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Pages
 Title
 Variable selection in varying multiindex coefficient models with applications to geneenvironmental interactions
 Creator
 Guan, Shunjie
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

Variable selection is an important topic in modern statistics literature. And varying multiindex coefficient model(VMICM) is a promising tool to study the synergistic interaction effects between genes and multiple environmental exposures. In this dissertation, we proposed a variable selection approach for VMICM, we also generalized such approach to generalized and quantile regression settings. Their theoretical properties, simulation performance and application in genetic research were...
Show moreVariable selection is an important topic in modern statistics literature. And varying multiindex coefficient model(VMICM) is a promising tool to study the synergistic interaction effects between genes and multiple environmental exposures. In this dissertation, we proposed a variable selection approach for VMICM, we also generalized such approach to generalized and quantile regression settings. Their theoretical properties, simulation performance and application in genetic research were studied.Complicated diseases have both environmental and genetic risk factors, and large amount of research have been devoted to identify geneenvironment (G×E) interaction. Defined as different effect of a genotype on disease risk in persons with different environmental exposures (Ottman (1996)), we can view environmental exposures as the modulating factors in the effect of a gene. Based on this idea, we derived a three stage variable selection approach to estimate different effects of gene variables: varying, constant and zero which respectively correspond to nonlinear G$\times$E effect, no G$\times$E effect and no genetic effect. For multiple environmental exposure variables, we also select and estimate important environmental variables that contribute to the synergistic interaction effect. We theoretically evaluated the oracle property of the three step estimation method. We conducted simulation studies to further evaluate the finite sample performance of the method, considering both continuous and discrete predictors. Application to a real data set demonstrated the utility of the method.In Chapter 3, we generalized such variable selection approach to binary response setting. Instead of minimizing penalized squared error loss, we chose to maximize penalized loglikelihood function. We also theoretically evaluated the oracle property of the proposed selection approach in binary response setting. We demonstrated the performance of the model via simulation. At last, we applied our model to a Type II diabetes data set.Compared to conditional mean regression, conditional quantile regression could provide a more comprehensive understanding of the distribution of the response variable at different quantile. Even if the center of distribution is our only interest, median regression (special case of quantile regression) could offer a more robust estimator. Hence, we extended our three stage variable selection approach to a quantile regression setting in Chapter 4. We demonstrated the finite sample performance of the model via extensive simulation. And we applied our model to a birth weight data set.
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 Title
 Understanding nonradiative recombination processes of the optoelectronic materials from first principles
 Creator
 Shu, Yinan
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

"The annual potential of the solar energy hit on the Earth is several times larger than the total energy consumption in the world. This huge amount of energy source makes it appealing as an alternative to conventional fuels. Due to the problems, for example, global warming, fossil fuel shortage, etc. arising from utilizing the conventional fuels, a tremendous amount of efforts have been applied toward the understanding and developing cost effective optoelectrical devices in the past decades....
Show more"The annual potential of the solar energy hit on the Earth is several times larger than the total energy consumption in the world. This huge amount of energy source makes it appealing as an alternative to conventional fuels. Due to the problems, for example, global warming, fossil fuel shortage, etc. arising from utilizing the conventional fuels, a tremendous amount of efforts have been applied toward the understanding and developing cost effective optoelectrical devices in the past decades. These efforts have pushed the efficiency of optoelectrical devices, say solar cells, increases from 0% to 46% as reported until 2015. All these facts indicate the significance of the optoelectrical devices not only regarding protecting our planet but also a large potential market. Empirical experience from experiment has played a key role in optimization of optoelectrical devices, however, a deeper understanding of the detailed electronbyelectron, atombyatom physical processes when material upon excitation is the key to gain a new sight into the field. It is also useful in developing the next generation of solar materials. Thanks to the advances in computer hardware, new algorithms, and methodologies developed in computational chemistry and physics in the past decades, we are now able to 1).model the real size materials, e.g. nanoparticles, to locate important geometries on the potential energy surfaces(PESs); 2).investigate excited state dynamics of the cluster models to mimic the real systems; 3).screen large amount of possible candidates to be optimized toward certain properties, so to help in the experiment design. In this thesis, I will discuss the efforts we have been doing during the past several years, especially in terms of understanding the nonradiative decay process of silicon nanoparticles with oxygen defects using ab initio nonadiabatic molecular dynamics as well as the accurate, efficient multireference electronic structure theories we have developed to fulfill our purpose. The new paradigm we have proposed in understanding the nonradiative recombination mechanisms is also applied to other systems, like water splitting catalyst. Besides in gaining a deeper understanding of the mechanism, we applied an evolutionary algorithm to optimize promising candidates towards specific properties, for example, organic light emitting diodes (OLED)."Pages iiiii.
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 Title
 Ultrafast science : a multiscale modeling approach to femtosecond electron diffraction and its applications
 Creator
 Portman, Jenni Minttu Eleonora
 Date
 2014
 Collection
 Electronic Theses & Dissertations
 Description

