Physical Sciences and Mathematics Commons^™

The Compact Implicit Integration Factor Scheme For The Solution Of Allen-Cahn Equations, Meshack K. Kiplagat

Theses and Dissertations

In this thesis we apply the compact implicit integration factor (cIIF) scheme towards solving the Allen-Cahn equations with zero-flux or periodic boundary conditions. The Allen-Cahn equation is a second-order nonlinear PDE which has been the focus of many applications spanning a wide range of fields, such as in material science where it was first introduced to model the phase separation of two metallic alloys, and in biology to study population dynamics, just to name a few. The compact implicit integration method works by first transforming the PDE into a system of ODEs by discretizing the spatial derivatives using the central …

Trace-Element And Physical Response To Melt Percolation In Summit (Greenland) Snow, Gifford J. Wong, Robert L. Hawley, Eric R. Lutz, Erich C. Osterberg

Dartmouth Scholarship

Surface melt on a glacier can perturb the glaciochemical record beyond the natural variability. While the centre of the Greenland ice sheet is usually devoid of surface melt, many high- Arctic and alpine ice cores document frequent summertime melt events. Current hypotheses interpreting melt-affected ice-core chemistry rely on preferential elution of certain major ions. However, the precise nature of chemistry alteration is unknown because it is difficult to distinguish natural variability from melt effects in a perennially melt-affected site. We use eight trace-element snow chemistry records recovered from Summit, Greenland, to study spatial variability and melt effects on insoluble trace …

Motion And Rigidity Of The Caribbean Plate And Geodetic Observations Of Dominica, Lesser Antilles, Jamie Annette Miller

Earth & Environmental Sciences Dissertations

The currently accepted kinematic model of the Caribbean plate presented by DeMets et al. (2007), is based on velocities from 6 continuous and 14 campaign GPS sites. This work attempts to refine the current plate model by evaluating data from an expanded number of stations with an improved spatial distribution. As a measure to better constrain the eastern margin, a study has been conducted on the island of Dominica which includes campaign GPS data collected over the last decade. The analysis of data from 117 sites includes campaign data in addition to the data from the continuous GPS stations that …

Appalachian Delta Plain Paleoecology Of The Cretaceous Woodbine Formation At The Arlington Archosaur Site, North Texas, Derek Jason Main

Earth & Environmental Sciences Dissertations

The Arlington Archosaur Site (AAS) is a North Texas fossil locality that preserves a Mid- Cretaceous ecosystem along a low lying coastal plain. The site lies within the Cenomanian (95 Mya) rocks of the Woodbine Formation in North Arlington, Tarrant County, TX. The depositional environment of the AAS is a coastal delta plain, principally a peat bog. The vertebrates recovered from the AAS include dinosauria (ornithopod and theropod), crocodyliform, chelonian and dipnoan. A large, nearly complete crocodyliform was excavated in the summer of 2009, and proved to be a new taxon; Deltasuchus motherali. The name of the new taxon was …

Dns Study For The Origin Of The Chaos In Late Boundary Layer Transition Over A Flat Plate, Manoj Kumar Thapa

Mathematics Dissertations

This dissertation is devoted to the investigation of the origin and mechanism of chaos ( asymmetric or disorganized flow) in late boundary layer transition over a flat plate without pressure gradient. This kind of flow not only exists at the very late stage of transition but also is a crucial component for turbulence formation- still not well understood. According to existing theories, the formation of the chaos in late boundary layer transition was considered due to big background disturbances (noises) and use of non-periodic spanwise boundary condition during numerical simulations. It was further assumed that universal coherent structures (ring-like vortices) …

Numerical Integration Of Matrix Riccati Differential Equations With Solution Singularities, Charles K. Garrett

Mathematics Dissertations

A matrix Riccati differential equation (MRDE) is a quadratic ODE of the form X' = A₂₁ + A₂₂X - XA₁₁ - XA₁₂X ; where X is a function of t with X : R Rnxm and the Aij's are constant or functions of t with matrix sizes to respect the size of X. It is well known that MRDEs may have singularities in their solution even if all the Aij are constant. In this dissertation, several di erent ideas for the meaning of the solution of an MRDE past a solution singularity are analyzed and it is shown how all …

