On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

Is pupil diameter influenced by refractive error?

Purpose: To investigate the relationship between pupil diameter and refractive error and how refractive correction, target luminance, and accommodation modulate this relationship. Methods: Sixty emmetropic, myopic, and hyperopic subjects (age range, 18 to 35 years) viewed an illuminated target (luminance: 10, 100, 200, 400, 1000, 2000, and 4100 cd/m2) within a Badal optical system, at 0 diopters (D) and −3 D vergence, with and without refractive correction. Refractive error was corrected using daily disposable contact lenses. Pupil diameter and accommodation were recorded continuously using a commercially available photorefractor. Results: No significant difference in pupil diameter was found between the refractive groups at 0 D or −3 D target vergence, in the corrected or uncorrected conditions. As expected, pupil diameter decreased with increasing luminance. Target vergence had no significant influence on pupil diameter. In the corrected condition, at 0 D target vergence, the accommodation response was similar in all refractive groups. At −3 D target vergence, the emmetropic and myopic groups accommodated significantly more than the hyperopic group at all luminance levels. There was no correlation between accommodation response and pupil diameter or refractive error in any refractive group. In the uncorrected condition, the accommodation response was significantly greater in the hyperopic group than in the myopic group at all luminance levels, particularly for near viewing. In the hyperopic group, the accommodation response was significantly correlated with refractive error but not pupil diameter. In the myopic group, accommodation response level was not correlated with refractive error or pupil diameter. Conclusions: Refractive error has no influence on pupil diameter, irrespective of refractive correction or accommodative demand. This suggests that the pupil is controlled by the pupillary light reflex and is not driven by retinal blur.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

A comparison of denoising methods for X-ray fluoroscopic images

Fluoroscopic images exhibit severe signal-dependent quantum noise, due to the reduced X-ray dose involved in image formation, that is generally modelled as Poisson-distributed. However, image gray-level transformations, commonly applied by fluoroscopic device to enhance contrast, modify the noise statistics and the relationship between image noise variance and expected pixel intensity. Image denoising is essential to improve quality of fluoroscopic images and their clinical information content. Simple average filters are commonly employed in real-time processing, but they tend to blur edges and details. An extensive comparison of advanced denoising algorithms specifically designed for both signal-dependent noise (AAS, BM3Dc, HHM, TLS) and independent additive noise (AV, BM3D, K-SVD) was presented. Simulated test images degraded by various levels of Poisson quantum noise and real clinical fluoroscopic images were considered. Typical gray-level transformations (e.g. white compression) were also applied in order to evaluate their effect on the denoising algorithms. Performances of the algorithms were evaluated in terms of peak-signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), mean square error (MSE), structural similarity index (SSIM) and computational time. On average, the filters designed for signal-dependent noise provided better image restorations than those assuming additive white Gaussian noise (AWGN). Collaborative denoising strategy was found to be the most effective in denoising of both simulated and real data, also in the presence of image gray-level transformations. White compression, by inherently reducing the greater noise variance of brighter pixels, appeared to support denoising algorithms in performing more effectively. © 2012 Elsevier Ltd. All rights reserved.

Real-time error compensation of a three-axis machine tool using a laser tracker

The concept of measurement-enabled production is based on integrating metrology systems into production processes and generated significant interest in industry, due to its potential to increase process capability and accuracy, which in turn reduces production times and eliminates defective parts. One of the most promising methods of integrating metrology into production is the usage of external metrology systems to compensate machine tool errors in real time. The development and experimental performance evaluation of a low-cost, prototype three-axis machine tool that is laser tracker assisted are described in this paper. Real-time corrections of the machine tool's absolute volumetric error have been achieved. As a result, significant increases in static repeatability and accuracy have been demonstrated, allowing the low-cost three-axis machine tool to reliably reach static positioning accuracies below 35 μm throughout its working volume without any prior calibration or error mapping. This is a significant technical development that demonstrated the feasibility of the proposed methods and can have wide-scale industrial applications by enabling low-cost and structural integrity machine tools that could be deployed flexibly as end-effectors of robotic automation, to achieve positional accuracies that were the preserve of large, high-precision machine tools.