The focus of this work is the study of processes at the edge of the current space and time resolutions. This includes both efforts in the development of an ultrafast electron microscope (UEM) and in the study of correlated electron systems that reflect measurements taken with this instrument.The development of a reliable ultrafast electron diffraction and imaging system requires a low emittance source of photoemitted electrons and an understanding of how the properties of the generated bunch...
Show moreThe focus of this work is the study of processes at the edge of the current space and time resolutions. This includes both efforts in the development of an ultrafast electron microscope (UEM) and in the study of correlated electron systems that reflect measurements taken with this instrument.The development of a reliable ultrafast electron diffraction and imaging system requires a low emittance source of photoemitted electrons and an understanding of how the properties of the generated bunch depend on the photocathode properties. In order to gain more understanding of this process, we combine the socalled threestep photoemission model with Nparticle electron simulations. By using the Fast Multipole Method to treat space charge effects, we are able to follow the time evolution of pulses containing over 106 electrons and investigate the role of laser fluence and extraction field on the total number of electrons that escape the surface as well as virtual cathode physics and the limits to spatiotemporal and spectroscopic resolution originating from the image charge on the surface and from the profile of the exciting laser pulse. The results of these simulations are compared to experimental images of the photoemission process collected using the shadow imaging technique. By contrasting the effect of varying surface properties (leading to expanding or pinned image charge) and laser profiles (Gaussian, uniform and elliptical) under different extraction field strengths and numbers of generated electrons, we quantify the effect of these experimental parameters on macroscopic pulse properties such as emittance, brightness (4D and 6D), coherence length and energy spread. Based on our results, we outline optimal conditions of pulse generation for UEM systems.With our knowledge of the photoemitted pulse properties, we also present our development of a design for the whole UEM column using the Analytic Gaussian model. We summarize the derivation of the equations governing this mean field model and show how the contributions due to the photoemission gun and the relativistic motion of the electrons can be added to this formalism to make it applicable for our system. We then explain the procedure used for optimizing the lens and RF cavity strengths and analyze both the effect of each separate optical element and their role in the column. We discuss the limits of this model and calculate the achievable temporal and spatial resolutions under different photoemission conditions.We conclude the present work with an investigation of Tantalum Disulphide (TaS_{2}), a material that presents interesting ultrafast phenomena that can be probed using the UEM. TaS_{2} is a transitionmetal layered compound that for T<190K displays a commensurate charge density wave (CCDW) phase characterized by insulating behavior with the opening of a gap at the Fermi energy. To better understand the CCDW phase and explain its quantum mechanical origin, we perform density functional theory calculations of the electronic band structure of 1TTaS_{2} and quantify the effect that spin orbit coupling and Hubbard repulsion have on the ground state. Our results show that neither of these interactions is sufficient to reproduce the insulating gap seen in experiment, an observation which is confirmed by our calculation of the phonon band structure and absorption spectrum. We also consider the effect of different stacking configurations of the TaS_{2} layers and find evidence of gap opening for bilayers in the presence of disordered stacking.
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 Title
 Truck tire/pavement interaction analysis by the finite element method
 Creator
 Meng, Lan
 Date
 2002
 Collection
 Electronic Theses & Dissertations
 Title
 Transport properties of random Schrödinger operators on correlated environments
 Creator
 Bezerra de Matos, Rodrigo
 Date
 2020
 Collection
 Electronic Theses & Dissertations
 Description

