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Full-Text Articles in Physical Sciences and Mathematics

The Electrochemical Study Of Simulated Spent Nuclear Fuel (Simfuel) Corrosion Under Permanent Disposal Conditions, Ziyan Zhu Nov 2018

The Electrochemical Study Of Simulated Spent Nuclear Fuel (Simfuel) Corrosion Under Permanent Disposal Conditions, Ziyan Zhu

Electronic Thesis and Dissertation Repository

The safety assessment of spent nuclear fuel under permanent disposal conditions requires examination of the corrosion of the spent fuel waste form (UO2) inside a failed waste container. The objective of this research project was to develop a detailed mechanism of the UO2 corrosion process when exposed to groundwater. The redox conditions within a failed container in a deep geologic repository will be complex. The oxidant, H2O2, produced by the α-radiolysis of groundwater, will be the main driving force for fuel corrosion. However, the efficiency of fuel dissolution will be determined by the competition between ...


Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang Oct 2018

Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang

Electronic Thesis and Dissertation Repository

In this thesis, we apply bifurcation theory to study two biological systems. Main attention is focused on complex dynamical behaviors such as stability and bifurcation of limit cycles. Hopf bifurcation is particularly considered to show bistable or even tristable phenomenon which may occur in biological systems. Recurrence is also investigated to show that such complex behavior is common in biological systems.

First we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. Main attention is focused on the sta- bility and bifurcation of equilibria when the prey has a ...


Ecology And Evolution Of Dispersal In Metapopulations, Jingjing Xu Oct 2018

Ecology And Evolution Of Dispersal In Metapopulations, Jingjing Xu

Electronic Thesis and Dissertation Repository

Dispersal plays a key role in the persistence of metapopulations, as the balance between local extinction and colonization is affected by dispersal. Herein, I present three pieces of work related to dispersal. The first two are devoted to the ecological aspect of delayed dispersal in metapopulations. The first one focuses on how dispersal may disrupt the social structure on patches from which dispersers depart. Examinations of bifurcation diagrams of the dynamical system show a metapopulation will, in general, be either in the state of global extinction or persistence, and dispersal only has a limited effect on metapopulation persistence. The second ...


Copper-Nanoparticle Decorated Graphene Thin Films: Applications In Metal-Assisted Etching And Synthesis Of Next-Generation Graphene-Based Nanomaterials, Jaewoo Park Oct 2018

Copper-Nanoparticle Decorated Graphene Thin Films: Applications In Metal-Assisted Etching And Synthesis Of Next-Generation Graphene-Based Nanomaterials, Jaewoo Park

Electronic Thesis and Dissertation Repository

Since 2006, the experimental discovery of graphene, a single-layer of carbon atoms, has spurred tremendous efforts towards new graphene-based materials. In graphene research, there is a recent trend towards next-generation materials in which graphene layers are locally modified in a controlled fashion at the nanoscale and tailored for specific applications. Examples include nanoparticle-decorated graphene thin films with surface potential tailored for nanoelectronics or advanced catalysis, graphene nanoribbons, graphene quantum dots, and the scalable fabrication of tiny pores in graphene, which are suitable to applications requiring ultrathin molecular sieving membranes. This research is focused on the development of new applications of ...


Computational Studies On Nucleic Acid-Ion Interactions In Droplets And Bulk Solution, Mahmoud Sharawy Oct 2018

Computational Studies On Nucleic Acid-Ion Interactions In Droplets And Bulk Solution, Mahmoud Sharawy

Electronic Thesis and Dissertation Repository

Interactions of macromolecules with ions in solution have a long history of study because of their ubiquitous nature. These interactions are essential for the stability and function of macromolecules such as nucleic acids. Nucleic acids are involved in many natural biochemical processes. For example, deoxyribonucleic acid (DNA) provides more than storage of genetic information. The guanine-rich structures, at the ends of the DNA, participate in regulating the gene expression in the living cell by forming guanine quadruplex (G-quadruplex) structures. These structures provide a possible drug target for the treatment of cancer. Nucleic acids are polyions under physiological pH of 7 ...


