Bertha N. Langley / Typescript / M.S. Florida State College for Women 1914 / Includes bibliographical references

No description available.

No description available.

>Magister Scientiae - MSc / The thesis aims to determine the depositional environments, rock types and petrophysical characteristics of the reservoirs in Wells E-S3, E-S5 and F-AH4 of Area X in the Bredasdorp Basin, offshore South Africa. The three wells were studied using methods including core description, petrophysical analysis, seismic facies and multivariate statistics in order to evaluate their reservoir potential. The thesis includes digital wireline log signatures, 2D seismic data, well data and core analysis from selected depths. Based on core description, five lithofacies were identified as claystone (HM1), fine to coarse grained sandstone (HM2), very fine to medium grained sandstone (HM3), fine to medium grained sandstone (HM4) and conglomerate (HM5). Deltaic and shallow marine depositional environments were also interpreted from the core description based on the sedimentary structures and ichnofossils. The results obtained from the petrophysical analysis indicate that the sandstone reservoirs show a relatively fair to good porosity (range 13-20 %), water saturation (range 17-45 %) and a predicted permeability (range 4- 108 mD) for Wells E-S3, E-S5 andF-AH4. The seismic facies model of the study area shows five seismic facies described as parallel, variable amplitude variable continuity, semi-continuous high amplitude, divergent variable amplitude and chaotic seismic facies as well as a probable shallow marine, deltaic and submarine fan depositional system. Linking lithofacies to seismic facies maps helped to understand and predict the distribution and quality of reservoir packages in the studied wells. Multivariate statistical methods of factor, discriminant and cluster analysis were used. For Wells E-S3, E-S5 and F-AH4, two factors were derived from the wireline log data reflecting oil and non- oil bearing depths. Cluster analysis delineated oil and non-oil bearing groups with similar wireline properties. This thesis demonstrates that the approach taken is useful because petrophysical analysis, seismic facies and multivariate statistics has provided useful information on reservoir quality such as net to gross, depths of hydrocarbon saturation and depositional environment.

Estimating parameters for reactive contaminant transport models can be a very computationally intensive. Typically this involves solving a forward problem many times, with many degrees of freedom that must be computed each time. We show that reduced order modeling (ROM) by proper orthogonal decomposition (POD) can be used to approximate the solution to the forward model using many fewer degrees of freedom. We provide background on the finite element method and reduced order modeling in one spatial dimension, and apply both methods to a system of linear uncoupled time-dependent equations simulating reactive transport in a column. By comparing the reduced order and finite element approximations, we demonstrate that the reduced model, while having many fewer degrees of freedom to compute, gives a good approximation of the high-dimensional (finite element) model. Our results indicate that one may substitute a reduced model in place of a high-dimensional model to solve the forward problem in parameter estimation with many fewer degrees of freedom. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2011. / November 4, 2011. / column experiment, computational hydrology, parameter estimation, proper orthogonal decomposition, reactive transport, reduced order modeling / Includes bibliographical references. / Janet Peterson, Professor Directing Thesis; Ming Ye, Professor Co-Directing Thesis; Sachin Shanbhag, Committee Member.

