The field of authorship attribution seeks to characterize an author’s writing style well enough to determine whether he or she has written a text of interest. One subfield of authorship attribution, stylometry, seeks to find the necessary literary attributes to quantify an author’s writing style. The research presented here sought to determine the efficacy of sentiment analysis as a new stylometric feature, by comparing its performance in attributing authorship against the performance of traditional stylometric features. Experimentation, with a corpus of sci-fi texts, found sentiment analysis to have a much lower performance in assigning authorship than the traditional stylometric features.

Swarms are groups of agents, which we model as point particles, whose collective behavior emerges from individual interactions. We study a first-order swarming model in a periodic coordinate system with pairwise social forces, investigating its stable configurations for differing numbers of agents relative to the periodic width. Two states emerge from numerical simulations in one dimension: even spacing throughout the period, or clumping within a certain portion of the period. A mathematical analysis of the energy of the system allows us to determine stability of these configurations. We also perform numerical simulations for evolution to equilibrium over time, and find results in agreement with our mathematical analysis. For certain values of the periodic width relative to the number of agents, our numerical simulations show that either clumping or even spacing can be stable equilibria, and which equilibrium is reached depends on on starting conditions, indicating hysteresis.

In this thesis, a hierarchical multiscale method was developed to predict rolling contact fatigue lives of mechanical systems. In the proposed multiscale method, the molecular modeling and simulation of lubricant was conducted to investigate the friction between rolling contact surfaces. The calculated friction coefficient was passed to the continuum model of rolling contact components to predict fatigue lives. Molecular dynamics modeling and simulation of thin film lubrication and lubricated contact surfaces were carried out to investigate mechanisms of hydrodynamic lubrication at nano-scale first. Although various lubricant alkane chains were considered in the molecular model, the chain length of eight united molecules were mainly employed in this thesis. In addition, the effects of temperature and nano-particles (debris) on the friction forces were discussed. It was found that the existing of nano-particles (debris) could increase the friction force between contact surfaces with hydrodynamic lubrication. In the continuum model of the developed multiscale method, finite element analysis was employed to predict rolling contact fatigue life of rolling contact components, including bearing and gear-tooth. Specifically, the fatigue crack initiation of bearing was studied, and then the fatigue crack initiation and propagation in gear-tooth. In addition, the enhancement of gear-tooth fatigue life by using composite patches was discussed as well. It should be noted that the friction coefficient used in the continuum model was calculated in the molecular model. It is one-way message passing in the developed multiscale method. Another continuum method was studied and developed in this thesis to provide alternate methods for the continuum model in the proposed multiscale framework. Peridynamics method has advantages in modeling and simulation of discontinuities, including cracks, over the conventional finite element methods. The applications of Peridynamics in predicting fatigue crack initiation and propagation lives were discussed in this thesis.

L'objectif de cette thèse est de développer et d'analyser des techniques numériques basées sur la méthode e Boltzmann sur réseau (LBM) pour résoudre des systèmes non linéaires de type advection-réaction-diffusion provenant de la physique et de la biologie. Avec la LBM, des problèmes portant sur des quantités moyennées densité, potentiel, vitesse, etc) sont exprimés à l'échelle particulaire. Nous approchons la solution de l'équation e Boltzmann relative au comportement d'un champs de particules puis nous recomposons les quantités moyennées solutions des équations traitées. Dans un premier temps, nous développons un cadre général approprié permettant de traiter plusieurs types de systèmes non linéaires (paraboliques, elliptiques, ou couplées ' variables réelles ou complexes), avec des applications à des modèles tels que Burger-Fisher, écoulement de fluides en milieu poreux, Helmoltz, Patlar-Keller-Segel, ou encore Schrodinger. Pour chaque problème, nous analysons le comportement asymptotique de la méthode, quand le nombre de Knudsen tend vers zéro (par le développement de Chapman-Enskog) et nous effectuons l'analyse numérique de la convergence et de la stabilité de la méthode. Dans un deuxième temps, nous nous intéressons à un problème réaliste d'électrophysiologie cardio-vasculaire. Nous adaptons la méthode LBM développée pour approcher les solutions d'un système de type bidomaine permettant de simuler le comportement de potentiels électriques et les interactions ioniques ans la région du myocarde. L'étude et la modélisation d'un tel type de problème est un enjeu sanitaire majeur ans le traitement des pathologies liées par exemple à l'arythmie cardiaque. Notre but étant d'obtenir des comportements réalistes, nous introduisons au sein de ce système bidomaine des opérateurs de retard afin de tenir compte des temps de retard dans les transmissions de signaux. Une fois l'existence et l'unicité de la solution démontrées, nous proposons une série de simulations avec des paramètres physiques et biologiques réalistes afin de valider la méthode proposée. / In this thesis, we develop and analyze numerical techniques based on the lattice Boltzmann method LBM) for solving systems of nonlinear advection-diffusion-reaction equations from physics and biology. Wi BM, problems relating to averaged quantities (density, potential, velocities, etc.) are expressed at the particle scale. We approach the solution of Boltzmann equation relating to the behavior of a particle field and then we recompose the averaged quantities solutions of treated systems. In the first part, we develop an appropriate general framework to deal with several types of non-linear systems (parabolic, elliptic, or coupled, with real or complex variables), with applications to models such as Burger-Fisher, fluid flow in a porous medium, Helmoltz, Patlar-Keller-Segel, or Schrodinger. For each problem, we analyze the asymptotic behavior of the method, when the number of Knudsen tends to zero (by the development of Chapman-Enskog) and we perform the numerical analysis of convergence and stability of the method. In the second part, we have taken an interest in a realistic problem of cardio-vascular electrophysiology. We adapt the developed LBM method to approach e solutions of a bidomain type system for simulating the behavior of electrical potentials and ionic interactions in myocardial region. The study and modeling of this type of problem is a major health issue in the treatment of pathologies related, for example, to cardiac arrhythmia. Since our goal is to obtain realistic behaviors, we introduce time-delay operators into this coupled system in order to take into account delay in signal transmissions. Once the existence and uniqueness of solution have been demonstrated, we propose a series of simulations with realistic physical and biological parameters to validate the proposed method.