Metabolomics For Biomonitoring: Evaluation, Recommendations, And Test Of Efficacy, Sarah M. Mckenzie Oct 2018

Metabolomics For Biomonitoring: Evaluation, Recommendations, And Test Of Efficacy, Sarah M. Mckenzie

Electronic Thesis and Dissertation Repository

Effective biomonitoring of aquatic environments is an integral component of ecosystem protection. The metabolome is an emerging indicator that may have the potential to serve as an ideal bioindicator due to its intrinsic capacity to detect physiological changes in organisms that could foreshadow ecosystem change. My thesis consisted of two complementary objectives. First, the metabolome was evaluated against several established criteria for an ideal bioindicator and found to have significant potential. Recommendations were also made regarding implementation of the metabolome into existing biomonitoring programs. Second, the metabolome of Hexagenia spp. was evaluated as a potential indicator for environmental effects of ...


P-T-X Constraints On Ilmenite Unit Cell And Relationship To Kimberlitic And Non-Kimberlitic Sources, Mitchell R. Galarneau Oct 2018

P-T-X Constraints On Ilmenite Unit Cell And Relationship To Kimberlitic And Non-Kimberlitic Sources, Mitchell R. Galarneau

Electronic Thesis and Dissertation Repository

This research investigates the mineral ilmenite, focusing on the relationship between crystal structure and geochemical and/or pressure data. Ilmenites were obtained from diamond-rich and diamond-poor kimberlites and non-kimberlitic localities, to discriminate between these populations. Crystallographic results showed a delineation between kimberlitic and non-kimberlitic ilmenites at a c-axis value of 14.02 (±0.01) Å. Adding geochemistry and pressure enhances the separation of kimberlitic and non-kimberlitic samples; however, this isn’t the case for diamond-rich versus diamond-poor kimberlites, even with three-dimensional and cluster analyses. A subset of kimberlitic ilmenites (manganese rich) were found with c-axis values and geochemical concentrations similar ...


High Resolution Ion Beam Investigations Of The Mechanisms Of Titanium Anodization, Mitchell A. Brocklebank Oct 2018

High Resolution Ion Beam Investigations Of The Mechanisms Of Titanium Anodization, Mitchell A. Brocklebank

Electronic Thesis and Dissertation Repository

The unique behaviour of thin films, and their surfaces and interfaces, significantly impact material and device properties. Probing these structures with ion beams (IB) provides quantitative composition and thicknesses measurements. In this dissertation, the IB techniques of medium energy ion scattering (MEIS), nuclear reaction profiling (NRP) and Rutherford backscattering spectrometry (RBS) are used to analyze energy losses in ultra-thin films, as well as elucidate the mechanisms of anodic film growth.

Accurate stopping cross sections of protons, ε, in the medium energy range (50-170 kV) often show deviations from Bragg’s rule. Here, εTi, εSi, and εTiO2, where ...


Selected Topics In Quantization And Renormalization Of Gauge Fields, Chenguang Zhao Sep 2018

Selected Topics In Quantization And Renormalization Of Gauge Fields, Chenguang Zhao

Electronic Thesis and Dissertation Repository

My thesis covers several topics in the quantization and renormalization of gauge fields, ranging from the application of Dirac constraint procedure on the light front, to the manipulation of Faddeev-Popov method to enable use of the transverse-traceless gauge in first order gravity. Last, I study renormalization group ambiguities and carry out a new characterization method for models with one, two and five couplings.

In chapter 2 we apply the Dirac constraint procedure to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting ...


Statistical Tools For Assessment Of Spatial Properties Of Mutations Observed Under The Microarray Platform, Bin Luo Sep 2018

Statistical Tools For Assessment Of Spatial Properties Of Mutations Observed Under The Microarray Platform, Bin Luo

Electronic Thesis and Dissertation Repository

Mutations are alterations of the DNA nucleotide sequence of the genome. Analyses of spatial properties of mutations are critical for understanding certain mutational mechanisms relevant to genetic disease, diversity, and evolution. The studies in this thesis focus on two types of mutations: point mutations, i.e., single nucleotide polymorphism (SNP) genotype differences, and mutations in segments, i.e., copy number variations (CNVs). The microarray platform, such as the Mouse Diversity Genotyping Array (MDGA), detects these mutations genome-wide with lower cost compared to whole genome sequencing, and thus is considered for suitability as a screening tool for large populations. Yet it ...


