4 resultados para Interpolation and function approximation (numerical analysis)

em Digital Commons - Michigan Tech


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The continual eruptive activity, occurrence of an ancestral catastrophic collapse, and inherent geologic features of Pacaya volcano (Guatemala) demands an evaluation of potential collapse hazards. This thesis merges techniques in the field and laboratory for a better rock mass characterization of volcanic slopes and slope stability evaluation. New field geological, structural, rock mechanical and geotechnical data on Pacaya is reported and is integrated with laboratory tests to better define the physical-mechanical rock mass properties. Additionally, this data is used in numerical models for the quantitative evaluation of lateral instability of large sector collapses and shallow landslides. Regional tectonics and local structures indicate that the local stress regime is transtensional, with an ENE-WSW sigma 3 stress component. Aligned features trending NNW-SSE can be considered as an expression of this weakness zone that favors magma upwelling to the surface. Numerical modeling suggests that a large-scale collapse could be triggered by reasonable ranges of magma pressure (greater than or equal to 7.7 MPa if constant along a central dyke) and seismic acceleration (greater than or equal to 460 cm/s2), and that a layer of pyroclastic deposits beneath the edifice could have been a factor which controlled the ancestral collapse. Finally, the formation of shear cracks within zones of maximum shear strain could provide conduits for lateral flow, which would account for long lava flows erupted at lower elevations.

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Osteoarthritis (OA) is a debilitating disease that is becoming more prevalent in today’s society. OA affects approximately 28 million adults in the United States alone and when present in the knee joint, usually leads to a total knee replacement. Numerous studies have been conducted to determine possible methods to halt the initiation of OA, but the structural integrity of the menisci has been shown have a direct effect on the progression of OA. Menisci are two C-shaped structures that are attached to the tibial plateau and aid in facilitating proper load transmission within the knee. The meniscal cross-section is wedge-like to fit the contour of the femoral condyles and help attenuate stresses on the tibial plateau. While meniscal tears are common, only the outer 1/3 of the meniscus is vascularized and has the capacity to heal, hence tears of the inner 2/3rds are generally treated via meniscectomy, leading to OA. To help combat this OA epidemic, an effective biomimetric meniscal replacement is needed. Numerous mechanical and biochemical studies have been conducted on the human meniscus, but very little is known about the mechanical properties on the nano-scale and how meniscal constituents are distributed in the meniscal cross-section. The regional (anterior, central and posterior) nano-mechanical properties of the meniscal superficial layers (both tibial and femoral contacting) and meniscal deep zone were investigated via nanoindentation to examine the regional inhomogeneity of both the lateral and medial menisci. Additionally, these results were compared to quantitative histological values to better formulate a structure-function relationship on the nano-scale. These data will prove imperative for further advancements of a tissue engineered meniscal replacement.

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The developmental processes and functions of an organism are controlled by the genes and the proteins that are derived from these genes. The identification of key genes and the reconstruction of gene networks can provide a model to help us understand the regulatory mechanisms for the initiation and progression of biological processes or functional abnormalities (e.g. diseases) in living organisms. In this dissertation, I have developed statistical methods to identify the genes and transcription factors (TFs) involved in biological processes, constructed their regulatory networks, and also evaluated some existing association methods to find robust methods for coexpression analyses. Two kinds of data sets were used for this work: genotype data and gene expression microarray data. On the basis of these data sets, this dissertation has two major parts, together forming six chapters. The first part deals with developing association methods for rare variants using genotype data (chapter 4 and 5). The second part deals with developing and/or evaluating statistical methods to identify genes and TFs involved in biological processes, and construction of their regulatory networks using gene expression data (chapter 2, 3, and 6). For the first part, I have developed two methods to find the groupwise association of rare variants with given diseases or traits. The first method is based on kernel machine learning and can be applied to both quantitative as well as qualitative traits. Simulation results showed that the proposed method has improved power over the existing weighted sum method (WS) in most settings. The second method uses multiple phenotypes to select a few top significant genes. It then finds the association of each gene with each phenotype while controlling the population stratification by adjusting the data for ancestry using principal components. This method was applied to GAW 17 data and was able to find several disease risk genes. For the second part, I have worked on three problems. First problem involved evaluation of eight gene association methods. A very comprehensive comparison of these methods with further analysis clearly demonstrates the distinct and common performance of these eight gene association methods. For the second problem, an algorithm named the bottom-up graphical Gaussian model was developed to identify the TFs that regulate pathway genes and reconstruct their hierarchical regulatory networks. This algorithm has produced very significant results and it is the first report to produce such hierarchical networks for these pathways. The third problem dealt with developing another algorithm called the top-down graphical Gaussian model that identifies the network governed by a specific TF. The network produced by the algorithm is proven to be of very high accuracy.

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Power distribution systems are susceptible to extreme damage from natural hazards especially hurricanes. Hurricane winds can knock down distribution poles thereby causing damage to the system and power outages which can result in millions of dollars in lost revenue and restoration costs. Timber has been the dominant material used to support overhead lines in distribution systems. Recently however, utility companies have been searching for a cost-effective alternative to timber poles due to environmental concerns, durability, high cost of maintenance and need for improved aesthetics. Steel has emerged as a viable alternative to timber due to its advantages such as relatively lower maintenance cost, light weight, consistent performance, and invulnerability to wood-pecker attacks. Both timber and steel poles are prone to deterioration over time due to decay in the timber and corrosion of the steel. This research proposes a framework for conducting fragility analysis of timber and steel poles subjected to hurricane winds considering deterioration of the poles over time. Monte Carlo simulation was used to develop the fragility curves considering uncertainties in strength, geometry and wind loads. A framework for life-cycle cost analysis is also proposed to compare the steel and timber poles. The results show that steel poles can have superior reliability and lower life-cycle cost compared to timber poles, which makes them suitable substitutes.