The advent of geometric morphometrics and the revitalization of artificial neural networks have created powerful new tools to classify morphological structures to groups. Although these two approaches have already been combined, there has been less attention on how such combinations perform relative to more traditional methods. Here we use geometric morphometric data and neural networks to identify from which species upper-jaw teeth from carcharhiniform sharks in the genus Carcharhinus originated, and these results are compared to more traditional classification methods. In addition to the methodological applications of this comparison, an ability to identify shark teeth would facilitate the incorporation of shark teeth's vast fossil record into evolutionary studies. Using geometric morphometric data originating from Naylor and Marcus (1994), we built two types of neural networks, multilayer perceptrons and radial basis function neural networks to classify teeth from C. acronotus, C. leucas, C. limbatus, and C. plumbeus, as well as classifying the teeth using linear discriminate analysis. All classification schemes were trained using the right upper-jaw teeth of 15 individuals. Between these three methods, the multilayer perceptron performed the best, followed by linear discriminate analysis, and then the radial basis function neural network. All three classification systems appear to be more accurate than previous efforts to classify Carcharhinus teeth using linear distances between landmarks and linear discriminate analysis. In all three classification systems, misclassified teeth tended to originate either near the symphysis or near the jaw angle, though an additional peak occurred between these two structures. To assess whether smaller training sets would lead to comparable accuracies, we used a multilayer perceptron to classify teeth from the same species but now based on a training set of right upper-jaw teeth from only five individuals. Although not as accurate as the network based on 15 individuals, the network performed favorably. As a final test, we built a multilayer perceptron to classify teeth from C. altimus, C. obscurus, and C. plumbeus, which have more similar upper-jaw teeth than the original four species, based on training sets of five individuals. Again, the classification system performed better than a system that combines linear measurements and discriminate function analysis. Given the high accuracies for all three systems, it appears that the use of geometric morphometric data has a great impact on the accuracy of the classification system, whereas the exact method of classification tends to make less of a difference. These results may be applicable to other systems and other morphological structures. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2013. / November 8, 2013. / Artificial Neural Network, Carcharhinus, Classification, Geometric Morphometrics, Linear Discriminate Analysis, Teeth / Includes bibliographical references. / Dennis E. Slice, Professor Directing Thesis; Anke Meyer-Baese, Committee Member.

Many numerical methods based on Radial Basis Functions (RBFs) are gaining popularity in the geosciences due to their competitive accuracy, functionality on unstructured meshes, and natural extension into higher dimensions. One method in particular, the Radial Basis Function-generated Finite Differences (RBF-FD), is drawing attention due to its comparatively low computational complexity versus other RBF methods, high-order accuracy (6th to 10th order is common), and parallel nature. Similar to classical Finite Differences (FD), RBF-FD computes weighted differences of stencil node values to approximate derivatives at stencil centers. The method differs from classical FD in that the test functions used to calculate the differentiation weights aren-dimensional RBFs rather than one-dimensional polynomials. This allows for generalization ton-dimensional space on completely scattered node layouts. Although RBF-FD was first proposed nearly a decade ago, it is only now gaining a critical mass to compete against well known competitors in modeling like FD, Finite Volume and Finite Element. To truly contend, RBF-FD must transition from single threaded MATLAB environments to large-scale parallel architectures. Many HPC systems around the world have made the transition to Graphics Processing Unit (GPU) accelerators as a solution for added parallelism and higher throughput. Some systems offer significantly more GPUs than CPUs. As the problem size,N, grows larger, it behooves us to work on parallel architectures, be it CPUs or GPUs. In addition to demonstrating the ability to scale to hundreds or thousands of compute nodes, this work introduces parallelization strategies that span RBF-FD across multi-GPU clusters. The stability and accuracy of the parallel implementation is verified through the explicit solution of two PDEs. Additionally, a parallel implementation for implicit solutions is introduced as part of continued research efforts. This work establishes RBF-FD as a contender in the arena of distributed HPC numerical methods. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2013. / November 6, 2013. / High-order finite differencing, Multi-GPU computing, OpenCL, Parallel computing, Radial basis functions, RBF-FD / Includes bibliographical references. / Gordon Erlebacher, Professor Directing Dissertation; Mark Sussman, University Representative; Natasha Flyer, Committee Member; Dennis Slice, Committee Member; Ming Ye, Committee Member; Janet Peterson, Committee Member.