Hydrogen-Deuterium Exchange Mass Spectrometry And Molecular Dynamics Simulations For Studying Protein Structure And Dynamics, Yiming Xiao Sep 2018

Hydrogen-Deuterium Exchange Mass Spectrometry And Molecular Dynamics Simulations For Studying Protein Structure And Dynamics, Yiming Xiao

Electronic Thesis and Dissertation Repository

Deciphering properties of proteins are essential for human health and aiding in the development of new pharmaceuticals. This dissertation uses hydrogen-deuterium exchange (HDX) mass spectrometry (MS) and molecular dynamics (MD) simulations to study protein dynamics, for improving the understanding of protein folding/unfolding mechanisms, and ligand binding and allosteric regulation.

Chapter 2 uses HDX-MS for probing the conformational dynamics of myoglobin in the presence of N2 bubbles. We propose a dynamic model that reproduces the observed data: “semi-unfolded” “native” “globally unfolded” -> “aggregated”. Chapter 3 focuses on osteoprotegerin (OPG), which hinders bone resorption by inhibiting RANK/RANKL interactions. The dimerization ...


Mechanism Of Protein Charging And Supercharging In Electrospray Ionization: Molecular Dynamics Simulations And Experimental Investigations, Haidy S. Metwally Sep 2018

Mechanism Of Protein Charging And Supercharging In Electrospray Ionization: Molecular Dynamics Simulations And Experimental Investigations, Haidy S. Metwally

Electronic Thesis and Dissertation Repository

Electrospray ionization mass spectrometry (ESI-MS) is a powerful technique for investigating protein structures, conformations, and interactions. Despite its widespread use, many fundamental aspects of ESI remain poorly understood. In this thesis, we use a combination of molecular dynamics (MD) simulations and experiments to gain insights into the hidden complexities of ESI-MS.

Chapter 2 discusses the topic of salt-induced protein signal degradation. Salts such as NaCl, CsCl, and tetrabutyl ammonium chloride (NBu4Cl) interfere with MS data acquisition, leading to adduct formation and signal suppression. MD simulations provide an explanation for these salt interferences. Signal suppression can be broken down ...


Statistical Modeling Of Co2 Flux Data, Fang He Sep 2018

Statistical Modeling Of Co2 Flux Data, Fang He

Electronic Thesis and Dissertation Repository

Carbon dioxide (CO2) flux is important for agriculture and carbon cycle studies. Only a small proportion of the land is currently covered by proper equipment to directly collect CO2 flux data. The CO2 flux data has an obvious annual cycle with the phase changing from year to year. How to build a model to estimate the annual effect and seasonal dynamics is a challenging task. With the help of the Moderate Resolution Imaging Spectroradiometer (MODIS) which is carried by NASA satellites, corresponding data, such as normalized difference vegetation index (NDVI), is freely available from NASA. Our goals are modeling the ...


The Periglacial Landscape Of Mars: Insight Into The 'Decameter-Scale Rimmed Depressions' In Utopia Planitia, Arya Bina Aug 2018

The Periglacial Landscape Of Mars: Insight Into The 'Decameter-Scale Rimmed Depressions' In Utopia Planitia, Arya Bina

Electronic Thesis and Dissertation Repository

Currently, Mars appears to be in a ‘frozen’ and ‘dry’ state, with the clear majority of the planet’s surface maintaining year-round sub-zero temperatures. However, the discovery of features consistent with landforms found in periglacial environments on Earth, suggests a climate history for Mars that may have involved freeze and thaw cycles. Such landforms include hummocky, polygonised, scalloped, and pitted terrains, as well as ice-rich deposits and gullies, along the mid- to high-latitude bands, typically with no lower than 20o N/S. The detection of near-surface and surface ice via the Phoenix lander, excavation of ice via recent impact cratering ...