Groundwater systems are open and complex, rendering them prone to multiple conceptual interpretations and mathematical descriptions. When multiple models are acceptable based on available knowledge and data, model uncertainty arises. One way to assess the model uncertainty is postulating several alternative hydrologic models for a site and using model selection criteria to (1) rank these models, (2) eliminate some of them, and/or (3) weight and average predictions statistics generated by multiple models based on their model probabilities. This multimodel analysis has led to some debate among hydrogeologists about the merits and demerits of common model selection criteria such as AIC, AICc, BIC, and KIC. This dissertation contributes to the discussion by comparing the abilities of the two common Bayesian criteria (BIC and KIC) theoretically and numerically. The comparison results indicate that, using MCMC results as a reference, KIC yields more accurate approximations of model probability than does BIC. Although KIC reduces asymptotically to BIC, KIC provides consistently more reliable indications of model quality for a range of sample sizes. In the multimodel analysis, the model averaging predictive uncertainty is a weighted average of predictive uncertainties of individual models. So it is important to properly quantify individual model's predictive uncertainty. Confidence intervals based on regression theories and credible intervals based on Bayesian theories are conceptually different ways to quantify predictive uncertainties, and both are widely used in groundwater modeling. This dissertation explores their differences and similarities theoretically and numerically. The comparison results indicate that given Gaussian distributed observation errors, for linear or linearized nonlinear models, linear confidence and credible intervals are numerically identical when consistent prior parameter information is used. For nonlinear models, nonlinear confidence and credible intervals can be numerically identical if parameter confidence and credible regions based on approximate likelihood method are used and intrinsic model nonlinearity is small; but they differ in practice due to numerical difficulties in calculating both confidence and credible intervals. Model error is a more vital issue than differences between confidence and credible intervals for individual models, suggesting the importance of considering alternative models. Model calibration results are the basis for the model selection criteria to discriminate between models. However, how to incorporate calibration data errors into the calibration process is an unsettled problem. It has been seen that due to the improper use of the error probability structure in the calibration, the model selection criteria lead to an unrealistic situation in which one model receives overwhelmingly high averaging weight (even 100%), which cannot be justified by available data and knowledge. This dissertation finds that the errors reflected in the calibration should include two parts, measurement errors and model errors. To consider the probability structure of the total errors, I propose an iterative calibration method with two stages of parameter estimation. The multimodel analysis based on the estimation results leads to more reasonable averaging weights and better averaging predictive performance, compared to those with considering only measurement errors. Traditionally, data-worth analyses have relied on a single conceptual-mathematical model with prescribed parameters. Yet this renders model predictions prone to statistical bias and underestimation of uncertainty and thus affects the groundwater management decision. This dissertation proposes a multimodel approach to optimum data-worth analyses that is based on model averaging within a Bayesian framework. The developed multimodel Bayesian approach to data-worth analysis works well in a real geostatistical problem. In particular, the selection of target for additional data collection based on the approach is validated against actual data collected. The last part of the dissertation presents an efficient method of Bayesian uncertainty analysis. While Bayesian analysis is vital to quantify predictive uncertainty in groundwater modeling, its application has been hindered in multimodel uncertainty analysis because of computational cost of numerous models executions and the difficulty in sampling from the complicated posterior probability density functions of model parameters. This dissertation develops a new method to improve computational efficiency of Bayesian uncertainty analysis using sparse-grid method. The developed sparse-grid-based method for Bayesian uncertainty analysis demonstrates its superior accuracy and efficiency to classic importance sampling and MCMC sampler when applied to a groundwater flow model. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2012. / March 29, 2012. / Bayesian model averaging, Data worth, Model selection criteria, Multimodel analysis, Uncertainty measure / Includes bibliographical references. / Ming Ye, Professor Directing Dissertation; Xufeng Niu, University Representative; Peter Beerli, Committee Member; Gary Curtis, Committee Member; Michael Navon, Committee Member; Tomasz Plewa, Committee Member.

In the last 15 years, Video games have become a dominate form of entertainment. The popularity of video games means children are spending more of their free time play video games. Usually, the time spent on homework or studying is decreased to allow for the extended time spent on video games. In an effort to solve the problem, researchers have begun creating educational video games. Some studies have shown a significant increase in learning ability from video games or other interactive instruction. Educational games can be used in conjunction with formal educational methods to improve the retention among students. To facilitate the creation of games for science education, the RTPS library was created by Ian Johnson to simulate fluid dynamics in real-time. This thesis seeks to extend the RTPS library, to provide more realistic simulations. Rigid body dynamics have been added to the simulation framework. In addition, a two-way coupling between the rigid bodies and fluids have been implemented. Another contribution to the library, was the addition of fluid surface rendering to provide a more realistic looking simulation. Finally, a Qt interface was added to allow for modification of simulation parameters in real-time. In order to perform these simulations in real-time one must have a significant amount of computational power. Though processing power has seen consistent growth for many years, the demands for higher performance desktops grew faster than CPUs could satisfy. In 2006, general purpose graphics processing(GPGPU) was introduced with the CUDA programming language. This new language allowed developers access to an incredible amount of processing power. Some researchers were reporting up to 10 times speed-ups over a CPU. With this power, one can perform simulations on their desktop computers that were previously only feasible on super computers. GPGPU technology is utilized in this thesis to enable real-time simulations. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2012. / September 4, 2012. / Fluid Dynamics, Fluid Rendering, GPGPU, Physics Simulation, Real-Time, SPH / Includes bibliographical references. / Gordon Erlebacher, Professor Directing Thesis; Tomasz Plewa, Committee Member; Sachin Shanbhag, Committee Member.