This Ph.D. thesis presents recent developments in the theory of random Schrodinger operators. Differently from what is often studied in the subject, our main results consider potentials which are not independent at distinct sites but, rather, display some form of long range correlation. These are natural objects to investigate if one wishes to understand the long term behavior of a single particle which evolves in a disordered environment but also interacts with different members of this...
Show moreThis Ph.D. thesis presents recent developments in the theory of random Schrodinger operators. Differently from what is often studied in the subject, our main results consider potentials which are not independent at distinct sites but, rather, display some form of long range correlation. These are natural objects to investigate if one wishes to understand the long term behavior of a single particle which evolves in a disordered environment but also interacts with different members of this environment (other particles, spins, etc). In chapter 2 it is shown that, within the HartreeFock approximation for the disordered Hubbard Hamiltonian, weakly interacting Fermions at positive temperature exhibit localization, suitably defined as exponential decay of eigenfunction correlators. Our result holds in any dimension in the regime of large disorder and at any disorder in the one dimensional case. As a consequence of our methods, we are able to show Holder continuity of the integrated density of states with respect to energy, disorder and interaction using known techniques. This is based on joint work with Jeffrey Schenker. Chapter 3 is based on joint work with Jeffrey Schenker and Rajinder Mavi. There we present simple, physically motivated, examples where small geometric changes on a twodimensional graph G, combined with high disorder, have a significant impact on the spectral and dynamical properties of the random Schrodinger operator AG+V[omega] obtained by adding a random potential to the graph's adjacency operator. Differently from the standard Anderson model, the random potential will be constant along vertical line, hence the models exhibit long range correlations. Moreover, one of the models presented here is a natural example where the transient and recurrent components of the absolutely continuous spectrum, introduced by Avron and Simon in [9] coexist and allow us to capture a sharp phase transition present in the system.
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 Title
 Timedomain analysis of fractional wave equations and implementations of perfectly matched layers in nonlinear ultrasound simulations
 Creator
 Zhao, Xiaofeng
 Date
 2018
 Collection
 Electronic Theses & Dissertations
 Description

The attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different fractional partial differential equations. These models for the power law attenuation of medical ultrasound have been developed using fractional calculus, where each contains one or more timefractional or spacefractional derivatives. To demonstrate the similarities and differences in the solutions to causal and noncausal fractional partial differential...
Show moreThe attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different fractional partial differential equations. These models for the power law attenuation of medical ultrasound have been developed using fractional calculus, where each contains one or more timefractional or spacefractional derivatives. To demonstrate the similarities and differences in the solutions to causal and noncausal fractional partial differential equations, timedomain Green's functions are calculated numerically for the fractional wave equations. For three timefractional wave equations, namely the power law wave equation, the Szabo wave equation, and the Caputo wave equation, these Green's functions are evaluated for water with a power law exponent of y=2, liver with a power law exponent of y=1.139, and breast with a power law exponent of y=1.5. Simulation results show that the noncausal features of the numerically calculated timedomain response are only evident in the extreme nearfield region and that the causal and the noncausal Green's functions converge to the same timedomain waveform in the farfield. When noncausal timedomain Green's functions are convolved with finitebandwidth signals, the noncausal behavior in the timedomain is eliminated, which suggests that noncausal timedomain behavior only appears in a very limited set of circumstances and that these timefractional models are equally effective for most numerical calculations.For the calculation of spacefractional wave equations, timedomain Green's functions are numerically calculated for two spacefractional models, namely the ChenHolm and TreebyCox wave equations. Numerical results are computed for these in breast and liver. The results show that these two spacefractional wave equations are causal everywhere. Away from the origin, the timedomain Green's function for the dispersive TreebyCox spacefractional wave equation is very similar to the timedomain Green's functions calculated for the corresponding timefractional wave equations, but the timedomain Green's function for the nondispersive ChenHolm spacefractional wave equation is quite different. To highlight the similarities and differences between these, timedomain Green's functions are compared and evaluated at different distances for breast and liver parameters. When timedomain Green's functions are convolved with finitebandwidth signals, the phase velocity difference in these two spacefractional wave equations is responsible for a time delay that is especially evident in the farfield.The power law wave equation is also utilized to implement a perfectly matched layer (PML) for numerical calculations with the Khokhlov  Zabolotskaya  Kuznetsov (KZK) equation. KZK simulations previously required a computational grid with a large radial distance relative to the aperture radius to delay the reflections from the boundary. To decrease the size of the computational grid, an absorbing boundary layer derived from the power law wave equation. Simulations of linear pressure fields generated by a spherically focused transducer are evaluated for a short pulse. Numerical results for linear KZK simulations with and without the absorbing boundary layer are compared to the numerical results with a sufficiently large radial distance. Simulation results with and without the PML are also evaluated, where these show that the absorbing layer effectively attenuates the wavefronts that reach the boundary of the computational grid.
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 Title
 Theory and modeling of intense ion beams and diagnostic measurements in accelerator front ends
 Creator
 Wong, Chun Yan Jonathan
 Date
 2019
 Collection
 Electronic Theses & Dissertations
 Description