Exploring The Chemistry Of Asymmetric Phosphines & Phosphinidene Sulfides, Taylor E. Pritchard Aug 2018

Exploring The Chemistry Of Asymmetric Phosphines & Phosphinidene Sulfides, Taylor E. Pritchard

Electronic Thesis and Dissertation Repository

The field of low-coordinate main group chemistry has seen huge development in the last 30 years, with novel compounds that demonstrate unique structures and reactivity. Isolation of these species has relied on thoughtfully designed substituents normally containing substructure steric bulk. The area of phosphinidene chalcogenide isolation and transfer remains poorly understood by comparison. In this context, the major focus of thesis was on the development of a room-temperature method for the transfer of RP=S moieties with and without sterically demanding substituents. The preparation and complete characterization of new asymmetric phosphines with m-terphenyl ligands was also reported. In Chapter ...


Investigation Of Chaos In Biological Systems, Navaneeth Mohan Aug 2018

Investigation Of Chaos In Biological Systems, Navaneeth Mohan

Electronic Thesis and Dissertation Repository

Chaos is the seemingly irregular behavior arising from a deterministic system. Chaos is observed in many real-world systems. Edward Lorenz’s seminal discovery of chaotic behavior in a weather model has prompted researchers to develop tools that distinguish chaos from non-chaotic behavior. In the first chapter of this thesis, I survey the tools for detecting chaos namely, Poincaré maps, Lyapunov exponents, surrogate data analysis, recurrence plots and correlation integral plots. In chapter two, I investigate blood pressure fluctuations for chaotic signatures. Though my analysis reveals interesting evidence in support of chaos, the utility such an analysis lies in a different ...


Performance Impact Of Different Lower-Limb Setup Positions In The Backstroke Swimming Start, Gordon E. Barkwell Aug 2018

Performance Impact Of Different Lower-Limb Setup Positions In The Backstroke Swimming Start, Gordon E. Barkwell

Electronic Thesis and Dissertation Repository

The performance impact of different knee extension angles in the setup position for a backstroke start was evaluated using an instrumented starting surface. Ten backstroke swimmers completed maximum-effort starts in each of two setup positions: one with the knees flexed, and one with the knees extended. The start handles and touchpad were instrumented with tri-axial force plates. Activity of major hip and knee extensors was measured using surface electromyography. Body position was recorded throughout the start using two high-speed cameras. There was no difference in time to 10 m between the two conditions, indicating there is likely no advantage in ...


High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt Aug 2018

High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt

Electronic Thesis and Dissertation Repository

Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit a sparse ...


Topological Recursion And Random Finite Noncommutative Geometries, Shahab Azarfar Aug 2018

Topological Recursion And Random Finite Noncommutative Geometries, Shahab Azarfar

Electronic Thesis and Dissertation Repository

In this thesis, we investigate a model for quantum gravity on finite noncommutative spaces using the topological recursion method originated from random matrix theory. More precisely, we consider a particular type of finite noncommutative geometries, in the sense of Connes, called spectral triples of type ${(1,0)} \,$, introduced by Barrett. A random spectral triple of type ${(1,0)}$ has a fixed fermion space, and the moduli space of its Dirac operator ${D=\{ H , \cdot \} \, ,}$ ${H \in {\mathcal{H}_N}}$, encoding all the possible geometries over the fermion space, is the space of Hermitian matrices ${\mathcal{H}_N}$. A distribution of ...


Vibrating-Wire Rheometry, Cameron C. Hopkins Aug 2018

Vibrating-Wire Rheometry, Cameron C. Hopkins

Electronic Thesis and Dissertation Repository

This thesis consists of two projects on the behaviour of a novel vibrating-wire rheometer and a third project studying the gelation dynamics of aqueous solutions of Pluronic F127. In the first study, we use COMSOL to perform two-dimensional simulations of the oscillations of a wire in Newtonian and shear-thinning fluids. Our results show that the resonant behaviour of the wire agrees well with the theory of a wire vibrating in Newtonian fluids. In shear-thinning fluids, we find resonant behaviour similar to that in Newtonian fluids. In addition, we find that the shear-rate and viscosity in the fluid vary significantly in ...