The radiative transfer equation (RTE) models the transport of radiation through a participating medium. In particular, it captures how radiation is scattered, emitted, and absorbed as it interacts with the medium. This process arises in numerous application areas, including: neutron transport in nuclear reactors, radiation therapy in cancer treatment planning, and the investigation of forming galaxies in astrophysics. As a result, there is great interest in the solution of the RTE in many different fields. We consider the energy dependent form of the RTE and allow media containing regions of negligible absorption. This particular case is not often considered due to the additional dimension and stability issues which arise by allowing vanishing absorption. In this thesis, we establish the existence and uniqueness of the underlying boundary value problem. We then proceed to develop a stable numerical algorithm for solving the RTE. Alongside the construction of the method, we derive corresponding error estimates. To show the validity of the algorithm in practice, we apply the algorithm to four different example problems. We also use these examples to validate our theoretical results.

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different acceleration techniques are discussed with analysis of the asymptotic behavior of the iterates. Analogies between single variable and multivariable problems are detailed. We also explore some interesting phenomena while analyzing Newton's method for complex variables.

Very fine discretizations of differential operators often lead to large, sparse matrices A, where the condition number of A is large. Such ill-conditioning has well known effects on both solving linear systems and eigenvalue computations, and, in general, computing solutions with relative accuracy independent of the condition number is highly desirable. This dissertation is divided into two parts. In the first part, we discuss a method of preconditioning, developed by Ye, which allows solutions of Ax=b to be computed accurately. This, in turn, allows for accurate eigenvalue computations. We then use this method to develop discretizations that yield accurate computations of the smallest eigenvalue of the biharmonic operator across several domains. Numerical results from the various schemes are provided to demonstrate the performance of the methods. In the second part we address the role of the condition number of A in the context of multigrid algorithms. Under various assumptions, we use rigorous Fourier analysis on 2- and 3-grid iteration operators to analyze round off errors in floating point arithmetic. For better understanding of general results, we provide detailed bounds for a particular algorithm applied to the 1-dimensional Poisson equation. Numerical results are provided and compared with those obtained by the schemes discussed in part 1.

Free neutron and nuclear beta decay spectroscopy serves as a robust laboratory for investigations of the Standard Model of Particle Physics. Observables such as decay product angular correlations and energy spectra overconstrain the Standard Model and serve as a sensitive probe for Beyond the Standard Model physics. Improved measurement of these quantities is necessary to complement the TeV scale physics being conducted at the Large Hadron Collider. The UCNB, 45Ca, and Nab experiments aim to improve upon existing measurements of free neutron decay angular correlations and set new limits in the search for exotic couplings in beta decay. To achieve these experimental goals, a highly-pixelated, thick silicon detector with a 100 nm entrance window has been developed for precision beta spectroscopy and the direct detection of 30 keV beta decay protons. The detector has been characterized for its performance in energy reconstruction and particle arrival time determination. A Monte Carlo simulation of signal formation in the silicon detector and propagation through the electronics chain has been written to develop optimal signal analysis algorithms for minimally biased energy and timing extraction. A tagged-electron timing test has been proposed and investigated as a means to assess the validity of these Monte Carlo efforts. A universal platform for data acquisition (DAQ) has been designed and implemented in National Instrument's PXIe-5171R digitizer/FPGA hardware. The DAQ retains a ring buffer of the most recent 400 ms of data in all 256 channels, so that a waveform trace can be returned from any combination of pixels and resolution for complete energy reconstruction. Low-threshold triggers on individual channels were implemented in FPGA as a generic piecewise-polynomial filter for universal, real-time digital signal processing, which allows for arbitrary filter implementation on a pixel-by-pixel basis. This system is universal in the sense that it has complete flexible, complex, and debuggable triggering at both the pixel and global level without recompiling the firmware. The culmination of this work is a system capable of a 10 keV trigger threshold, 3 keV resolution, and maximum 300 ps arrival time systematic, even in the presence of large amplitude noise components.

Introduced in this paper is the time difference of arrival (TDoA) conic approximation method (TCAM), a technique for passive localization in three dimensions with unknown starting conditions. The TDoA of a mutually detected signal across pairs of detectors is used to calculate the relative angle between the signal source and the center point of the separation between the detectors in the pair. The relative angle is calculated from the TDoA using a mathematical model called the TDoA approximation of the zenith angle (TAZA). The TAZA angle defines the opening angle of a conic region of probability that contains the signal source, produced by each detector pair. The intersecting region of probability is determined from the conic regions of probability and represents the volumetric region with the highest probability of containing the signal source. TCAM was developed and tested using synthetic data in a simulated environment.

Spectral methods for partial differential equations with boundary conditions in complex domains are developed with the help of a fictitious domain approach. For rectangular embedding, spectral-Galerkin formulations with special trial and test functions are presented and discussed, as well as the well-posedness and the error analysis. For circular and annular embedding, dimension reduction is applied and a sequence of 1-D problems with artificial boundary values are solved. Applications of our methods include the fractional Laplace problem and the Helmholtz equations. In numerical examples, our methods show good performance on the boundary value problems in both smooth and polygonal complex domains, and the L2 errors decay exponentially for smooth solutions. For singular problems, high-order convergence rates can also be obtained.