We outline a new approach to objectively locate and define mesoscale oceanic features from satellite derived ocean color data. Modern edge detection algorithms are robust and accurate for most applications, oceanic satellite observations however introduce challenges that foil many differentiation based algorithms. The clouds, discontinuities, noise, and low variability of pertinent data prove confounding. In this work the input data is first quantized using a centroidal voronoi tesselation (CVT), removing noise and revealing the low variable fronts of interest. Clouds are then removed by assuming values of its surrounding neighbors, and the perimeters of these resulting cloudless regions localize the fronts to a small set. We then use the gradient of the quantized data as a compass to walk around the front and periodically select points to be knots for a Hermite spline. These Hermite splines yield an analytic representation of the fronts and provide practitioners with a convenient tool to calibrate their models. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2013. / November 18, 2013. / Edge Detection, Front Detection, Oceanography / Includes bibliographical references. / Gordon Erlebacher, Professor Co-Directing Thesis; Eric Chassignet, Professor Co-Directing Thesis; Ming Ye, Committee Member; Anke Meyer-Baese, Committee Member.

Over the past few decades an increased interest in reduced order modeling approaches has led to its application in areas such as real time simulations and parameter studies among many others. In the context of this work reduced order modeling seeks to solve differential equations using substantially fewer degrees of freedom compared to a standard approach like the finite element method. The finite element method is a Galerkin method which typically uses piecewise polynomial functions to approximate the solution of a differential equation. Wavelet functions have recently become a relevant topic in the area of computational science due to their attractive properties including differentiability and multi-resolution. This research seeks to combine a wavelet-Galerkin method with a reduced order approach to approximate the solution to a differential equation with a given set of parameters. This work will focus on showing that using a reduced order approach in a wavelet-Galerkin setting is a viable option in determining a reduced order solution to a differential equation. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2013. / October 30, 2013. / Daubechies, Finite Element Method, Partial Differential Equation, Proper Orthogonal Decomposition, Reduced Order Modeling, Wavelet / Includes bibliographical references. / Janet Peterson, Professor Directing Thesis; Max Gunzburger, Committee Member; Ming Ye, Committee Member.

We study the evolution of the collapsing core of a 15 solar mass blue supergiant supernova progenitor from the moment shortly after core bounce until 1.5 seconds later. We present a sample of two- and three-dimensional hydrodynamic models parameterized to match the explosion energetics of supernova SN 1987A. We focus on the characteristics of the flow inside the gain region and the interplay between hydrodynamics, self-gravity, and neutrino heating, taking into account uncertainty in the nuclear equation of state. We characterize the evolution and structure of the flow behind the shock in terms the accretion flow dynamics, shock perturbations, energy transport and neutrino heating effects, and convective and turbulent motions. We also analyze information provided by particle tracers embedded in the flow. Our models are computed with a high-resolution finite volume shock capturing hydrodynamic code. The code includes source terms due to neutrino-matter interactions from a light-bulb neutrino scheme that is used to prescribe the luminosities and energies of the neutrinos emerging from the core of the proto-neutron star. The proto-neutron star is excised from the computational domain, and its contraction is modeled by a time-dependent inner boundary condition. We find the spatial dimensionality of the models to be an important contributing factor in the explosion process. Compared to two-dimensional simulations, our three-dimensional models require lower neutrino luminosities to produce equally energetic explosions. We estimate that the convective engine in our models is $4$% more efficient in three dimensions than in two dimensions. We propose that this is due to the difference of morphology of convection between two- and three-dimensional models. Specifically, the greater efficiency of the convective engine found in three-dimensional simulations might be due to the larger surface-to-volume ratio of convective plumes, which aids in distributing energy deposited by neutrinos. We do not find evidence of the standing accretion shock instability in our models. Instead we identify a relatively long phase of quasi-steady convection below the shock, driven by neutrino heating. During this phase, the analysis of the energy transport in the post-shock region reveals characteristics closely resembling that of penetrative convection. We find that the flow structure grows from small scales and organizes into large, convective plumes on the size of the gain region. We use tracer particles to study the flow properties, and find substantial differences in residency times of fluid elements in the gain region between two-dimensional and three-dimensional models. These appear to originate at the base of the gain region and are due to differences in the structure of convection. We also identify differences in the evolution of energy of the fluid elements, how they are heated by neutrinos, and how they become gravitationally unbound. In particular, at the time when the explosion commences, we find that the unbound material has relatively long residency times in two-dimensional models, while in three dimensions a significant fraction of the explosion energy is carried by particles with relatively short residency times. We conduct a series of numerical experiments in which we methodically decrease the angular resolution in our three-dimensional models. We observe that the explosion energy decreases dramatically once the resolution is inadequate to capture the morphology of convection on large scales. Thus, we demonstrated that it is possible to connect successful, energetic, three-dimensional models with unsuccessful three-dimensional models just by decreasing numerical resolution, and thus the amount of resolved physics. This example shows that the role of dimensionality is secondary to correctly accounting for the basic physics of the explosion. The relatively low spatial resolution of current three-dimensional models allows for only rudimentary insights into the role of turbulence in driving the explosion. However, and contrary to some recent reports, we do not find evidence for turbulence being a key factor in reviving the stalled supernova shock. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2014. / April 15, 2014. / Convection, Hydrodynamics, Instabilities, Shock Waves, Supernovae / Includes bibliographical references. / Tomasz Plewa, Professor Directing Dissertation; Mark Sussman, University Representative; Anke Meyer-Baese, Committee Member; Gordon Erlebacher, Committee Member; Ionel M. Navon, Committee Member.