Smooth Quantile Processes For Right Censored Data, Katsuhiro Uechi

Mathematics Dissertations

The development of an estimator of a quantile function Q(p) is discussed. The smooth nonparametric estimator Qn(p) of a quantile function Q(p) is defined as the solution to Fn(Qn(p)) = p, where Fn is a smooth Kaplan-Meier estimator of an unknown continuous distribution function F(x). The asymptotic properties of the smooth quantile process, n(Qn(p) - Q(p)) , based on right censored lifetimes are studied. The asymptotic properties of the bootstrap quantile process, n(Q n(p) - Q(p)) are also investigated and shown to have the same limiting distribution as the smooth quantile process. The bootstrap method to approximate the sampling distribution …

Effects Of Discrete Time Delays And Parameters Variation On Dynamical Systems, Ibrahim Oumar Diakite

Mathematics Dissertations

To understand the effects of discrete time delays and of parameters variation on certain biological system models, we first consider a Delay Differential Equation model of human immunodeficiency virus (HIV). We investigate the effects of the discrete time on the virulence of the HIV strain, and present sufficient and necessary condition for the virulence of the pathogen to change as the time delay changes. We also consider the same delay differential model for HIV infection, and we investigate analytically and numerically the stability of the endemically infected equilibrium. Our analysis shows that certain key parameters, such as the rate of …

Haplotype-Based Statistical Inference For Case-Control Genetic Association Studies With Complex Sampling, Daoying Lin

Mathematics Dissertations

With the advances in human genome research, it is now believed that the risks of many complex diseases are triggered by the interplay of genetic susceptibilities and environmental exposures. The population-based case-control study (PBCCS) is widely used to investigate the role of genetic variants and environmental exposures in the etiology of complex diseases. There are numerous ways to implement the selection process of cases and controls. In its simplest form, a simple random sampling (SRS) design is used to choose cases and controls from diseased and disease-free population, respectively. Though SRS is easy to conduct and relevant statistical methodologies are …

The Polynomial Chaos Method With Applications To Random Differential Equations, Juan Antonio Licea Salazar

Mathematics Dissertations

The role of randomness in mathematical models is of paramount importance, with emphasis placed upon the accuracy and reliability of predictions a rational approach is the use of differential equations with random parameters to describe natural phenomena. Well known methods such as Monte Carlo methods and the method of moments have been implemented to approximate the solutions to random differential equations in the last few decades. In this work, analytic solutions to a particular Riccati type dierential equation and discrete delay dierential equation with random coefficients are derived, also, due to its spectral rate of convergence and simplicity, the polynomial …

Applications And Adaptations Of A Globally Convergent Numerical Method In Inverse Problems, Aubrey Rhoden

Mathematics Dissertations

In our terminology "globally convergent numerical method" means a numerical method whose convergence to a good approximation of the correct solution is independent of the initial approximation in inverse problems. A numerical imaging algorithm has been proposed to solve a coecient inverse problem for an elliptic equation and then the algorithm is validated with the data generated by computer simulation. Previouswork in this eld was focused on the steady-state optical problem with multiple source positions moving along a straight line as well as the frequency domain problem with sweeping frequency. This work includes the steady-state thermal tomography problem with multiple …

The Generalized Two-Component Hunter-Saxton System, Byungsoo Moon

Mathematics Dissertations

This thesis is concerned with the generalized two-component Hunter-Saxton system. In the periodic setting, we study the wave-breaking phenomenon and global existence for the generalized two-component Hunter-Saxton system. We obtain a brief derivation of the model. We also briefly sketch a standard local well-posednessresult using Kato's semigroup approach. We establish a wave-breaking criterion for solutions and some interesting results of wave-breaking solutions with certain initial profiles. We demonstrate the exact blow-up rate of strong solutions. Finally, we give a sufficient condition for global solutions.