Beam dynamics in front ends of ion accelerators is often subject to strong space charge and significant transverse coupling due to magnetic fields in the source and the use of focusing solenoids in the beam line. This thesis starts with an overview and a brief primer on beam dynamics to frame two research themes: simulation and analytic studies on beam dynamics, and improvements on transverse beam diagnostics. Each theme is first developed in a general treatment, followed by applications to...
Show moreBeam dynamics in front ends of ion accelerators is often subject to strong space charge and significant transverse coupling due to magnetic fields in the source and the use of focusing solenoids in the beam line. This thesis starts with an overview and a brief primer on beam dynamics to frame two research themes: simulation and analytic studies on beam dynamics, and improvements on transverse beam diagnostics. Each theme is first developed in a general treatment, followed by applications to the front end of the Facility for Rare Isotope Beams (FRIB). The first research theme includes: (1) numerical modelling of accelerator front ends, and (2) analytic studies of coupled transverse beam dynamics. In (1), a set of readily adaptable simulation tools based on the PIC code Warp is constructed to model the transport and manipulation of intense multispecies beams with high levels of detail. The tools are applied to investigate beam evolution in the FRIB front end including the species separation process. In (2), general analytic results on beams with rotational symmetry and the formalism of eigenemittances are derived to elucidate nonaxisymmetric initial conditions at the ion source and beam states advantageous for solenoid transport. The results are employed to construct LEBT/MEBT (low/medium energy beam transport) tuning schemes currently adopted at FRIB for transverse matching of strongly magnetized beams into the RFQ and cryomodules respectively. The second research theme presents improvements on transverse beam diagnostics including: (1) corrections in the conventional data analysis model of highresolution phase space measurements with Allison scanners, and (2) error minimization in beam matrix measurements and enhanced tomography capabilities using beam profile monitors. All techniques and algorithms under this theme have been verified using measurements at FRIB.
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 Title
 The mathematical models of nutritional plasticity and the bifurcation in a nonlocal diffusion equation
 Creator
 Liang, Yu, Ph. D.
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

The thesis consists of two parts. In the first part, I investigate the developmental mechanisms that regulate the nutritional plasticity of organ sizes in Drosophila melanganster, fruit fly. Here I focus on the insulinlike signalling pathway through which the developmental nutrition is signalled to growing organs. Two mathematical models, an ODE model and a PDE model, are established based on the IIS pathway. In the ODE model, the circulating gene expression of each components in IIS pathway...
Show moreThe thesis consists of two parts. In the first part, I investigate the developmental mechanisms that regulate the nutritional plasticity of organ sizes in Drosophila melanganster, fruit fly. Here I focus on the insulinlike signalling pathway through which the developmental nutrition is signalled to growing organs. Two mathematical models, an ODE model and a PDE model, are established based on the IIS pathway. In the ODE model, the circulating gene expression of each components in IIS pathway is considered as model variables. By analyzing the steady states of the ODE model under different parameter settings, the hypothesis that the difference of the nutritional plasticity among all organs of Drosophila is due to the variation of the total gene expressions of components in IIS pathway is verified. Furthermore, the forkhead transcription factor FOXO, a negative growth regulator that is activated when nutrition and insulin signaling are low is a key factor to maintain organspecific differences in nutritionalplasticity and insulinsensitivity. In the PDE model, I focus more on the molecule structure within each individual cell. The transportation of proteins between nucleus and cell membrane is modelled in the system. In simulations of the PDEs system, the hypothesis that the concentration of FOXO decrease as the concentration of insulin increase is verified.In the second part of the thesis, I study the bifurcation properties of the nonlocal diffusion equation:\[ L_{\epsilon} u + \lambda (u  u^3) = 0. \]where $L_{\epsilon} u$ is an integral defined as \[ L_{\epsilon} u = \int_{0}^{\pi} \epsilon^{3} J( \frac{yx}{\epsilon} ) ( u(y)  u(x) ) dy. \]and $J(x)$ is a nonnegative radially symmetric function with $J(0) > 0$. It is shown that as the scaling parameter $\epsilon$ is small enough the equation has the pitchfork bifurcations at the spectrum of the operator $L_{\epsilon} u$. A concrete example is considered. The bifurcations result is verified in the concrete example by solving the equation with Newton's Method.
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 Title
 The magnetic susceptibility of oxygen and nitric oxide at low field strength
 Creator
 Burris, Albert
 Date
 1943
 Collection
 Electronic Theses & Dissertations
 Title
 The estimation and hypothesis testing of treatment effects in nonequivalent control group designs when continuous growth models are assumed
 Creator
 Blumberg, Carol Joyce
 Date
 1982
 Collection
 Electronic Theses & Dissertations
 Title
 The continuoustime principalagent problem with moral hazard and recursive preferences
 Creator
 Sinha, Sumit Kumar
 Date
 2011
 Collection
 Electronic Theses & Dissertations
 Description

