We describe the theory and implementation of a multipole method for calculating the modes of microstructured optical fibers (MOFs). We develop tools for exploiting results obtained through the multipole method, including a discrete Bloch transform. Using the multipole method, we study in detail the physical nature of solid core MOF modes, and establish a distinction between localized defect modes and extended modes. Defect modes, including the fundamental mode, can undergo a localization transition we identify with the mode�s cutoff. We study numerically and theoretically the cutoff of the fundamental and the second mode extensively, and establish a cutoff diagram enabling us to predict with accuracy MOF properties, even for exotic MOF geometries. We study MOF dispersion and loss properties and develop unconventional MOF designs with low losses and ultra-flattened near-zero dispersion on a wide wavelength range. Using the cutoff-diagram we explain properties of these MOF designs.

>Magister Scientiae - MSc / Background and Aims Human Immunodeficiency Virus (HIV) type 1 group M subtype C (HIV-1C) accounts for nearly half of global HIV-1 infections, with South Africa (SA) being one of the countries with the highest infection burden. In recent years, SA has made great strides in tackling its HIV epidemic, resulting in the country being recognized globally as the one sub-Saharan country with the largest combination antiretroviral therapy (cART) programme. Regardless of the potency of cART, the efficacy of the treatment is limited and hampered by the emergence of drug resistance. The majority of research on HIV-1 infections, effect of antiretroviral (ARV) drugs and understanding resistance to ARV drugs has been extensively conducted, but mainly on HIV-1 subtype B (HIV-1B), with less information known about HIV-1C. HIV-1’s viral Integrase (IN) enzyme has become a viable target for highly specific cART, due to its importance in the infection and replication cycle of the virus. The lack of a complete HIV-1C IN protein structure has negatively impacted the progress on structural studies of nucleoprotein reaction intermediates. The mechanism of HIV-1 viral DNA’s integration has been studied extensively at biochemical and cellular levels, but not at a molecular level. This study aims to use in silico methods that involve molecular modeling and molecular dynamic (MD) simulations to prioritize mutations that could affect HIV-1C IN binding to DNA and the IN strand-transfer inhibitor (INSTI) dolutegravir (DTG). The purpose is to help tailor more effective personalized treatment options for patients living with HIV in SA. This study will in part use patient derived sequence data to identify mutations and model them into the protein structure to understand their impact on the HIV-1C IN protein structure folding and dynamics. Methods Our sample cohort consisted of 11 sample sequences derived from SA HIV-1 treatmentexperienced patients who were being treated with the INSTI raltegravir (RAL). The sequences were submitted to the Stanford HIV resistance database (HIVdb) to screen for any new/novel variants resulting from possible RAL failure. Some of these new variants were analyzed to analyse their effect, if any, on the binding of DTG to the HIV-1C IN protein. Additionally, an HIV-1C IN consensus sequence constructed from SA’s HIV-1 infected population was used to model a complete three-dimensional wild type (WT) HIV-1C IN homology model. All samples were sequenced by our collaborators at the Division of Medical Virology, Stellenbosch University together with the National Health Laboratory Services (NHLS), SA. The HIV-1CZA WT-IN protein enzyme was predicted using SWISS-MODEL, and the quality of the resulting model validated. Various analyses were conducted in order to study and assess the effect of the selected new variants on the protein structure and binding of DTG to the IN protein. The mutation Cutoff Scanning Matrix (mCSM) program was used to predict protein stability after mutation, while PyMol helped to study any changes in polar contact activity before and after mutation. PyMol was also used to generate four mutant HIV-1C IN complex structures and these structures together with the WT IN were subjected to production MD simulations for 150 nanoseconds (ns). Trajectory analyses of the MD simulations were also conducted and reported. Results A total of 21 new variants were detected in our sample cohort, from which only six were chosen for further analyses within the study. A homology model of HIV-1C IN was successfully constructed and validated. The structural quality assessment indicated high reliability of the HIV-1C IN tetrameric structure, with more than 90.0% confidence in modelled regions. Of the six selected variants, only one (S119P) was calculated to be slightly stabilizing to the protein