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Full-Text Articles in Physical Sciences and Mathematics

Detecting Tropical Cyclone Signals In Tree Rings Of Longleaf Pine (Pinus Palustris Mill.), Valdosta, Georgia, U.S.A., Savannah Anne Collins Dec 2014

Detecting Tropical Cyclone Signals In Tree Rings Of Longleaf Pine (Pinus Palustris Mill.), Valdosta, Georgia, U.S.A., Savannah Anne Collins

Masters Theses

The study of past hurricanes to help interpret the patterns of current and future tropical storms is vital to our economy, society, and infrastructure. Understanding how hurricanes are influenced by a warm climate is critical, and hurricane reconstructions from former periods of the Holocene (the last ~11,500 yr) will be beneficial. Paleotempestology is the study of past tropical cyclones and uses historical, biological, and geological proxies to reconstruct tropical cyclone activity to create a record of historical hurricane patterns. A tropical cyclone (TC) is a chaotic weather event that is influenced by several elements, including warm ocean waters from which …


Metamorphic Evolution Of Eastern Blue Ridge Calc-Silicates In Southwestern North Carolina, Northeastern Georgia, And Northwestern South Carolina, Gina Brianne Smith Dec 2014

Metamorphic Evolution Of Eastern Blue Ridge Calc-Silicates In Southwestern North Carolina, Northeastern Georgia, And Northwestern South Carolina, Gina Brianne Smith

Masters Theses

Calc-silicate rocks in the eastern Blue Ridge of SW North Carolina, NE Georgia, and NW South Carolina are products of contact and regional metamorphism. Two types of calc-silicates occur in this area: Type A rocks occur as contact metamorphosed xenoliths in the ~336 Ma Rabun Granodiorite batholith, and Type B rocks occur as mappable thin, elongate, ribbon-like units in the Tallulah Falls Formation east of the Rabun batholith. Petrographic and geochemical data confirm similar composition for both types and mineral assemblages that includes amphibole, garnet, epidote, diopside, quartz, and plagioclase with accessory zircon, sphene, and opaque minerals. Calcite, however, is …


Design And Model Of The Frame For Hagrid (Hybrid Array Of Gamma Ray Detectors), Santiago Munoz Dec 2014

Design And Model Of The Frame For Hagrid (Hybrid Array Of Gamma Ray Detectors), Santiago Munoz

Masters Theses

Transfer reactions in inverse kinematics have provided critical information in the study of exotic nuclei. However, transfer reactions with charged particles suffer from poor resolution. The measurement of gamma-rays offers several advantages: they provide not only good resolution in measurements but also other information about the nuclei like lifetimes of unstable states. The combination of these two methods would be the ideal situation to gather information about nuclear structure.

HAGRiD, which stands for The Hybrid Array of Gamma Ray Detectors, is a LaBr3(Ce) [lanthanum bromide crystal with a cerium activator] scintillation array to measure gamma rays from transfer reactions and …


Investigating The Effects Of Urbanization On Residual Forest Soils In Knox Co., Tennessee, Benjamin Lee Reichert Dec 2014

Investigating The Effects Of Urbanization On Residual Forest Soils In Knox Co., Tennessee, Benjamin Lee Reichert

Masters Theses

As the process of urbanization advances across the country, so does the importance of urban forests, which include both trees and the soils in which they grow. Soil microbial biomass, which plays a critical role in nutrient transformation in urban ecosystems, is affected by factors such as soil type and the availability of water, carbon, and nitrogen. However, the microbial dynamics of urban forest soils remain largely unknown. A key mechanistic link between plant species diversity and ecosystem function is heterotrophic microbial communities that inhabit the soil and mediate principal processes that control ecosystem carbon (C) and nitrogen (N) cycling. …


Structural And Metamorphic Evolution Of The Haimanta Group: Insights From P-T-T-D Path Modeling Of Rocks Near The Leo Pargil Dome, Nw India, Kyle Vincent White Dec 2014

Structural And Metamorphic Evolution Of The Haimanta Group: Insights From P-T-T-D Path Modeling Of Rocks Near The Leo Pargil Dome, Nw India, Kyle Vincent White