"The thesis deals with the three problems that belong to the intersection between stochastic analysis and financial economics. The problems are: 1. Continuoustime PrincipalAgent Problem with moral hazard under recursive preferences. 2. General maximization principle with application to problems that arise in financial economics. 3. A Functional version of Ito formula."P. 1.
 Title
 Testing of regression functions when responses are missing at random
 Creator
 Li, Xiaoyu
 Date
 2012
 Collection
 Electronic Theses & Dissertations
 Description

This thesis consists two chapters. The first chapter proposes a class of minimum distance tests for fitting a parametric regression model to a regression function when some responses are missing at random. These tests are based on a class of minimum integrated square distances between a kernel type estimator of a regression function and the parametric regression function being fitted. The estimators of the regression function are based on two completed data sets constructed by imputation and...
Show moreThis thesis consists two chapters. The first chapter proposes a class of minimum distance tests for fitting a parametric regression model to a regression function when some responses are missing at random. These tests are based on a class of minimum integrated square distances between a kernel type estimator of a regression function and the parametric regression function being fitted. The estimators of the regression function are based on two completed data sets constructed by imputation and inverse probability weighting methods. The corresponding test statistics are shown to have asymptotic normal distributions under null hypothesis. Some simulation results are also presented.The second chapter considers the problem of testing the equality of two nonparametric regression curves against a onesided alternatives based on two samples with possibly distinct design and error densities, when responses are missing at random. This chapter proposes a class of tests using imputation and covariate matching. The asymptotic distributions of these test statistics are shown to be Gaussian under null hypothesis and a class of local nonparametric alternatives. The consistency of these tests against a large class of fixed alternatives is also established. This chapter also includes a simulation study, which assesses the finite sample behavior of a member of this class of tests.
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 Title
 Surface matching and chemical scoring to detect unrelated proteins binding similar small molecules
 Creator
 Van Voorst, Jeffrey Ryan
 Date
 2011
 Collection
 Electronic Theses & Dissertations
 Description