structure, with the other five found to be destabilizing to the IN protein structure. Variant S119P showed a loss in polar contacts that could destabilize the protein structure, while variant Y143R, resulted in the gain of polar contacts which could reduce flexibility of the 140’s region affecting drug binding. Similarly, mutant systems P3 (S119P, Y143R) and P4 (V150A, M154I) showed reduced hydrogen bond formation and the weakest non-bonded pairwise interaction energy. These two systems, P3 and P4, also showed significantly reduced to none polar contacts between DTG, magnesium (MG) ions and the IN protein, compared to the WT IN and P2 mutant IN systems. Interestingly, the WT structure and systems P1 (I113V) and P2 (L63I, V75M, Y143R) showed the highest non-bonded interaction energy, compared to systems P3 and P4. This was further supported by the polar interaction analyses of simulation clusters from the WT IN and mutant IN system P2 (L63I, V75M, Y143R), which were the only protein structures that formed polar contacts with DTG, MG ions and DDE motif residues, while P1 only made contacts with DNA and IN residues. Conclusion Findings from this study leads to a conclusion that double mutants (S119P, Y143R) and (V150A, M154I) may result in a reduction in the efficacy of DTG, especially when in combination. Furthermore, variants identified in systems P1 and P2 may still allow for effective DTG binding to IN and outcompete viral DNA for host DNA to prevent strand transfer. To the best of our knowledge, this is the first study that uses the consensus WT HIV1C IN sequence to build an accurate 3D homology model to understand the effect of less frequently detected/reported variants on DTG binding in a South African context. https://etd.

[pt] Os processos industriais de uma maneira geral são compostos de várias etapas que promovem a transformação de materiais, seja na sua forma primária, ou na forma de subprodutos, que vão posteriormente formar o produto final. Neste contexto, na indústria fabricação de pneus, existe uma etapa bastante específica que é o corte de borracha, etapa esta, que pode ser realizada de várias formas e técnicas sendo que uma delas, é o corte por ultrassom. Apesar do corte por ultrassom ser eficiente e proporcionar ao material um acabamento nas superfícies superior aos demais, os sistemas de corte por este método apresentam fraturas excessivas do componente que realiza o corte, chamado de sonotrodo. Neste trabalho, foram investigadas algumas das causas possíveis (causas raízes) para as falhas apresentadas pelos sonotrodos. O estudo envolveu a análise química qualitativa do material, a análise de tensões utilizando o método de elementos finitos, ensaios mecanográficos e caracterização mecânica do material. Os resultados obtidos permitiram a identificação do mecanismo de dano acumulado no componente durante sua vida em serviço, permitindo a indicação de possíveis causas raiz que levam o sonotrodo a falhar de maneira prematura. / [en] Industrial processes generally are comprised of several steps that promote the transformation of materials, whether in their primary form, or as by-products, which will subsequently form the final product. In this context, the tire manufacturing industry, there is a very specific step is the cutting of rubber; this step can be performed in various ways and techniques one of which is the cutting by ultrasound. Although efficient cutting and the cut material presenting a finish of the cut surfaces higher than the other cutting systems ultrasound have excessive fractures component that performs cutting, called sonotrode. In this study, we investigated some of the possible (root cause) for failures made by sonotrode. The study involved a qualitative chemical analysis of the material, stress analysis using the finite element method, metallographic tests and mechanical characterization of the material. The results obtained allowed the identification of the accumulated damage mechanism in the component during its service life, allowing indication of possible root because that lead the sonotrode to fail prematurely.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20887号 / 理博第4339号 / 新制||理||1623(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 福島 竜輝, 教授 中島 啓, 教授 牧野 和久 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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In clinical research, it is sometimes desirable to dichotomize a continuous variable so that the information expressed using a dichotomous variable is more straightforward for clinicians to interpret and communicate. The distribution of a continuous variable can differ between two populations defined by the case status. Under such a scenario, the dichotomization process can be based on distributions of the continuous variable in two distinct populations. The resulting dichotomous