High Order Numerical Schemes For Pdes And Applications To Cfd, Huankun Fu

Mathematics Dissertations

In the past two decades, many efforts have been made in developing high-order schemes with high resolution, such as compact scheme, essentially non-oscillatory scheme (ENO), weighted essentially non-oscillatory scheme (WENO).The present dissertation comprises the analysis and numerical testing of two high order methods. The first one refers to the modification of pseudo spectral method which can be used to partial differential equations(PDEs) with non-periodic boundary conditions. The second one is in high order finite difference class and is the mixing of weighted non-oscillatory scheme and compact scheme (MWCS) with using global weights instead of local ones. Numerical tests are performed …

Numerical Studies For M-Matrix Algebraic Riccati Equations, Weichao Wang

Mathematics Dissertations

A new doubling algorithm - Alternating-Directional Doubling Algorithm (ADDA) - is developed for computing the unique minimal nonnegative solution of an M-Matrix Algebraic Riccati Equation (MARE). It is argued by both theoretical analysis and numerical experiments that ADDA is always faster than two existing doubling algorithms - SDA of Guo, Lin, and Xu (Numer. Math., 103 (2006), pp. 393-412) and SDA-ss of Bini, Meini, and Poloni (Numer. Math., 116 (2010), pp. 553-578) for the same purpose. A deflation technique is then presented for an irreducible singular M-matrix Algebraic Riccati Equation (MARE). The technique improves the rateof convergence of a doubling …

Comparison Of Bayesian Nonparametric Density Estimation Methods, Adel Bedoui

Open Access Theses & Dissertations

Density estimation has a long history in statistics. There are two main approaches to density, estimation parametric and nonparametric. The first approach requires specification of a family of densities f and estimation of the unknown parameter $\theta$ using a suitable estimation method, for example, maximum likelihood estimation. This approach may be prone to bias that arises from either estimation of the parameter or from incorrect specification of the probability distribution. The second approach, does not assume a specific parametric family.

In this thesis, we implement three density estimation methods that use Bayesian nonparametric approaches utilizing Markov Chain Monte Carlo methods. …

Software Development For A 3d Gravity Inversion And Application To Study Of The Border Ranges Fault System, South-Central Alaska, Rolando Cardenas

Open Access Theses & Dissertations

The Border Ranges Fault System (BRFS) bounds the Cook Inlet and Susitna Basins, and is an important petroleum province within south-central Alaska. A primary goal of our research is to test several plausible models of structure along the BRFS using a novel three-dimensional inversion technique utilizing gravity data, constrained with other geophysical, borehole and surface geological information. This research involves the development of 3D inversion modeling software using C++ Builder from Embarcadero's XE2 Suite. The novel inversion approach directly models known geology with a priori uncertainties assigned to the geologic model to allow researchers to compare alternative interpretations. This technique …

Improved Efficiency Of Rna Secondary Structure Prediction Using Distributed Computing, Gerardo A. Cardenas

Open Access Theses & Dissertations

The rapidly growing amounts of available biomolecular sequence data, which may represent information from small gene fragments to large complete genomes, have led to the a great need for powerful computational resources for data analysis and storage. With the decoding of the human and other genomes, RNA secondary structure prediction has become an important area of interest in biology and medicine because they help in understanding the mechanisms of many biological processes such as gene regulation and viral replication, and in designing RNA-based therapies to treat various diseases. Due to the complexity of their algorithms, many existing and upcoming computational …

A Declarative Domain Independent Approach For Querying And Generating Visualizations, Nicholas Ricky Del Rio

Open Access Theses & Dissertations

Constructing visualizations using modular visualization environments (MVEs) requires knowledge about visualization transformation theory as well as implementation specific details about how to programmatically chain together relevant sets of modules into pipe and filter-like architectures known as pipelines. Constructing visualization pipelines introduces a number of challenges including: understanding how to transform raw data into forms that can be ingested by MVEs, identifying target modules that map data into graphical data, and understanding how to further transform resulting graphical data into forms that can be presented. Users typically must immerse themselves in a deluge of documentation and usage examples before becoming proficient …

Automatic Memory Management Policies For Low Power, Memory Limited, And Delay Intolerant Devices, Md Abu Jahid