Intraoperative prediction of refractive error using a prototype surgical aberrometer

Purpose: To ascertain the agreement level between intra-operative refraction using a prototype surgical Hartmann-Shack aberrometer and subjective refraction a month later. Methods: Fifty-four consecutive patients had their pseudophakic refractive measured with the aberrometer intra-operatively at the end of their cataract surgery. A masked optometrist performed subjective refraction 4 weeks later. The two sets of data were then analysed for correlation. Results: The mean spherical equivalent was −0.14 ± 0.37 D (Range: −1.41 to +1.72 D) with the prototype aberrometer and −0.34 ± 0.32 (−1.64 to +1.88 D) with subjective refraction. The measurements positively correlated to a very high degree (r =+0.81, p < 0.01). In 84.3% of cases the two measurements were within 0.50D of each other. Conclusion: The aberrometer can verify the aimed refractive status of the eye intraoperatively to avoid a refractive surprise. The aberrometer is a useful tool for real time assessment of the ocular refractive status.

Integrated surface-ground water modeling in wetlands with improved methods to simulate vegetative resistance to flow

In topographically flat wetlands, where shallow water table and conductive soil may develop as a result of wet and dry seasons, the connection between surface water and groundwater is not only present, but perhaps the key factor dominating the magnitude and direction of water flux. Due to their complex characteristics, modeling waterflow through wetlands using more realistic process formulations (integrated surface-ground water and vegetative resistance) is an actual necessity. This dissertation focused on developing an integrated surface – subsurface hydrologic simulation numerical model by programming and testing the coupling of the USGS MODFLOW-2005 Groundwater Flow Process (GWF) package (USGS, 2005) with the 2D surface water routing model: FLO-2D (O’Brien et al., 1993). The coupling included the necessary procedures to numerically integrate and verify both models as a single computational software system that will heretofore be referred to as WHIMFLO-2D (Wetlands Hydrology Integrated Model). An improved physical formulation of flow resistance through vegetation in shallow waters based on the concept of drag force was also implemented for the simulations of floodplains, while the use of the classical methods (e.g., Manning, Chezy, Darcy-Weisbach) to calculate flow resistance has been maintained for the canals and deeper waters. A preliminary demonstration exercise WHIMFLO-2D in an existing field site was developed for the Loxahatchee Impoundment Landscape Assessment (LILA), an 80 acre area, located at the Arthur R. Marshall Loxahatchee National Wild Life Refuge in Boynton Beach, Florida. After applying a number of simplifying assumptions, results have illustrated the ability of the model to simulate the hydrology of a wetland. In this illustrative case, a comparison between measured and simulated stages level showed an average error of 0.31% with a maximum error of 2.8%. Comparison of measured and simulated groundwater head levels showed an average error of 0.18% with a maximum of 2.9%. The coupling of FLO-2D model with MODFLOW-2005 model and the incorporation of the dynamic effect of flow resistance due to vegetation performed in the new modeling tool WHIMFLO-2D is an important contribution to the field of numerical modeling of hydrologic flow in wetlands.

Development of methods for spatial modeling of sediments quality in Lake Okeechobee, Florida

