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.

A complex intronic enhancer regulates expression of the CFTR gene by direct interaction with the promoter.

Genes can maintain spatiotemporal expression patterns by long-range interactions between cis-acting elements. The cystic fibrosis transmembrane conductance regulator gene (CFTR) is expressed primarily in epithelial cells. An element located within a DNase I-hypersensitive site (DHS) 10 kb into the first intron was previously shown to augment CFTR promoter activity in a tissue-specific manner. Here, we reveal the mechanism by which this element influences CFTR transcription. We employed a high-resolution method of mapping DHS using tiled microarrays to accurately locate the intron 1 DHS. Transfection of promoter-reporter constructs demonstrated that the element displays classical tissue-specific enhancer properties and can independently recruit factors necessary for transcription initiation. In vitro DNase I footprinting analysis identified a protected region that corresponds to a conserved, predicted binding site for hepatocyte nuclear factor 1 (HNF1). We demonstrate by electromobility shift assays (EMSA) and chromatin immunoprecipitation (ChIP) that HNF1 binds to this element both in vitro and in vivo. Moreover, using chromosome conformation capture (3C) analysis, we show that this element interacts with the CFTR promoter in CFTR-expressing cells. These data provide the first insight into the three- dimensional (3D) structure of the CFTR locus and confirm the contribution of intronic cis-acting elements to the regulation of CFTR gene expression.

Martin Heidegger's Mathematical Dialectic: Uncovering the Structure of Modernity

Martin Heidegger is generally regarded as one of the most significant—if also the most controversial—philosophers of the 20th century. Most scholarly engagement with Heidegger’s thought on Modernity approaches his work with a special focus on either his critique of technology, or on his more general critique of subjectivity. This dissertation project attempts to elucidate Martin Heidegger’s diagnosis of modernity, and, by extension, his thought as a whole, from the neglected standpoint of his understanding of mathematics, which he explicitly identifies as the essence of modernity.

Accordingly, our project attempts to work through the development of Modernity, as Heidegger understands it, on the basis of what we call a “mathematical dialectic.“ The basis of our analysis is that Heidegger’s understanding of Modernity, both on its own terms and in the context of his theory of history [Seinsgeschichte], is best understood in terms of the interaction between two essential, “mathematical” characteristics, namely, self-grounding and homogeneity. This project first investigates the mathematical qualities of these components of Modernity individually, and then attempts to trace the historical and philosophical development of Modernity on the basis of the interaction between these two components—an interaction that is, we argue, itself regulated by the structure of the mathematical, according to Heidegger’s understanding of the term.

The project undertaken here intends not only to serve as an interpretive, scholarly function of elucidating Heidegger’s understanding of Modernity, but also to advance the larger aim of defending the prescience, structural coherence, and relevance of Heidegger’s diagnosis of Modernity as such.

Seismic Response Analysis of a Full-Scale Base-Isolated Structure via Measurements and Modeling

The full-scale base-isolated structure studied in this dissertation is the only base-isolated building in South Island of New Zealand. It sustained hundreds of earthquake ground motions from September 2010 and well into 2012. Several large earthquake responses were recorded in December 2011 by NEES@UCLA and by GeoNet recording station nearby Christchurch Women's Hospital. The primary focus of this dissertation is to advance the state-of-the art of the methods to evaluate performance of seismic-isolated structures and the effects of soil-structure interaction by developing new data processing methodologies to overcome current limitations and by implementing advanced numerical modeling in OpenSees for direct analysis of soil-structure interaction.