Open Access Theses & Dissertations

Mobile devices such as smartphones and tablets are energy and memory limited, and implement graphical user interfaces that are intolerant of computational delays. Mobile device platforms supporting apps implemented in languages that require automatic memory man- agement, such as the Dalvik (Java) virtual machine within Google's Android, have become dominant. It is essential that automatic memory management avoid causing unacceptable interface delays while responsibly managing energy and memory resource usage. Dalvik's automatic memory management policies for heap growth and garbage collection scheduling utilize heuristics tuned to minimize memory footprint. These policies result in only marginally acceptable response times and garbage …

Model Fusion: A New Approach To Processing Heterogeneous Data, Omar Ochoa

Open Access Theses & Dissertations

In many practical situations, it is necessary to extract

information from data of different types. For example, in geosciences, several sources of data can be used to determine the interior structure of the earth: the first arriving waves from earthquakes and from man-made sources, measurements of the earth's gravity field, measurements of the dispersion of surface waves generated by earthquakes, etc. At present, most existing data processing techniques deal only with data of one type.

A joint use of all the information derived from multiple types of data sources is an important theoretical and practical challenge. Such a joint use …

Geochemical Characterization Of Mineral Dust Sources In The Chihuahuan Desert And Southern High Plains Regions, Porfirio Peinado

Open Access Theses & Dissertations

The Chihuahuan Desert (northern Chihuahua, southern New Mexico, and far west Texas) and the southern High Plains (west Texas and eastern New Mexico) regions have been identified as one of the most persistent dust producing regions of North America. Regional-scale dust storms have been observed by satellite imagery to identify sources of dust, resulting in collection and examination of physical soil samples to better understand the source signatures (geochemical characteristics) of dust origins in these two regions.

The soil characteristics were examined through several techniques: Particle Size Distribution, X-Ray Diffraction (XRD), Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES), and Total …

Unconstrained L1 Optimization With Applications To Signal And Image Processing, Carlos Andres Ramirez

Open Access Theses & Dissertations

In recent years, the applied mathematical community has witnessed a revolution that is changing the paradigm of classical signal and image processing. Novel and e efficient numerical algorithms have emerged for solving new challenges in large scale signal retrieval, where both constrained and unconstrained L1 minimization methods play a fundamental role.

In this work, we present a new methodology for solving unconstrained L1 minimization problems in the context of image and signal processing. Our approach consists in solving a sequence of relaxed unconstrained minimization problems depending on a positive regularization parameter that converges to zero. The optimality conditions of each …

Developing A Sustainable Ecotourism Foundation In Indonesian National Parks Using Cross-Cultural Adaptation And Communication Framing, Adriana Salas

Open Access Theses & Dissertations

Previous research on ecotourism in Southeast Asia has focused on its positive and negative effects for conservation. However, the focus in this particular study is to look at what it takes to run a successful ecotourism site in four diverse areas in Indonesia using communication elements like cross-cultural adaptation and communication framing. Communication should be used as a baseline for a successful site and should be used as the most useful tool to address issues and challenges in ecotourism project development.

A successful ecotourism site must carefully look at how their ideas and programs are framed. Ecotourism must also create …

Evaluation Of Emission Control Strategies To Reduce Ozone Pollution In The Paso Del Norte Region Using A Photochemical Air Quality Modeling System, Victor Hugo Valenzuela

Open Access Theses & Dissertations

Air pollution emissions control strategies to reduce ozone precursor pollutants are analyzed by applying a photochemical modeling system. Simulations of air quality conditions during an ozone episode which occurred in June, 2006 are undertaken by increasing or reducing area source emissions in Ciudad Juárez, Chihuahua, Mexico.

Two air pollutants are primary drivers in the formation of tropospheric ozone. Oxides of nitrogen (NOx) and volatile organic compounds (VOC) undergo multiple chemical reactions under favorable meteorological conditions to form ozone, which is a secondary pollutant that irritates respiratory systems in sensitive individuals especially the elderly and young children.