The major objectives of this dissertation were to develop optimal spatial techniques to model the spatial-temporal changes of the lake sediments and their nutrients from 1988 to 2006, and evaluate the impacts of the hurricanes occurred during 1998–2006. Mud zone reduced about 10.5% from 1988 to 1998, and increased about 6.2% from 1998 to 2006. Mud areas, volumes and weight were calculated using validated Kriging models. From 1988 to 1998, mud thicknesses increased up to 26 cm in the central lake area. The mud area and volume decreased about 13.78% and 10.26%, respectively. From 1998 to 2006, mud depths declined by up to 41 cm in the central lake area, mud volume reduced about 27%. Mud weight increased up to 29.32% from 1988 to 1998, but reduced over 20% from 1998 to 2006. The reduction of mud sediments is likely due to re-suspension and redistribution by waves and currents produced by large storm events, particularly Hurricanes Frances and Jeanne in 2004 and Wilma in 2005. Regression, kriging, geographically weighted regression (GWR) and regression-kriging models have been calibrated and validated for the spatial analysis of the sediments TP and TN of the lake. GWR models provide the most accurate predictions for TP and TN based on model performance and error analysis. TP values declined from an average of 651 to 593 mg/kg from 1998 to 2006, especially in the lake’s western and southern regions. From 1988 to 1998, TP declined in the northern and southern areas, and increased in the central-western part of the lake. The TP weights increased about 37.99%–43.68% from 1988 to 1998 and decreased about 29.72%–34.42% from 1998 to 2006. From 1988 to 1998, TN decreased in most areas, especially in the northern and southern lake regions; western littoral zone had the biggest increase, up to 40,000 mg/kg. From 1998 to 2006, TN declined from an average of 9,363 to 8,926 mg/kg, especially in the central and southern regions. The biggest increases occurred in the northern lake and southern edge areas. TN weights increased about 15%–16.2% from 1988 to 1998, and decreased about 7%–11% from 1998 to 2006.

Evaluation of the evidential value of the elemental composition of glass, ink and paper by laser-based microspectrochemical methods

Elemental analysis can become an important piece of evidence to assist the solution of a case. The work presented in this dissertation aims to evaluate the evidential value of the elemental composition of three particular matrices: ink, paper and glass. In the first part of this study, the analytical performance of LIBS and LA-ICP-MS methods was evaluated for paper, writing inks and printing inks. A total of 350 ink specimens were examined including black and blue gel inks, ballpoint inks, inkjets and toners originating from several manufacturing sources and/or batches. The paper collection set consisted of over 200 paper specimens originating from 20 different paper sources produced by 10 different plants. Micro-homogeneity studies show smaller variation of elemental compositions within a single source (i.e., sheet, pen or cartridge) than the observed variation between different sources (i.e., brands, types, batches). Significant and detectable differences in the elemental profile of the inks and paper were observed between samples originating from different sources (discrimination of 87–100% of samples, depending on the sample set under investigation and the method applied). These results support the use of elemental analysis, using LA-ICP-MS and LIBS, for the examination of documents and provide additional discrimination to the currently used techniques in document examination. In the second part of this study, a direct comparison between four analytical methods (µ-XRF, solution-ICP-MS, LA-ICP-MS and LIBS) was conducted for glass analyses using interlaboratory studies. The data provided by 21 participants were used to assess the performance of the analytical methods in associating glass samples from the same source and differentiating different sources, as well as the use of different match criteria (confidence interval (±6s, ±5s, ±4s, ±3s, ±2s), modified confidence interval, t-test (sequential univariate, p=0.05 and p=0.01), t-test with Bonferroni correction (for multivariate comparisons), range overlap, and Hotelling's T2 tests. Error rates (Type 1 and Type 2) are reported for the use of each of these match criteria and depend on the heterogeneity of the glass sources, the repeatability between analytical measurements, and the number of elements that were measured. The study provided recommendations for analytical performance-based parameters for µ-XRF and LA-ICP-MS as well as the best performing match criteria for both analytical techniques, which can be applied now by forensic glass examiners.