This dissertation presents a novel method for recovering force-displacement relations within the isolators of building structures with unknown nonlinearities from sparse seismic-response measurements of floor accelerations. The method requires only direct matrix calculations (factorizations and multiplications); no iterative trial-and-error methods are required. The method requires a mass matrix, or at least an estimate of the floor masses. A stiffness matrix may be used, but is not necessary. Essentially, the method operates on a matrix of incomplete measurements of floor accelerations. In the special case of complete floor measurements of systems with linear dynamics, real modes, and equal floor masses, the principal components of this matrix are the modal responses. In the more general case of partial measurements and nonlinear dynamics, the method extracts a number of linearly-dependent components from Hankel matrices of measured horizontal response accelerations, assembles these components row-wise and extracts principal components from the singular value decomposition of this large matrix of linearly-dependent components. These principal components are then interpolated between floors in a way that minimizes the curvature energy of the interpolation. This interpolation step can make use of a reduced-order stiffness matrix, a backward difference matrix or a central difference matrix. The measured and interpolated floor acceleration components at all floors are then assembled and multiplied by a mass matrix. The recovered in-service force-displacement relations are then incorporated into the OpenSees soil structure interaction model.

Numerical simulations of soil-structure interaction involving non-uniform soil behavior are conducted following the development of the complete soil-structure interaction model of Christchurch Women's Hospital in OpenSees. In these 2D OpenSees models, the superstructure is modeled as two-dimensional frames in short span and long span respectively. The lead rubber bearings are modeled as elastomeric bearing (Bouc Wen) elements. The soil underlying the concrete raft foundation is modeled with linear elastic plane strain quadrilateral element. The non-uniformity of the soil profile is incorporated by extraction and interpolation of shear wave velocity profile from the Canterbury Geotechnical Database. The validity of the complete two-dimensional soil-structure interaction OpenSees model for the hospital is checked by comparing the results of peak floor responses and force-displacement relations within the isolation system achieved from OpenSees simulations to the recorded measurements. General explanations and implications, supported by displacement drifts, floor acceleration and displacement responses, force-displacement relations are described to address the effects of soil-structure interaction.

Into the Bends of Time and Musical Forces in Jazz: Group Interaction and Double-time in “My Foolish Heart” as performed by the Bill Evans Trio with Scott LaFaro and Paul Motian.

Into the Bends of Time is a 40-minute work in seven movements for a large chamber orchestra with electronics, utilizing real-time computer-assisted processing of music performed by live musicians. The piece explores various combinations of interactive relationships between players and electronics, ranging from relatively basic processing effects to musical gestures achieved through stages of computer analysis, in which resulting sounds are crafted according to parameters of the incoming musical material. Additionally, some elements of interaction are multi-dimensional, in that they rely on the participation of two or more performers fulfilling distinct roles in the interactive process with the computer in order to generate musical material. Through processes of controlled randomness, several electronic effects induce elements of chance into their realization so that no two performances of this work are exactly alike. The piece gets its name from the notion that real-time computer-assisted processing, in which sound pressure waves are transduced into electrical energy, converted to digital data, artfully modified, converted back into electrical energy and transduced into sound waves, represents a “bending” of time.

The Bill Evans Trio featuring bassist Scott LaFaro and drummer Paul Motian is widely regarded as one of the most important and influential piano trios in the history of jazz, lauded for its unparalleled level of group interaction. Most analyses of Bill Evans’ recordings, however, focus on his playing alone and fail to take group interaction into account. This paper examines one performance in particular, of Victor Young’s “My Foolish Heart” as recorded in a live performance by the Bill Evans Trio in 1961. In Part One, I discuss Steve Larson’s theory of musical forces (expanded by Robert S. Hatten) and its applicability to jazz performance. I examine other recordings of ballads by this same trio in order to draw observations about normative ballad performance practice. I discuss meter and phrase structure and show how the relationship between the two is fixed in a formal structure of repeated choruses. I then develop a model of perpetual motion based on the musical forces inherent in this structure. In Part Two, I offer a full transcription and close analysis of “My Foolish Heart,” showing how elements of group interaction work with and against the musical forces inherent in the model of perpetual motion to achieve an unconventional, dynamic use of double-time. I explore the concept of a unified agential persona and discuss its role in imparting the song’s inherent rhetorical tension to the instrumental musical discourse.