variable can be used as an endpoint in future studies. Even though dichotomization has not been extensively studied, dichotomization has been commonly carried out in clinical trials. We developed a methodology on dichotomization based on maximizing the correlation between the two populations and the dichotomous variable. We have investigated several commonly assumed distributions (e.g., normal, log-normal and gamma distribution) of the continuous variable for the two populations and developed a numerical algorithm for the proposed method to determine the optimal cutoff point. The two populations can differ in form and/or parameters. The proposed method of finding the optimal cutoff was also extended to adjust for covariates. In real world scenarios where the two samples from the two populations are not completely identified, we recommended using the EM method to first estimate the parameters associated with the two populations before applying the proposed method to find the optimal cutoff point. The performance of the proposed method with the numerical algorithm and the EM method has been studied for several theoretical distributions and using simulated data. These methods were also applied to a varicella vaccine example. / Statistics

Soil-bentonite cutoff walls are commonly used to contain contaminants in the subsurface. A key property in determining the effectiveness of a cutoff wall is its hydraulic conductivity. There are important difficulties and uncertainties regarding the accuracy of commonly used methods of measuring the hydraulic conductivity of cutoff walls. When predicting contaminant transport through cutoff walls, common practice is to use the average hydraulic conductivity of the wall. There are some cases, however, such as circumferential cutoff walls with inward hydraulic gradients, where it is also important to consider the variability in hydraulic conductivity from point to point in the wall in contaminant transport studies. A pilot-scale facility was envisioned where subsurface barrier issues such as those mentioned above could be studied. In 1998, the Subsurface Barrier Test Facility (SBTF) was constructed. In this facility, pilot-scale subsurface barriers can be installed using real construction equipment and tested in a controlled environment. The effectiveness of various methods of measuring the hydraulic conductivity of cutoff walls was studied by building and testing three pilot-scale soil-bentonite cutoff walls at the SBTF. The following currently used test methods were evaluated: API tests on grab samples, lab tests on undisturbed samples, piezometer tests (slug tests), and piezocone soundings. The use of slug tests in cutoff walls was improved in this research in the areas of avoiding hydraulic fracture and accounting for the close proximity of the trench walls. The SBTF allows for measurement of the global, average hydraulic conductivity of an installed pilot-scale cutoff wall, which is a useful value to compare to the results of the above-mentioned tests. The two main factors differentiating the results of the different test methods used for the pilot-scale walls were remolding and sample size. Remolding of the API samples significantly reduced the hydraulic conductivity of these samples compared to the hydraulic conductivity measured in lab tests on undisturbed samples, which were of similar size. For the other tests, the degree and extent of remolding were less significant compared to in the API tests. For these tests, the scale of the measurement is believed to be the main factor differentiating the results. Hydraulic conductivity was found to increase as the sample volume increased, with the global measurement of the average hydraulic conductivity producing the highest value. The influence of variability in hydraulic conductivity on contaminant transport through cutoff walls was studied from a theoretical standpoint using the one-dimensional advection-diffusion equation. Charts were developed that can be used to estimate the flux through a cutoff wall based on knowledge of the average hydraulic conductivity of the wall and an estimate of the variability in hydraulic conductivity. Data sets of hydraulic conductivity from lab tests on soil-bentonite samples from four cutoff wall case histories were used to estimate typical values of variability. The contaminant transport analyses showed that the effect of variability may be significant when the hydraulic gradient opposes the concentration gradient, which is the case for a circumferential cutoff wall with an inward hydraulic gradient. The goal of a circumferential cutoff wall with an inward hydraulic gradient is to reduce the outward diffusive flux of contaminant by inducing an inward advective flux. The effect of variability in hydraulic conductivity is to reduce the effectiveness of this scheme. / Ph. D.