Quantifying Temperatures In The Early Solar Nebula And On Parent Bodies Using Cation Ordering In Spinel From Cais In Carbonaceous Chondrites, Victoria Houde Aug 2018

Quantifying Temperatures In The Early Solar Nebula And On Parent Bodies Using Cation Ordering In Spinel From Cais In Carbonaceous Chondrites, Victoria Houde

Electronic Thesis and Dissertation Repository

Understanding the early solar system requires studying early-formed materials. Calcium-Aluminium-Rich Inclusions (CAIs) are the oldest materials in the solar system. Spinel (MgAl2O4) is common in CAIs. Its cation distribution relates to formation, or most recent equilibration, temperature. This can be measured using 27Al Magic Angle Spinning (MAS) Nuclear Magnetic Resonance (NMR) spectroscopy. Calibration curves can be used to calculate temperature.

Micro X-ray Diffraction identified spinel-containing CAIs in four of seven meteorites tested. 27Al MAS NMR and 27Al Triple Quantum (3Q) MAS NMR was acquired at 21.1 Tesla. Temperature estimates were calculated for each ...


Ureilite Meteorite Record Of Shock Metamorphism And Parent Body Processes, Yaozhu Li Aug 2018

Ureilite Meteorite Record Of Shock Metamorphism And Parent Body Processes, Yaozhu Li

Electronic Thesis and Dissertation Repository

Ureilites are an abundant non-chondritic meteorite class that are petrographically similar to terrestrial ultramafic rocks, consisting mostly of coarse-grained olivine and pyroxene, with remarkably low occurrence of plagioclase feldspar. This work examines a suite of ureilites (six monomict ureilites and one polymict ureilite), primarily focusing on the mineral olivine as a recorder of shock damage. Optical petrography and Raman spectroscopy provide context information, and in-situmicro-X-ray diffraction (𝜇XRD) is used to obtain quantitative measurements of diffraction peak Full-Width-Half Maxima upon integration along the chi direction on 2D XRD patterns. Ureilites show an increasing streak length of FWHMχ and asterism (discrete ...


The Development Of Metal Complexes As Components Of Fluorescent And Nuclear Imaging Probes, William Turnbull Aug 2018

The Development Of Metal Complexes As Components Of Fluorescent And Nuclear Imaging Probes, William Turnbull

Electronic Thesis and Dissertation Repository

The advent of molecular imaging as a discipline has drastically improved our ability to understand the biochemical and cellular events that drive life, death and disease. This thesis will document the discovery of new metal chelators for Re/99mTc, new methods of incorporating these metals into peptide structures, as well as new fluorescent compounds. These novel methods and compounds may be used in the development of molecular imaging probes for single photon emission computed tomography (SPECT) and optical imaging techniques, with applications for differentiating cancerous tissue from benign and healthy.

Chapter 2 discusses the development of a dual modality ...


Characterization Of Kelyphite Rims: Relevance To Diamond Exploration, Mallory N.G. Metcalf Aug 2018

Characterization Of Kelyphite Rims: Relevance To Diamond Exploration, Mallory N.G. Metcalf

Electronic Thesis and Dissertation Repository

A detailed investigation into the mineralogy and chemistry of kelyphitic rims/veins on garnets was conducted using µXRD, EPMA and Raman spectroscopy for a suite of samples from economic and non-economic kimberlites in Canada and South Africa. Mineralogy demonstrates the influence of metasomatic fluids during the reactions which produced kelyphite in all localities and was used to propose P-T regions where kelyphite could have formed. Using chemical analyses of host garnets and the mineralogy obtained for kelyphite, modified chemical reactions representing Types 1 and 2 kelyphite are provided to describe kelyphite reactions in open systems. Elastically-strained secondary garnet is common ...


Impact Craters On Titan: Finalizing Titan's Crater Population, Joshua E. Hedgepeth Aug 2018

Impact Craters On Titan: Finalizing Titan's Crater Population, Joshua E. Hedgepeth

Electronic Thesis and Dissertation Repository

Titan is one of the most dynamic moons in the solar system. It is smaller than Earth and much colder, yet Titan is eerily similar to Earth, with rivers, rain, and seas, as well as sand seas that wrap around the equator. However, the rivers are made of hydrocarbons rather than water and the sand made of organics rather rock. We can use Titan’s impact craters to study how these processes modify the surface by comparing the craters depths, diameters and rim heights of Titan’s craters with fresh craters. Therefore, we have used the complete data set from ...