This work focuses on developing and analyzing novel, efficient sparse-grid algorithms for solving several types of stochastic ordinary/partial differential equations and corresponding inverse problem, such as parameter identification. First, we consider linear parabolic partial differential equations with random diffusion coefficients, forcing term and initial condition. Error analysis for a stochastic collocation method is carried out in a wider range of situations than previous literatures, including input data that depend nonlinearly on the random variables and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate the exponential decay of the interpolation error in the probability space for both semi-discrete and fully-discrete solutions. Second, we consider multi-dimensional backward stochastic differential equations driven by a vector of white noise. A sparse-grid scheme are proposed to discretize the target equation in the multi-dimensional time-space domain. In our scheme, the time discretization is conducted by the multi-step scheme. In the multi-dimensional spatial domain, the conditional mathematical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and adaptive hierarchical sparse-grid interpolation. Error estimates are rigorously proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Third, we investigate the propagation of input uncertainty through nonlocal diffusion models. Since the stochastic local diffusion equations, e.g. heat equations, have already been well studied, we are interested in extending the existing numerical methods to solve nonlocal diffusion problems. In this work, we use sparse-grid stochastic collocation method to solve nonlocal diffusion equations with colored noise and Monte-Carlo method to solve the ones with white noise. Our numerical experiments show that the existing methods can achieve the desired accuracy in the nonlocal setting. Moreover, in the white noise case, the nonlocal diffusion operator can reduce the variance of the solution because the nonlocal diffusion operator has "smoothing" effect on the random field. At last, stochastic inverse problem is investigated. We propose sparse-grid Bayesian algorithm to improve the efficiency of the classic Bayesian methods. Using sparse-grid interpolation and integration, we construct a surrogate posterior probability density function and determine an appropriate alternative density which can capture the main features of the true PPDF to improve the simulation efficiency in the framework of indirect sampling. By applying this method to a groundwater flow model, we demonstrate its better accuracy when compared to brute-force MCMC simulation results. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester, 2012. / June 22, 2012. / Beysian analysis, inverse problem, nonlocal diffusion, sparse grid, stochastic differential equations, uncertainty quantification / Includes bibliographical references. / Max D. Gunzburger, Professor Directing Dissertation; Xiaoming Wang, University Representative; Janet Peterson, Committee Member; Xiaoqiang Wang, Committee Member; Ming Ye, Committee Member; Clayton Webster, Committee Member; John Burkardt, Committee Member.

Reduced Order Models (ROM) provide a low-dimensional alternative form of a system of differential equations. Such a form permits faster computation of solutions. In this paper, Poisson's Equation in two dimensions, the Heat Equation in one dimension, and a Nonlinear Reaction-Diffusion equation in one dimension are solved using the Galerkin formulation of the Finite Element Method (FEM) in conjunction with Newton's Method. Reduced Order Modeling (ROM) by Proper Orthogonal Decomposition (POD) is then used to accelerate the solution of successive linear systems required by Newton's Method. This is done to show the viability of the method on a simple problem. The Navier-Stokes (NS) Equations are introduced and solved by FEM. A ROM using both POD and clustering by Centroidal Voronoi Tesselation (CVT) are then used to solve the NS equations, and the results are compared with the FEM solution. The specific NS problem we consider has inhomogeneous Dirichlet boundary conditions and the treatment of the boundary conditions is explained. The resulting decrease in computation time required for solving the various equations are compared with ROM methods. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2012. / October 5, 2012. / Finite Element Methods, Navier-Stokes Equations, Nonlinear PDEs, Reduced Order Modeling / Includes bibliographical references. / Janet Peterson, Professor Directing Thesis; Tomasz Plewa, Committee Member; Sachin Shanbhag, Committee Member.

This dissertation presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT) which are to be used for multiphysics, multidomain applications. As an introduction, we discuss grid generation on the sphere in a broad fashion. Next, we discuss the theory of CVTs in general, and specifically on the sphere. Subsequently we consider the iterative processes, such as Lloyd's algorithm, which are used to construct them. Following this, we describe a method for density functions via images so that we can shape generator density in an intuitive, yet arbitrary, manner, and then a method by which SCVTs can be easily adapted to conform to arbitrary sets of line segments, or shorelines. Then, we discuss sample meshes, used for various physical and nonphysical applications. Penultimately, we discuss two sample applications, as a proof of concept, where we adapt the Shallow Water Model from Model for Predictions Across Scales (MPAS) to use our grids for a more accurate border, and we also discuss elliptic interface problems both with and without hanging nodes. Finally, we share a few concluding remarks. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2011. / November 3, 2011. / Includes bibliographical references. / Max Gunzburger, Professor Co-Directing Dissertation; Janet Peterson, Professor Co-Directing Dissertation; Kyle Gallivan, University Representative; Gordon Erlebacher, Committee Member; Xiaoqiang Wang, Committee Member; Todd Ringler, Committee Member.