Masters Theses

The metasedimentary rocks of the Haimanta Group in the upper Sutlej Valley, NW India, record an extensive history of Himalayan deformation and metamorphism. Situated beneath the low-grade metasediments of the Tethyan Sedimentary sequence in the hanging wall of the South Tibetan detachment system (STDS), these poly-deformed rocks record Eocene–Oligocene burial metamorphism, crustal thickening and shortening, decompression and mid-crustal melting in the early Miocene, and exhumation along extensional shear zones related to the orogen-parallel exhumation of the Leo Pargil dome (LPD). Low-pressure assemblages (cordierite + sillimanite + quartz) overgrow Barrovian porphyroblasts in Haimanta Group rocks in the NE portion of Sutlej …


Laser-Induced Breakdown Spectroscopy For Analysis Of High Density Methane-Oxygen Mixtures, Matthew Dackman Dec 2014

Laser-Induced Breakdown Spectroscopy For Analysis Of High Density Methane-Oxygen Mixtures, Matthew Dackman

Masters Theses

The applicability of laser-induced breakdown spectroscopy (LIBS) toward greater than atmospheric density combustion diagnostics is examined. Specifically, this involves ascertaining the feasibility of measuring chemical equivalence ratios directly from atomic emission spectra at high density. The need for such measurement arises from the desire to quantify real time, localized combustion performance in weakly mixed flows. Insufficiently mixed flows generally result in unwanted byproducts, possess the propensity for overall combustion instability, and are increasingly likely to experience localized flame extinction.

We simulate methane/oxygen combustion in ambient pressures ranging 1 to 4 atmospheres, demonstrating these results to be analogous to what would …


Estimating Streambank Erosion Using Gps-Based Watershed-Scale Video Mapping And Usepa Bancs For The Development Of Sediment Tmdls, Kelsey Jo Hensley Dec 2014

Estimating Streambank Erosion Using Gps-Based Watershed-Scale Video Mapping And Usepa Bancs For The Development Of Sediment Tmdls, Kelsey Jo Hensley

Masters Theses

According to the United States Environmental Protection Agency (USEPA), sediment is one of the most common water pollutants in the nation’s rivers. Consequently, the identification of streambank locations with high erosion potential is important in reducing sediment input via management and monitoring practices. Furthermore, the estimation of erosion rates and sediment loads can assist in the development of Total Maximum Daily Loads (TMDLs). The objective of this study was to integrate two USEPA-recommended approaches with the Streambank Video Mapping System (SVMS) in order to predict site-specific Total Daily Sediment Loads (TDSLs) and calculate sediment TMDLs for streambank erosion over several …


Transport Of Fecal Pollution Indicators: Impacts From The Land Spreading Of Liquid Manure On Water Quality, Derek Lee Street Dec 2014

Transport Of Fecal Pollution Indicators: Impacts From The Land Spreading Of Liquid Manure On Water Quality, Derek Lee Street

Masters Theses

This thesis is a case study to determine if groundwater and/or drainage tiles are important pathways for fecal migration to streams resulting from the application of liquid manure to cropland at a small dairy farm, the Little River Animal and Environmental Unit, near Townsend, TN. Traditional biological indicators, coliforms and E.coli, were used in conjunction with a bovine specific Bacteroides assay to measure fecal microbes. Total nitrates, turbidity, and other chemical parameters for water quality also were used to identify related fecal contamination. This thesis covers three separate manure applications. The first manure application occurred in May 2013, the …


Modeling Celiac Disease, Jillian M. Trask Aug 2014

Modeling Celiac Disease, Jillian M. Trask

Masters Theses

Those who suffer from Celiac Disease have an autoimmune response to the protein complex gluten. The goal of this work is to better understand the biological mechanisms in Celiac Disease through modeling with a system of ordinary differential equations. We first develop a model for the way in which gluten induces a response in zonulin in those with Celiac Disease and estimate parameters for such a model using limited data. We then extend this model to include the interactions between zonulin and the permeability of the intestine, and the effect of this interaction on the immune response. Finally, we perform …