The U.S. Environmental Protection …

Interaction Of Ceo2 And Zno Nanoparticles Towards The Symbiotic Association Of Alfalfa (Medicago Sativa) And Sinorhizobium Meliloti In Soil, Susmita Bandyopadhyay

Open Access Theses & Dissertations

The production of engineered nanoparticles (ENPs) has rapidly increased due to their wide range of applications in the field of electronics, medicine, chemistry and biology. Consequently, concerns have risen about the environmental release and potential negative impact of NPs. A few reports have described the effects of TiO2 NPs and quantum dots upon nitrogen fixing bacteria. However, the understanding of the interaction of NPs in plant-microbe interface (symbiotic association), like alfalfa (Medicago sativa L.)-Sinorhizobium meliloti, is still in its infancy. Alfalfa is the world's most important forage crop. It grows in association with S. meliloti, which is very important in …

Olivine Ca Content Measured By Icp-Oes To Estimate P-T, Bradley Benavides

Open Access Theses & Dissertations

Ca is a trace element in olivine and its concentration is pressure and temperature dependent, providing a rare opportunity to estimate pressure conditions at which mantle-derived rocks (xenoliths) last equilibrated. This P-T dependence has previously been calibrated for mantle xenoliths, and we applied this technique to samples from Jasper Seamount (Jasper Seamount), an oceanic intraplate volcano (OIV) off the coast of the Baja California Peninsula of Mexico. Preliminary compositions for xenoliths from this location appear to define a magmatic plumbing system that features magma storage near the bottom of the crust. A more detailed analysis of the samples is required …

Lead And Associated Heavy Metal Distribution In Ciudad Juarez, Mexico, Samia Elfituri Grimida

Open Access Theses & Dissertations

Concern over the extent and sources of heavy metals exposure has arisen worldwide since their significant effects have been discovered in the environment. There is general agreement that research is needed to examine the residual lead and its association to heavy metals contamination in soil and quantify the health hazards. This research was directed to quantify and document the geographic distribution of lead and associated heavy metals concentration in Ciudad Juarez, Mexico. Lead, cadmium, chromium, zinc, and copper were selected to analysis. The soil samples used in this research were collected during a previous Encountors Binational Community Lead Study (RO1ES …

Efficient, Scalable, Parallel, Matrix-Matrix Multiplication, Enrique Portillo

Open Access Theses & Dissertations

For the past decade, power/energy consumption has become a limiting factor for large-scale and embedded High Performance Computing (HPC) systems. This is especially true for systems that include accelerators, e.g., high-end computing devices, such as Graphics Processing Units (GPUs), with terascale computing capabilities and high power draws that greatly surpass that of multi-core CPUs. Accordingly, improving the node-level power/energy efficiency of an application can have a direct and positive impact on both classes of HPC systems.

The research reported in this thesis explores the use of software techniques to enhance the execution-time and power-consumption performance of applications executed on a …

Estimating Variations In Locking Depth For The Mojave Segment Of The San Andreas Fault Over The Past 1500 Years From Paleoseismic Stress Drop, Teira Solis

Open Access Theses & Dissertations

The most fundamental model for characterizing earthquake occurrence [Reid, 1910] assumes a constant stress accumulation rate on a locked fault segment, which eventually fails at a threshold stress level. While this model provides a conceptual framework for investigating the conditions that prepare a fault for failure, there is little evidence that faults rupture periodically or at a uniform threshold stress. Moreover, this model fails to explain the large differences in earthquake recurrence intervals and paleoseismic slip for segments of major fault systems: why do some faults rupture on the order of 10's of years, while others require 100's of years …

Automatic Elucidation Of Gpi Molecular Structures With Grid Computing Technology, Juan Clemente Aguilar Bonavides

Open Access Theses & Dissertations

Glycosylphosphatidylinositol (GPI)-anchored proteins are involved in many biological processes and are of medical importance. The identification and analysis of the entire collection of free and protein-linked GPIs within an organism (i.e., GPIomics) requires highly sensitive instruments. At present, liquid chromatography-tandem mass spectrometry (LC-MS/MS or -MSⁿ) is the most efficient laboratory technique for these tasks. As a typical MSⁿ experiment produces hundreds of thousands of spectra, the data analysis creates a major bottleneck in high-throughput GPIomic projects. Yet, no computational tool for characterizing the chemical structures of GPI is available to date. We propose a library-search algorithm to …