Integrated Surface-Ground Water Modeling in Wetlands With Improved Methods to Simulate Vegetative Resistance to Flow

This dissertation focused on developing an integrated surface – subsurface hydrologic simulation numerical model by programming and testing the coupling of the USGS MODFLOW-2005 Groundwater Flow Process (GWF) package (USGS, 2005) with the 2D surface water routing model: FLO-2D (O’Brien et al., 1993). The coupling included the necessary procedures to numerically integrate and verify both models as a single computational software system that will heretofore be referred to as WHIMFLO-2D (Wetlands Hydrology Integrated Model). An improved physical formulation of flow resistance through vegetation in shallow waters based on the concept of drag force was also implemented for the simulations of floodplains, while the use of the classical methods (e.g., Manning, Chezy, Darcy-Weisbach) to calculate flow resistance has been maintained for the canals and deeper waters. A preliminary demonstration exercise WHIMFLO-2D in an existing field site was developed for the Loxahatchee Impoundment Landscape Assessment (LILA), an 80 acre area, located at the Arthur R. Marshall Loxahatchee National Wild Life Refuge in Boynton Beach, Florida. After applying a number of simplifying assumptions, results have illustrated the ability of the model to simulate the hydrology of a wetland. In this illustrative case, a comparison between measured and simulated stages level showed an average error of 0.31% with a maximum error of 2.8%. Comparison of measured and simulated groundwater head levels showed an average error of 0.18% with a maximum of 2.9%.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

Comparison of nitrogen isotopic values from different preparation methods

We are writing to comment on the work of Tamburini et al. (2003, doi:10.1029/2000PA000616). During the course of subsequent discussions between the authors and ourselves, it has become clear that the published sedimentary nitrogen isotopic values for Ocean Drilling Program (ODP) Site 724 are in error. Our reanalysis of sediment samples from the same intervals has revealed a significant offset from the original d15N data, requiring a revised assessment of their initial interpretation. The purposes of this comment are to (1) address the origin of these errors; (2) outline a protocol for future validation of nitrogen isotopic analyses; and (3) provide revised interpretations of the sedimentary d15N data in terms of the regional relative contributions of denitrification and nitrogen fixation and mean state of the southwest monsoon. (2) Nitrogen isotopic values measured on late Quaternary sediments at Arabian Sea ODP Site 724 by Tamburini et al. (2003, doi:10.1029/2000PA000616) are inexplicably different from a number of published records of d15N from very nearby on the Oman margin (Altabet et al., 1995, doi:10.1038/373506a0; 1999, doi:10.1029/1999PA900035; 2002, doi:10.1038/415159a; Higginson et al., 2004, doi:10.1016/j.gca.2004.03.015) and elsewhere in the Arabian Sea (Reichart et al., 1998, doi:10.1029/98PA02203). These data were generated using similar instrumentation (elemental analyzer coupled with an isotope ratio mass spectrometer) and analytical methodology to those already published. Concerned by this clear discrepancy, we analyzed aliquots of sediment from the same depth intervals for nitrogen abundance and bulk sedimentary nitrogen isotopes. We have been unable to duplicate the values published by Tamburini et al. (2003, doi:10.1029/2000PA000616 ), even after analysis of multiple replicates and due consideration of natural sediment heterogeneities and postrecovery sample storage.

Methods for Hypothesis Testing in Animal Carcinogenicity Experiments

Thesis (Ph.D.)--University of Washington, 2016-08

Reading comprehension of czech pupils at the beginning of primary school: comparison betweenanalytic-synthetic and genetic methods

In Czech schools two teaching methods of reading are used: the analytic-synthetic (conventional) and genetic (created in the 1990s). They differ in theoretical foundations and in methodology. The aim of this paper is to describe the above mentioned theoretical approaches and present the results of study that followed the differences in the development of initial reading skills between these methods. A total of 452 first grade children (age 6-8) were assessed by a battery of reading tests at the beginning and at the end of the first grade and at the beginning of the second grade. 350 pupils participated all three times. Based on data analysis the developmental dynamics of reading skills in both methods and the main differences in several aspects of reading abilities (e.g. the speed of reading, reading technique, error rate in reading) are described. The main focus is on the reading comprehension development. Results show that pupils instructed using genetic approach scored significantly better on used reading comprehension tests, especially in the first grade. Statistically significant differences occurred between classes independently of each method. Therefore, other factors such as teacher´s role and class composition are discussed.