Structure Analysis Of Sn Bilayer Films On Si (111), Weisong Tu Aug 2014

Structure Analysis Of Sn Bilayer Films On Si (111), Weisong Tu

Masters Theses

Chemical doping is a well-established method for controlling the electronic properties of bulk semiconductors and, e.g, complex oxide materials. In this process, dopant atoms are located at substitutional lattice locations, from where they introduce free charge carriers to the host material. These carriers greatly improve the electrical conductivity of the host material and can even induce an insulator-metal transition at high doping levels. Dopants, however, also introduce scattering centers that are detrimental to conductivity, especially in low-dimensional systems such as nanowires and ultrathin films. These problems can be overcome by using a modulation doping approach in which the dopant atoms …


Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic Aug 2014

Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic

Masters Theses

Schramm-Loewner Evolution (SLE) has both mathematical and physical roots that extend as far back as the early 20th century. We present the progression of these humble roots from the Ideal Gas Law, all the way to the renormalization group and conformal field theory, to better understand the impact SLE has had on modern statistical mechanics. We then explore the potential application of the percolation exploration process to crack propagation processes, illustrating the interplay between mathematics and physics.


An Analysis Of The Suspended Sediment Rating Curve Parameters In The Upper Mississippi River Basin At The Monthly And Annual Levels, Vi Thi Tuong Tran Aug 2014

An Analysis Of The Suspended Sediment Rating Curve Parameters In The Upper Mississippi River Basin At The Monthly And Annual Levels, Vi Thi Tuong Tran

Masters Theses

Suspended sediment rating curve parameters were analyzed to investigate the relationship of suspended load and discharge in the Upper Mississippi River Basin (UMRB) at the annual and monthly levels. The rating curve parameters were obtained from the power function of load and discharge: Load = a × (Discharge)b [(Discharge)^b]. The function was solved by ordinary least squares regression on its logarithmic form.

The annual rating coefficient a and exponent b ranged from 0 to 0.25 (kg/s)(s/m3)b [(kg/s)(s/m^3)^b] and from 0.91 to 4.27, respectively. The monthly rating coefficient a and exponent b ranged from 0 to 0.239 …


Aluminum Monoxide Emission Measurements Following Laser-Induced Breakdown For Plasma Characterization, David Michael Surmick Aug 2014

Aluminum Monoxide Emission Measurements Following Laser-Induced Breakdown For Plasma Characterization, David Michael Surmick

Masters Theses

In this work, spectroscopic emissions from laser ablated aluminum samples are used to characterize the time dependent decay of laser-induced plasma. The plasma is created by tightly focusing nanosecond pulsed laser radiation. Time resolved measurements of the plasma are made with a gated, intensified linear diode array coupled to an optical multichannel analyzer and/or an intensified charged coupled device. Time resolution is achieved by synchronizing the laser with the measurement rate of the array detector.

Computed diatomic molecular aluminum monoxide emissions were used to infer the temperature of the plasma as a function of time. This was completed by comparing …


Characterizing The Relationship Of Part Of The Inner Piedmont And Pine Mountain Window, Georgia, From Detailed Geologic Mapping, Geochemistry, Geochronology, And Structural Analysis At The Southwestern End Of The Cat Square Terrane, Justin Randolph Rehrer Aug 2014

Characterizing The Relationship Of Part Of The Inner Piedmont And Pine Mountain Window, Georgia, From Detailed Geologic Mapping, Geochemistry, Geochronology, And Structural Analysis At The Southwestern End Of The Cat Square Terrane, Justin Randolph Rehrer

Masters Theses

Geologic investigations at the southwestern end of the Cat Square terrane (CSt) in central Georgia provided new insight into the complex tectonic history of the Pine Mountain window (PMw) and neighboring Inner Piedmont terranes. Detailed 1:24,000-scale geologic mapping of an approximately 180 km2 area near Barnesville, Georgia has provided the foundation for further geochemical, geochronologic, and structural analyses refining models for tectonic development and emplacement of the CSt and PMw.