The origins of thermonuclear supernovae remain poorly understood--a troubling fact, given their importance in astrophysics and cosmology. A leading theory posits that these events arise from the merger of white dwarfs in a close binary system. In this study we examine the possibility of prompt ignition, in which a runaway fusion reaction is initiated in the early stages of the merger. We present a set of three-dimensional white dwarf merger simulations performed with the help of a high-resolution adaptive mesh refinement hydrocode. We consider three binary systems of different mass ratios composed of carbon/oxygen white dwarfs with total mass exceeding the Chandrasekhar mass. We additionally explore the effects of mesh resolution on important simulation parameters. We find that two distinct behaviors emerge depending on the progenitor mass ratio. For systems of components with differing masses, a boundary layer forms around the accretor. For systems of nearly equal mass, the merger product displays deep entraintment of each star into the other. We closely monitor thermonuclear burning that begins when sufficiently dense material is shocked during early stages of the merger process. Analysis of ignition times lead us to conclude that for binary systems with components of unequal mass whose combined mass is close to the Chandrasekhar limit, there is a negligible chance of prompt ignition. Simulations of similar systems with a combined mass of 2 solar masses suggest that prompt ignition may be possible, but require further study using higher-resolution. The system with components of nearly equal mass does not seem likely to undergo prompt ignition, and higher resolution simulations are unlikely to change this conclusion. We additionally find that white dwarf merger simulations require high resolution. Insufficient resolution can qualitatively change simulation outcomes, either by smoothing important fluctuations in density and temperature, or by altering the dynamics of the system such that additional physics processes, such as gravity, are incorrectly represented. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Spring Semester, 2014. / April 14, 2014. / Binaries: Close, Hydrodynamics: Instabilities, Stars: Accretion, White Dwarfs, Supernovae:General / Includes bibliographical references. / Tomasz Plewa, Professor Directing Thesis; Mark Sussman, Committee Member; Gordon Erlebacher, Committee Member.

This dissertation studies a graphical processing unit (GPU) construction of Bayesian neural networks (BNNs) using large training data sets. The goal is to create a program for the mapping of phenomenological Minimal Supersymmetric Standard Model (pMSSM) parameters to their predictions. This would allow for a more robust method of studying the Minimal Supersymmetric Standard Model, which is of much interest at the Large Hadron Collider (LHC) experiment CERN. A systematic study of the speedup achieved in the GPU application compared to a Central Processing Unit (CPU) implementation are presented. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2014. / April 1, 2014. / Bayesian Neural Networks, GPU, pMSSM, Scientific Computing / Includes bibliographical references. / Anke Meyer-Baese, Professor Directing Dissertation; Harrison Prosper, Professor Directing Dissertation; Jorge Piekarewicz, University Representative; Sachin Shanbhag, Committee Member; Peter Beerli, Committee Member.

Metadynamics is a popular tool to explore free energy landscapes and it has been use to elucidate various chemical or biochemical processes. The height of updating Gaussian function is very important for proper free energy convergence to the target free energy surface. Both higher and lower Gaussian heights have advantages and disadvantages, a balance is required. This thesis presents the implementation of the Wang-Landau recursion scheme in metadynamics simulations to adjust the height of the unit Gaussian function. Compared with classical fixed Gaussian heights, this dynamic adjustable method was demonstrated to efficiently yield better converged free energy surfaces. In addition, through combination with the realization of an energy space random walk, the Wang-Landau recursion scheme can be readily used to deal with the pseudoergodicity problem in molecular dynamic simulations. The use of this scheme is proven to efficiently and robustly obtain a biased free energy function within this thesis. / A Thesis Submitted to the School of Computational Science in Partial FulfiLlment of the Requirements for the Degree of Master of Science. / Summer Semester, 2008. / June 20, 2008. / Essential Energy Space Random Walk, Metadynamics Simulations, Wang-Landau Method / Includes bibliographical references. / Wei Yang, Professor Directing Thesis; Gordon Erlebacher, Committee Member; Janet Peterson, Committee Member.