SURFACE MATCHING AND CHEMICAL SCORING TO DETECT UNRELATED PROTEINS BINDING SIMILAR SMALL MOLECULESByJeffrey Ryan Van VoorstHow can one deduce if two clefts or pockets in different protein structures bind the same small molecule if there is no significant sequence or structural similarity between the proteins? Human pattern recognition, based on extensive structural biology or ligand design experience, is the best choice when the number of sites is small. However, to be able to scale to the...
Show moreSURFACE MATCHING AND CHEMICAL SCORING TO DETECT UNRELATED PROTEINS BINDING SIMILAR SMALL MOLECULESByJeffrey Ryan Van VoorstHow can one deduce if two clefts or pockets in different protein structures bind the same small molecule if there is no significant sequence or structural similarity between the proteins? Human pattern recognition, based on extensive structural biology or ligand design experience, is the best choice when the number of sites is small. However, to be able to scale to the thousands of structures in structural databases requires implementing that experience as computational method. The primary advantage of such a computational tool is to be able to focus human expertise on a much smaller set of enriched binding sites.Although a number of tools have been developed for this purpose by many groups [61, 51, 86, 88, 91], to our knowledge, a basic hypothesis remains untested: two proteins that bind the same small molecule have binding sites with similar chemical and shape features, even when the proteins do not share significant sequence or structural similarity. A computational method to compare protein small molecule binding sites based on surface and chemical complementarity is proposed and implemented as a software package named SimSite3D. This method is protein structure based, does not rely on explicit protein sequence or main chain similarities, and does not require the alignment of atomic centers. It has been engineered to provide a detailed search of one fragment site versus a dataset of about 13,000 full ligand sites in 2&ndash4 hours (on one processor core).Several contributions are presented in this dissertation. First, several examples are presented where SimSite3D is able to find significant matches between binding sites that have similar ligand fragments bound but are unrelated in sequence or structure. Second, including the complementarity of binding site molecular surfaces helps to distinguish between sites that share a similar chemical motif, but do not necessarily bind the same molecule. Third, a number of clear examples are provided to illustrate the challenges in comparing binding sites which should be addressed in order for a binding site comparison method to gain widespread acceptance similar to that enjoyed by BLAST[3, 4]. Finally, an optimization method for addressing protein (and small molecule) flexibility in the context of binding site comparisons is presented, prototyped, and tested.Throughout the work, computational models were chosen to strike a delicate balance between achieving sufficient accuracy of alignments, discriminating between accurate and poor alignments, and discriminating between similar and dissimilar sites. Each of these criteria is important. Due to the nature of the binding site comparison problem, each criterion presents a separate challenge and may require compromises to balance performance to achieve acceptable performance in all three categories.At the present, the problem of addressing flexibility when comparing binding site surfaces has not been presented or published by any other research group. In fact, the problem of modeling flexibility to determine correspondences between binding sites is an untouched problem of great importance. Therefore, the final goal of this dissertation is to prototype and evaluate a method that uses inverse kinematics and gradient based optimization to optimize a given objective function subject to allowed protein motions encoded as stereochemical constraints. In particular, we seek to simultaneously maximize the surface and chemical complementarity of two closely aligned sites subject to directed changes in side chain dihedral angles.
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 Title
 Study of the far field of a pulsed spray from an automotive fuel injector
 Creator
 Roshanghalb, Farid
 Date
 2015
 Collection
 Electronic Theses & Dissertations
 Description

Pulsed liquid sprays from automotive fuel injectors are inherently complicated and the formationand development of sprays involve multiple physical processes which take place both simultaneouslyand sequentially. The pulsed spray characteristics far from the injector orifice are affectedby complicated mechanisms of primary and secondary breakup at and close to the injector tip.This complexity usually requires researchers to make assumptions about breakup mechanisms. Inaddition, several...
Show morePulsed liquid sprays from automotive fuel injectors are inherently complicated and the formationand development of sprays involve multiple physical processes which take place both simultaneouslyand sequentially. The pulsed spray characteristics far from the injector orifice are affectedby complicated mechanisms of primary and secondary breakup at and close to the injector tip.This complexity usually requires researchers to make assumptions about breakup mechanisms. Inaddition, several droplet collision models have been proposed for sprays, but when used in conjunctionwith breakup mechanism models, the accuracy and limitation of collision models havebeen difficult to judge. This study is intended to explore, examine and compare different collisionmodels in a pulsed fuel spray. Since trustworthy laser diffraction measurements of dropletsize distribution can be performed far from the injector orifice, these data can be used as accurateinitial conditions for simulating downstream spray development. Since the pulsed sprays from automotivefuel injectors are relatively dense ones, this study eliminates the complexity of simulatingtwophase flow equations for breakup and instead solves the simpler fluid mechanics problem ofthe Lagrangian trajectory of spray droplets, together with a droplet collision model. It was foundthat for the singlehole sprays of this study, when the droplet size distribution is known at someplane downstream of the breakup region, the development of the spray can be modeled accuratelyby using a simple Lagrangian model which calculates the droplet collision impact parameteranalytically at each collision.
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 Title
 Study of a class of LandauLifshitz equations of ferromagnetism without exchange energy
 Creator
 Deng, Wei
 Date
 2012
 Collection
 Electronic Theses & Dissertations
 Description