Whole-rock geochemical analyses of several CSt amphibolites yielded data suggesting a continental back-arc setting for genesis of the Cat Square basin (CSb). Major element data confirm derivation from a basaltic …


Comparison Of Triangle And Tetrad Discrimination Methodology In Applied, Industrial Manner, Sara Lyn Carlisle Aug 2014

Comparison Of Triangle And Tetrad Discrimination Methodology In Applied, Industrial Manner, Sara Lyn Carlisle

Masters Theses

The triangle method has been widely used in the food industry for many years when conducting sensory discrimination testing. Recently, however, another discrimination testing method, the tetrad, has begun to gain popularity. Based on currently published research, the tetrad method possesses statistical advantages over the triangle and would require fewer panelists, reduce testing time, and use less sample material. More testing is needed to confirm these advantages in an applied, industrial approach on a wider range of products. Over thirty triangles and thirty tetrads with untrained panelists have been completed in order to compare the two methods. Products tested ranged …


Data Analytics Of University Student Records, Mark Blaise Decotes Aug 2014

Data Analytics Of University Student Records, Mark Blaise Decotes

Masters Theses

Understanding the proper navigation of a college curriculum is a daunting task for students, faculty, and staff. Collegiate courses offer enough intellectual challenge without the unnecessary confusion caused by course scheduling issues. Administrative faculty who execute curriculum changes need both quantitative data and empirical evidence to support their notions about which courses are cornerstone. Students require clear understanding of paths through their courses and majors that give them the optimal chance of success. In this work, we re-envision the analysis of student records from several decades by opening up these datasets to new ways of interactivity. We represent curricula through …


The Isotope Effect On Proton Conduction And Glass Transition In Phosphoric Acid, Maximilian Ferdinand Heres Aug 2014

The Isotope Effect On Proton Conduction And Glass Transition In Phosphoric Acid, Maximilian Ferdinand Heres

Masters Theses

Hydrogen fuel cells combine hydrogen and oxygen to create water and electricity. Polymer electrolyte membranes (PEM) make up barriers within the fuel cell allowing only protons to pass through, while keeping other components separate. Many PEM contain phosphoric acid (PA) as a building block due to its excellent proton conducting properties. Improved ionic conductivity in PEM can lead to the development of better, more efficient fuel cells.

While ionic conductivity in PA at high temperatures is extensively characterized, the low temperature dynamics are not so well explored. Below the glass transition, molecular motion is frozen and proton motion is forced …


Thick Target Yield Of Th-229 Via Low Energy Proton Bombardment Of Th-232, Justin Reed Griswold Aug 2014

Thick Target Yield Of Th-229 Via Low Energy Proton Bombardment Of Th-232, Justin Reed Griswold

Masters Theses

Actinium-225 is one of the more effective radioisotopes used in alpha radioimmunotherapy. Due to its ten-day half-life, it is more efficient to create its precursor, 229Th [Thorium-229] (t1/2[half-life] = 7932 ± 55 years). In this work, 229Th was produced via 40 MeV [Mega electron Volts] proton bombardment of a thick 232Th [Thorium-232] target. The irradiation took place at the Holifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Lab (ORNL). The target, consisting of 23 stacked natural thorium foils (137 mg/cm2 [milligrams per square centimeter] each), was irradiated with 50 nA [nanoamps] of …


Radiation-Induced Radicals In Polyurea-Crosslinked Silica Aerogel, Benjamin Michael Walters Aug 2014

Radiation-Induced Radicals In Polyurea-Crosslinked Silica Aerogel, Benjamin Michael Walters

Masters Theses

Free radicals are atoms or molecules with an odd number of electrons in an outer shell. Since electrons typically occur in pairs, this leaves one electron that is unpaired. In seek of another electron to pair with, free radicals react with and steal electrons from neighboring molecules, which then become free radicals themselves. This can start a chain reaction, cascading into large scale damage.

Ionizing radiation can tear through molecules, just as bullets can tear through things that we see. If free radicals can be detected, and seen to increase in a material upon radiation exposure, this can indicate molecular …


Calcitized Evaporites In The Precambrian: Deposition And Diagenesis In A Low Sulfate Ocean, Ashley René Manning Berg Aug 2014

Calcitized Evaporites In The Precambrian: Deposition And Diagenesis In A Low Sulfate Ocean, Ashley René Manning Berg

Masters Theses

One of the most profound byproducts of the Great Oxidation Event (GOE) was the onset of oxidative weathering on land and the riverine delivery of sulfate to marine systems. The marine sulfur system therefore plays a critical role in reconstructing the oxygenation of the early Earth. Although the exact nature of marine oxygenation in aftermath of GOE remains uncertain, examination and modeling of marine sulfate suggest that sulfate concentrations remained below 2 millimolar (mM) until at least the middle Mesoproterozoic, and may have only reached about 10 mM in the latest Neoproterozoic. Such a low concentration of marine sulfate had …