A soil-bentonite cutoff wall is a type of subsurface vertical barrier constructed by back-filling a trench with a mixture of soil, bentonite, and water. Although soil-bentonite cutoff walls are common, their mechanical behavior is not well understood. Current design procedures do not consider the final stress state of the consolidated soil-bentonite backfill or deformations in adjacent ground. The final stress state in the completed wall is important because it influences the hydraulic conductivity of the cutoff (Barrier 1995), the cutoff's susceptibility to hydraulic fracture, and the magnitude of deformations adjacent to the cutoff wall. Deformations adjacent to the cutoff wall can be significant and can cause damage to adjacent structures. The objectives of this research are to 1) add to the current body of knowledge of the properties of soil-bentonite mixtures, 2) evaluate constitutive models and select a model to represent soil-bentonite, 3) model a soil-bentonite cutoff wall using finite elements, and 4) investigate the influence of several factors on the deformations in adjacent ground. These objectives were met by first summarizing information from the literature on soil-bentonite properties and then performing a laboratory testing program on different soil-bentonite mixtures. Five constitutive models were evaluated to determine how well they match the data from the laboratory testing program. A model referred to as the RS model was chosen to best represent soil-bentonite, and provided a good match of the soil-bentonite behavior. The RS model, which is a special case of a more complicated existing model, is a non-associative Modified Cam Clay type model that has parameters to change the yield surface and plastic potential surface into ellipses of varying shapes. The RS model was implemented into the finite element program SAGE. A finite element model was developed using SAGE to simulate all stages of construction of a soil-bentonite cutoff wall including excavation of a trench under bentonite-water slurry, replacement of the bentonite-water slurry with soil-bentonite backfill, and consolidation of the soil-bentonite backfill. The model was calibrated with a well-documented case history, and predicted deformations in adjacent ground were close to measured deformations. Evaluation of the model indicates that there is good confidence in the prediction of deformations in adjacent ground, but there is lower confidence in the predicted stresses in the consolidated soil-bentonite and settlement of the backfill in the trench. A parametric study was then performed using the finite element model assuming sand sites of varying density and OCR. Deformations in adjacent ground were calculated for various soil conditions, soil-bentonite properties, and trench configurations. A correlation was found between maximum calculated settlement in adjacent ground and factor of safety against trench / Ph. D.

We study a random walk on the special unitary group SU(N) consisting of a product of matrices chosen Haar uniformly from a fixed conjugacy class. In particular, we make use of the representation theory of matrix Lie groups to show two results about the rate of convergence of the random walk's distribution to the Haar measure in total variation distance. We derive a lower bound in total variation distance before a threshold number of steps, which appears to be an example of a cut-off phenomenon, and for dimension N=2 we prove exponentially fast convergence.

The concept of measurement invariance is essential in ensuring psychological and educational tests are interpreted consistently across diverse groups. This dissertation investigated the practical challenges associated with measurement invariance, specifically on how measurement invariance delta fit indexes are affected by non-normal data. Non-normal data distributions are common in real-world scenarios, yet many statistical methods and measurement invariance delta fit indexes are based on the assumption of normally distributed data. This raises concerns about the accuracy and reliability of conclusions drawn from such analyses. The primary objective of this research is to examine how commonly used delta fit indexes of measurement invariance respond under conditions of non-normality. The present research was built upon Cao and Liang (2022a)’s study to test the sensitivities of a series of delta fit indexes, and further scrutinizes the role of non-normal data distributions. A series of simulation studies was conducted, where data sets with varying degrees of skewness and kurtosis were generated. These data sets were then examined by multi-group confirmatory factor analysis (MGCFA) using the Satorra-Bentler scaled chi-square difference test, a method specifically designed to adjust for non-normality. The performance of delta fit indexes such as the Delta Comparative Fit Index (∆CFI), Delta Standardized Root Mean Square residual (∆SRMR) and Delta Root Mean Square Error of Approximation (∆RMSEA) were assessed. These findings have significant implications for professionals and scholars in psychology and education. They provide constructive information related to key aspects of research and practice in these fields related to measurement, contributing to the broader discussion on measurement invariance by highlighting challenges and offering solutions for assessing model fit in non-normal data scenarios.