Syzygy Order Of Big Polygon Spaces, Jianing Huang Aug 2018

Syzygy Order Of Big Polygon Spaces, Jianing Huang

Electronic Thesis and Dissertation Repository

For a compact smooth manifold with a torus action, its equivariant cohomology is a finitely generated module over a polynomial ring encoding information about the space and the action. For such a module, we can associate a purely algebraic notion called syzygy order. Syzygy order of equivariant cohomology is closely related to the exactness of Atiyah-Bredon sequence in equivariant cohomology. In this thesis we study a family of compact orientable manifolds with torus actions called big polygon spaces. We compute the syzygy orders of their equivariant cohomologies. The main tool used is a quotient criterion for syzygies in equivariant cohomology ...


Design, Synthesis, And Oxidation Reactivity Of Palladacyclic Complexes Containing N-Donor Ligands, Ava Behnia Aug 2018

Design, Synthesis, And Oxidation Reactivity Of Palladacyclic Complexes Containing N-Donor Ligands, Ava Behnia

Electronic Thesis and Dissertation Repository

This thesis describes the synthesis and reactivity of complexes containing the cycloneophyl-Pd(II) group, PdCH2CMe2C6H4, in combination with N-donor ligands. These compounds contain both alkyl- and arylpalladium bonds and the selectivity of bond cleavage in reactions with oxidants and protic reagents is studied, often involving oxidative addition and reductive elimination reaction sequences.

The diimine ligand in [Pd(CH2CMe2C6H4)(MesN=CH-CH=NMes)] does not support formation of stable palladium(IV) complexes, but reactions with Br2 or I2 lead to reductive elimination by C-C bond ...


Geomechanical Modelling Of Induced Seismicity, Bodi Zhao Jul 2018

Geomechanical Modelling Of Induced Seismicity, Bodi Zhao

Electronic Thesis and Dissertation Repository

In recent years, there has been a dramatic increase in seismicity (earthquakes) due to anthropogenic activities related to the unconventional oil and gas exploration in the Western Canada Sedimentary Basin (WCSB) and the central U.S. There are compelling evidences that hydraulic fracturing and wastewater injection operations in those areas play a key role in induced seismicity. To better understand the physical mechanisms involved, this thesis aims to explore the mechanisms responsible for occurrence of induced earthquakes: mainshock-aftershock triggering mechanism and poroelastic response. In the first approach, the obtained results indicate the relationship between the Coulomb stress changes after 4 ...


Compositional Variations Of Titan's Impact Craters Indicates Active Surface Erosion, Alyssa Werynski Jul 2018

Compositional Variations Of Titan's Impact Craters Indicates Active Surface Erosion, Alyssa Werynski

Electronic Thesis and Dissertation Repository

Impact craters on Titan are relatively scarce, but provide ample information about the subsurface properties and modification processes present there. This study utilizes impact craters to examine compositional variations across Titan’s surface and their subsequent modification. Fifteen craters and their ejecta blankets were studied. Subsurface composition was inferred from emissivity data from Cassini’s RADAR instrument, and surficial composition from Cassini’s Visible and Infrared Mapping Spectrometer (VIMS). Results show subsurface composition of these craters is controlled by their degradation state and local environment. Older craters are more infilled with organics than younger, and dunes craters show more organic ...


The Statistical Exploration In The $G$-Expectation Framework: The Pseudo Simulation And Estimation Of Variance Uncertainty, Yifan Li Jul 2018

The Statistical Exploration In The $G$-Expectation Framework: The Pseudo Simulation And Estimation Of Variance Uncertainty, Yifan Li

Electronic Thesis and Dissertation Repository

The $G$-expectation framework, motivated by problems with \emph{uncertainty}, is a new generalization of the classical probability framework. Similar to the Choquet expectation, the $G$-expectation can be represented as the supremum of a class of linear expectations. In the past two decades, it has developed into a complete stochastic structure connected with a large family of nonlinear PDEs. Nonetheless, to apply it to real-world problems with uncertainty, it is fundamentally necessary to build up the associated statistical methodology.

This thesis explores the \emph{computation, simulation, and estimation} of the $G$-normal distribution (a typical distribution with variance uncertainty ...