Mineralized Microbialites As Archives Of Environmental Evolution Of A Hypersaline Lake Basin: Laguna Negra, Catamarca Province, Argentina, Joy Buongiorno Aug 2014

Mineralized Microbialites As Archives Of Environmental Evolution Of A Hypersaline Lake Basin: Laguna Negra, Catamarca Province, Argentina, Joy Buongiorno

Masters Theses

Environmental fluctuations related to climate, biological productivity, and evaporation can be recorded by sedimentary archives within lacustrine depositional systems. Sediments within terminal, closed-basin lakes are amongst the most sensitive paleoenvironmental indicators, and have great potential for permitting detailed reconstruction of environmental conditions via a variety of geochemical and isotopic proxies. Microbialites, however, have been largely overlooked as repositories of paleoenvironmental data. Here, we investigate mineralized microbialites within Laguna Negra, a high-altitude (4100 meters above sea level) hypersaline, closed-basin lake in the Argentinian Puna region and explore the potential recovery of environmental signals from these unique sedimentary archives. Mineralized microbialites within …


Measuring Carbon Dioxide (Co2) Flux Of Agricultural Practices In Sub-Saharan Africa, Debra Blumberg O'Dell Aug 2014

Measuring Carbon Dioxide (Co2) Flux Of Agricultural Practices In Sub-Saharan Africa, Debra Blumberg O'Dell

Masters Theses

Agriculture has an important role in addressing two of the world’s most pressing problems: meeting global food demand and mitigating climate change. If agriculture is not practiced sustainably it will fail to meet future food demand and likely intensify the pace of global climate change. There are some agricultural practices, such as Conservation Agriculture, that can produce food sustainably and have the potential to mitigate climate change. However it is not clear which agricultural practices contribute to climate mitigation and by how much. By measuring the carbon dioxide (CO2) emissions of specific agricultural practices, the ability of practices to sequester …


Crystallization Kinetics Of Olivine-Phyric Shergottites, Megan Elizabeth Ennis May 2014

Crystallization Kinetics Of Olivine-Phyric Shergottites, Megan Elizabeth Ennis

Masters Theses

Petrographic and geochemical techniques applied to Martian meteorites can reveal their petrogenesis, and ultimately the magmatic evolution and thermal history of Mars. Two quantitative textural tools, crystal size distribution (CSD) and spatial distribution pattern (SDP) analysis, are utilized to describe the early crystallizing phases, olivine and pyroxene, of one olivine-phyric shergottite (EET 79001A, DaG 476, and Dho 019) from each sampling locality as inferred from Mars ejection ages. Qualitative observations of trace element zonation patterns (P, Cr, and Al) in olivine are used in conjunction with CSD and SDP to characterize the crystallization history of these samples. Previously reported CSDs …


Minimal-Density, Raid-6 Codes: An Approach For W = 9, Bryan Andrew Burke May 2014

Minimal-Density, Raid-6 Codes: An Approach For W = 9, Bryan Andrew Burke

Masters Theses

RAID-6 erasure codes provide vital data integrity in modern storage systems. There is a class of RAID-6 codes called “Minimal Density Codes,” which have desirable performance properties. These codes are parameterized by a “word size,” w, and constructions of these codes are known when w and w + 1 are prime numbers. However, there are obvious gaps for which there is no theory. An exhaustive search was used to fill in the important gap when w = 8, which is highly applicable to real-world systems, since it is a power of 2. This paper extends that approach to address the …


Characterizing The Morphology Of Solvent Annealed Pcbm/P3ht Bilayers Using Gixrd And Raman Spectroscopy, Tyler Evan Mcpherson May 2014

Characterizing The Morphology Of Solvent Annealed Pcbm/P3ht Bilayers Using Gixrd And Raman Spectroscopy, Tyler Evan Mcpherson

Masters Theses

A growing demand for new forms of renewable energy has been at the forefront of scientific research. Organic photovoltaics (OPVs) provide a promising alternative to the expensive inorganic solar cells used today. Poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61-butyric acid methyl ester (PCBM) are common donor and acceptor materials used in the active layer of an OPV device. These systems have reached power conversion efficiencies of approximately 12 %. However, little is known about the actual morphology. A better understanding of the morphology would allow researchers to optimize device fabrication to increase the device performance. As-cast devices are limited by the processing …