Estimating groundwater nitrate fate and transport is an important task in water resources and environmental management because excess nitrate loads may have negative impacts on human and environmental health. This work discusses the development of a simplified nitrate transport model and its implementation as a geographic information system (GIS)-based screening tool, whose purpose is to estimate nitrate loads to surface water bodies from onsite wastewater-treatment systems (OWTS). Key features of this project are the reduced data demands due to the use of a simplified model, as well as ease of use compared to traditional groundwater flow and transport models, achieved by embedding the model within a GIS. The simplified conceptual model consists of a simplified groundwater flow model in the surficial aquifer, and a simplified transport model that makes use of an analytical solution to the advection-dispersion equation, used for determining nitrate fate and transport. Denitrification is modeled using first order decay in the analytical solution with the decay constant obtained from literature and/or site-specific data. The groundwater flow model uses readily available topographic data to approximate the hydraulic gradient, which is then used to calculate seepage velocity magnitude and direction. The flow model is evaluated by comparing the results to a previous numerical modeling study of the U.S. Naval Air Station, Jacksonville (NAS) performed by the USGS. The results show that for areas in the vicinity of the NAS, the model is capable of predicting groundwater travel times from a source to a surface water body to within ±20 years of the USGS model, 75% of the time. The transport model uses an analytical solution based on the one by Domenico and Robbins (1985), the results of which are then further processed so that they may be applied to more general, real-world scenarios. The solution, as well as the processing steps are tested using artificially constructed scenarios, each meant to evaluate a certain aspect of the solution. For comparison purposes, each scenario is solved using a well known numerical contaminant transport model. The results show that the analytical solution provides a reasonable approximation to the numerical result. However, it generally underestimates the concentration distribution to varying degrees depending on choice of parameters, especially along the plume centerline. These results are in agreement with previous studies (Srinivasan et al., 2007; West et al., 2007). The adaptation of the analytical solution to more realistic scenarios results in an adequate approximation to the numerically calculated plume, except in areas near the advection front, where the model produces a plume whose shape differs noticeably from the numerical solution. Load calculations are carried out using a mass balance approach where the system is considered to be in the steady state. The steady-state condition allows for a load estimate by subtracting the mass removal rate due to denitrification from the input mass rate. The input mass rate is calculated by taking into account advection and dispersion while the mass removal rate due to denitrification is calculated from the definition of a first order reaction. Comparison with the synthetic scenarios of the transport model shows that for the test cases, when decay rates are low, the model agrees well with the load calculation from the numerical model. As decay rates increase and the plume becomes shorter, the input load is overestimated by about 9% in the test cases and the mass removed due to denitrification is underestimated by 30% in the worst case. These results are likely due to the underestimation of concentration values by the analytical solution of the transport model. / A Thesis Submitted to the Department of Scientific Computing in Partial Fulfillment of the Requirements for the Degree of Master of Science. / Fall Semester, 2010. / October 22, 2010. / Simplified model, Denitrification, OWTS, GIS, Septic tank, Contaminant transport, Nitrate contamination / Includes bibliographical references. / Ming Ye, Professor Directing Thesis; Janet Peterson, Committee Member; Sachin Shanbhag, Committee Member; James Wilgenbusch, Committee Member.

In this thesis, we discuss the development of a new Boids system that simulates flocking behavior inside the Blender Game Engine and within the framework of the Real-Time Par- ticles System (RTPS) library developed by Ian Johnson. The collective behavior of Boids is characterized as an emergent behavior caused by following three steering behaviors: sep- aration, alignment, and cohesion. The implementation leverages OpenCL to maintain the portability of the Blender across different graphics cards and operating systems. Bench- marks of the RTPS-FLOCK system show that our implementation speeds up Blender's original Boids implementation (which only runs outside the game engine) by more than an order of magnitude. We demonstrate our boids system in three ways. First, we illustrate how symmetry of the steering behavior is maintained in time. Second, we consider the behavior of a "swarm of bees" approaching their hive. And third, we simulate the motion of a "crowd" constrained to a two-dimensional plane. / A Thesis Submitted to the Department of ScientifiC Computing in Partial FulfiLlment of the Requirements for the Degree of Master of Science. / Summer Semester, 2011. / June 24, 2011. / RTPS, Blender, boids, flocking / Includes bibliographical references. / Gordon Erlebacher, Professor Directing Thesis; Ming Ye, Committee Member; Xiaoqiang Wang, Committee Member.