic to trachytic in composition, but has inherited the geochemical signature of high Cr, Ni, and Ba from magma mixing with the mafic alkaline rocks. The volcanic section that most closely correlates in time with ore-related porphyries is very heterogeneous containing clasts of scoriaceous latite, latitic minette and flows of melanephelinite, shoshonite and olivine latite in addition to the volumetrically dominant dacite/trachyte. Bingham ore-related porphyries show ample evidence of prior mixing with mafic alkaline magmas. Intrusive porphyries that have not been previously studied well have several chemical and mineralogical indications of magma mixing. These "mixed" lithologies include the hybrid quartz monzonite porphyry, biotite porphyry, and minette dikes. Even some of the more silicic latite and monzonite porphyries retain high Cr and Ba contents indicative of mixing and contain trace amounts of sapphire ( Magma mixing calculations suggest about 10% of the monzonitic/latitic ore-related magma may have been derived from mafic alkaline magma similar to the melanephelinite. If the original S content of the mafic magma was about 2000-4000 ppm, comparable to similar magmas, then the mafic magma may have been responsible for contributing more than half of the S and a significant portion of the Cu, Au, and PGE in the Bingham deposit.

Magnetorheological (MR) fluids offer solutions to many engineering challenges. The success of MR fluid is apparent in many disciplines, ranging from the automotive and civil engineering communities to the biomedical engineering community. This well documented success of MR fluids continues to motivate current and future applications of MR fluid. One such application that has been considered recently is MR fluid devices for use in impact and other high velocity applications. In such applications, the fluid environment within the device may be well beyond the scope of our understanding for these fluids. To date, little has been done to explore the suitability of MR fluids in such high velocity and high shear applications. While future applications may expose the fluid to adverse flow conditions, we must also consider current and existing applications which expose the fluid to extreme flow environments. Consider, for example, an MR damper intended for automotive primary suspensions, in which shear rates may exceed 10^5 s^-1. Flow conditions within these dampers far exceed existing fluid behavior characterization. The aim of the current study is to identify the behavior of the fluid under these extreme operating conditions. Specifically, this study intends to identify the behavior of MR fluid subject to high rates of shear and high flow velocities. A high shear rheometer is built which allows for the high velocity testing of MR fluids. The rheometer is capable of fluid velocities ranging from 1 m/s to 37 m/s, with corresponding shear rates ranging from 0.14x10^5 s^-1 to 2.5x10^5 s^-1. Fluid behavior is characterized in both the off-state and the on-state. The off-state testing was conducted in order to identify the high shear viscosity of the fluid. Because the high shear behavior of MR fluid is largely governed by the behavior of the carrier fluid, the carrier fluid behavior was also identified at high shear. Experiments were conducted using the high shear rheometer and the MR fluid was shown to exhibit nearly Newtonian post-yield behavior. A slight thickening was observed for growing shear rates. This slight thickening can be attributed to the behavior of the carrier fluid, which exhibited considerable thickening at high shear. The purpose of the on-state testing was to characterize the MR effect at high flow velocities. As such, the MR fluid was run through the rheometer at various flow velocities and a number of magnetic field strengths. The term "dwell time" is introduced and defined as the amount of time the fluid spends in the presence of a magnetic field. Two active valve lengths were considered, which when coupled to the fluid velocities, generated dwell times ranging from 12 ms to 0.18 ms. The yield stress was found from the experimental measurements and the results indicate that the magnitude of the yield stress is sensitive to fluid dwell time. As fluid dwell times decrease, the yield stress developed in the fluid decreases. The results from the on-state testing clearly demonstrate a need to consider fluid dwell times in high velocity applications. Should the dwell time fall below the response time of the fluid, the yield stress developed in the fluid may only achieve a fraction of the expected value. These results imply that high velocity applications may be subject to diminished controllability for falling dwell times. Results from this study may serve to aid in the design of MR fluid devices intended for high velocity applications. Furthermore, the identified behavior may lead to further developments in MR fluid technology. In particular, the identified behavior may be used to develop or identify an MR fluid well suited for high velocity and high shear applications. / Ph. D.