A Multidimensional Analysis Of The Great Green Wall: The Environmental And Social Effects Of Reafforestation In Senegal, Anna Eugenia Alsobrook May 2014

A Multidimensional Analysis Of The Great Green Wall: The Environmental And Social Effects Of Reafforestation In Senegal, Anna Eugenia Alsobrook

Masters Theses

The north-central region of Senegal is home to the Great Green Wall (GGW)—a reafforestation project aimed at restoring decades–old, degraded land conditions by establishing tree belts and community gardens. Its presence on the ground has changed the local landscape and altered the social institutions governing the daily lives of the people it aims to protect.

My study is an in-progress assessment of the GGW towards its two major goals: 1) improving the lives of the people of the Sahel and increasing their capacity to adapt to climate change and drought, and 2) improving the state of the ecosystem and increasing …


Mathematical Modeling Of T Cell Clustering Following Malaria Infection In Mice, Reka Katalin Kelemen May 2014

Mathematical Modeling Of T Cell Clustering Following Malaria Infection In Mice, Reka Katalin Kelemen

Masters Theses

Malaria is the result of the immune system's unsuccessful clearance of hepatocytes (liver cells) infected by the eukaryotic pathogen of the Plasmodium genus. It has been shown that CD8 T cells are required and sufficient for protective immunity against malaria in mice [29, 36], but the mechanisms by which they find and eliminate infected hepatocytes are not known yet. Recently we reported the formation of CD8 T cell clusters consisting of up to 25 cells around infected cells [8]. Our mathematical modeling and data analysis revealed that malaria-specific T cells likely recruit each other and also non-malaria-specific T cells to …


An Analysis Of The Patterns Of Crime And Socioeconomic Status Visualized Through Self-Organized Maps, Jason Carlin Kaufman May 2014

An Analysis Of The Patterns Of Crime And Socioeconomic Status Visualized Through Self-Organized Maps, Jason Carlin Kaufman

Masters Theses

This work is research to explore the association of spatial patterns between crime and socioeconomic status (SES) through the use of self-organized maps (SOM). It had been found that the spatial patterns of crime could be associated with those of socioeconomic, and this work sought to further these analyses in order to better understand how crime patterns and SES were related. To explore this association, patterns of crime and SES were examined in three cities: Nashville, TN; Portland, OR; and Tucson, AZ. Three SOMs were used in each city: one to analyze the patterns of crime, a second to analyze …


Using Ultra Performance Liquid Chromatography-Mass Spectrometric Based Metabolomics To Determine The Metabolic Differences Due To Low Temperature Or Genetic Mutation In Salmonella Enterica, Nicole Rhonda Mooney May 2014

Using Ultra Performance Liquid Chromatography-Mass Spectrometric Based Metabolomics To Determine The Metabolic Differences Due To Low Temperature Or Genetic Mutation In Salmonella Enterica, Nicole Rhonda Mooney

Masters Theses

Metabolomics aims to identify and quantify all of the small molecules within a cell. The relative concentrations of metabolites within cells grown under different experimental conditions, or different species, can be compared using pool size data. Exposing cellular cultures to isotopically labeled compounds allows the progress of metabolites through metabolic pathways to be tracked, known as flux. In the first experiment, the metabolic effects of exposure to lower than optimal temperatures in wild type Salmonella enterica, i.e. cold shock, were determined. The metabolites involved in glycolysis, the citric acid cycle, and the pentose phosphate pathway had less efficient labeling …


The Complementing Condition In Elasticity, Lavanya Ramanan May 2014

The Complementing Condition In Elasticity, Lavanya Ramanan

Masters Theses

We consider a boundary value problem of nonlinear elasticity on a domain [omega] in R3 [3-dimensional space] and compute the Complementing Condition for the linearized equations at a point X0 [x zero] on boundary of omega. We assume a stored energy function depending on the first and third invariants of the deformation F and that the strong-ellipticity condition holds in [omega] . A surface traction boundary condition is imposed at X0.
The Complementing Condition is calculated from a system of 3 second-order ordinary differential equations (0 less than and equal to t less than infinity) with boundary …