A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

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.

Robust test method for time-course microarray experiments.

BACKGROUND: In a time-course microarray experiment, the expression level for each gene is observed across a number of time-points in order to characterize the temporal trajectories of the gene-expression profiles. For many of these experiments, the scientific aim is the identification of genes for which the trajectories depend on an experimental or phenotypic factor. There is an extensive recent body of literature on statistical methodology for addressing this analytical problem. Most of the existing methods are based on estimating the time-course trajectories using parametric or non-parametric mean regression methods. The sensitivity of these regression methods to outliers, an issue that is well documented in the statistical literature, should be of concern when analyzing microarray data. RESULTS: In this paper, we propose a robust testing method for identifying genes whose expression time profiles depend on a factor. Furthermore, we propose a multiple testing procedure to adjust for multiplicity. CONCLUSIONS: Through an extensive simulation study, we will illustrate the performance of our method. Finally, we will report the results from applying our method to a case study and discussing potential extensions.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

The relationship between blood IL-12p40 level and melanoma progression

© 2014 UICC.Cytokines such as Interleukin (IL)212p70 ("IL-12") and IL-23 can influence tumor progression. We tested the hypothesis that blood levels of IL-12p40, the common subunit of both cytokines, are associated with melanoma progression. Blood from 2,048 white melanoma patients were collected at a single institution between March 1998 and March 2011. Plasma levels of IL-12p40 were determined for 573 patients (discovery), 249 patients (Validation 1) and 244 patients (Validation 2). Per 10-unit change of IL-12p40 level was used to investigate associations with melanoma patient outcome among all patients or among patients with early or advanced stage. Among stage I/II melanoma patients in the pooled data set, after adjustment for sex, age, stage and blood draw time from diagnosis, elevated IL-12p40 was associated with melanoma recurrence [hazard ratio (HR)51.04 per 10-unit increase in IL-12p40, 95% CI 1.02-1.06, p58.48 × 10-5]; Elevated IL-12p40 was also associated with a poorer melanoma specific survival (HR51.06, 95% CI 1.03-1.09, p53.35 × 10-5) and overall survival (HR51.05, 95% CI 1.03-1.08, p58.78 × 10-7) in multivariate analysis. Among stage III/IV melanoma patients in the pooled data set, no significant association was detected between elevated IL-12p40 and overall survival, or with melanoma specific survival, with or without adjustment for the above covariates. Early stage melanoma patients with elevated IL-12p40 levels are more likely to develop disease recurrence and have a poorer survival. Further investigation with a larger sample size will be needed to determine the role of IL-12p40 in advanced stage melanoma patients.

The effectiveness of low-level laser therapy for nonspecific chronic low back pain: a systematic review and meta-analysis.

BACKGROUND: In recent decades, low-level laser therapy (LLLT) has been widely used to relieve pain caused by different musculoskeletal disorders. Though widely used, its reported therapeutic outcomes are varied and conflicting. Results similarly conflict regarding its usage in patients with nonspecific chronic low back pain (NSCLBP). This study investigated the efficacy of low-level laser therapy (LLLT) for the treatment of NSCLBP by a systematic literature search with meta-analyses on selected studies. METHOD: MEDLINE, EMBASE, ISI Web of Science and Cochrane Library were systematically searched from January 2000 to November 2014. Included studies were randomized controlled trials (RCTs) written in English that compared LLLT with placebo treatment in NSCLBP patients. The efficacy effect size was estimated by the weighted mean difference (WMD). Standard random-effects meta-analysis was used, and inconsistency was evaluated by the I-squared index (I(2)). RESULTS: Of 221 studies, seven RCTs (one triple-blind, four double-blind, one single-blind, one not mentioning blinding, totaling 394 patients) met the criteria for inclusion. Based on five studies, the WMD in visual analog scale (VAS) pain outcome score after treatment was significantly lower in the LLLT group compared with placebo (WMD = -13.57 [95 % CI = -17.42, -9.72], I(2) = 0 %). No significant treatment effect was identified for disability scores or spinal range of motion outcomes. CONCLUSIONS: Our findings indicate that LLLT is an effective method for relieving pain in NSCLBP patients. However, there is still a lack of evidence supporting its effect on function.