LandauLifshitz equations of ferromagnetism, which are based on several competing energy contributions, are important mathematical models for the evolution of magnetization field $\m$ of a ferromagnetic material. Many problems, such as existence, stability, regularity, asymptotic behavior, thinfilm limit and numerical computation, have been well studied for the LandauLifshitz equations that include the socalled exchange energy. However, these problems turn out to be quite challenging for...
Show moreLandauLifshitz equations of ferromagnetism, which are based on several competing energy contributions, are important mathematical models for the evolution of magnetization field $\m$ of a ferromagnetic material. Many problems, such as existence, stability, regularity, asymptotic behavior, thinfilm limit and numerical computation, have been well studied for the LandauLifshitz equations that include the socalled exchange energy. However, these problems turn out to be quite challenging for equations without the exchange energy. The main reason is that when the exchange energy is included, one automatically has the magnetization vector $\m\in L^\infty((0,\infty);H^1(\Omega))$ from energy estimates, which gives some compactness and stability that are needed for using the standard methods; however, in the cases without the exchange energy, one only has $\m\in L^\infty((0,\infty);L^\infty(\Omega))$, which is too rough to get the needed compactness and stability. In this thesis, we investigate some problems for models of reduced LandauLifshitz equations with noexchange energy.In Chapter 1, we introduce the LandauLifshitz theory of ferromagnetism and summarize the main results of the thesis. The readers can check out the main results quickly in this chapter and then go to the corresponding chapters for details of proof, more discussions and further references.In Chapter 2, we study the {\em quasistationary limit} of a simple LandauLifshitzMaxwell system with the permittivity parameter $\epsilon$ approaching zero and, using this quasistationary limit, establish the existence of global weak solutions to the reduced LandauLifshitz equations with initial value $\m_0\in L^\infty(\Omega).$In Chapter 3, we establish a local $L^2$stability theorem for the global weak solutions in finite time. The key in the proof of stability theorem is that we split the nonlocal term $H_\m$ into two parts: one is bounded in $L^\infty(\Omega)$ and the other bounded in $L^2(\Omega)$. Using this stability theorem, we also provide another proof for the existence of global weak solutions for a full expression of the noexchange energy with applied field $\a(x)\in L^\infty(\Omega)$.In Chapter 4, we prove a higher time regularity for the regular solutions, using mainly induction method, together with several interpolation results. In this chapter, we also study the weak $\omega$limit sets for the socalled {\em softcase} and study the asymptotic behaviors for the special case when $\Omega$ is ellipsoid and initial values $\m_0$ are constant.In Chapter 5, we investigate a different model called the fractional LandauLifshitz equations and establish the existence of global weak solutions with initial value $\m_0\in H^\alpha(\Omega)$, where $0<\alpha<1$. In this new model, in contrast to the case when only the nonlocal term $H_\m$ is included, we have some compactness in $H^\alpha(\Omega)$, which enables us to apply the Galerkin method to establish the existence of global weak solution.
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 Title
 Structure and evolutionary dynamics in fitness landscapes
 Creator
 Pakanati, Anuraag R.
 Date
 2015
 Collection
 Electronic Theses & Dissertations
 Description

Evolution can be conceptualized as an optimization algorithm that allows populations to search through genotypes for those that produce high fitness solutions. This search process is commonly depicted as exploring a “fitness landscape”, which combines similarity relationships among genotypes with the concept of a genotypefitness map. As populations adapt to their fitness landscape, they accumulate information about the fitness landscape in which they live. A greater understanding of...
Show moreEvolution can be conceptualized as an optimization algorithm that allows populations to search through genotypes for those that produce high fitness solutions. This search process is commonly depicted as exploring a “fitness landscape”, which combines similarity relationships among genotypes with the concept of a genotypefitness map. As populations adapt to their fitness landscape, they accumulate information about the fitness landscape in which they live. A greater understanding of evolution on fitness landscapes will help elucidate fundamental evolutionary processes. I examine methods of estimating information acquisition in evolving populations and find that these techniques have largely ignored the effects of common descent. Since information is estimated by measuring conserved genomic regions across a population, common descent can create a severe bias by increasing similarities among unselected regions. I introduce a correction method to compensate for the effects of common descent on genomic information and empirically demonstrate its efficacy.Next, I explore three instantiations of NK, Avida, and RNA fitness landscapes to better understand structural properties such as the distribution of peaks and the size of basins of attraction. I find that the fitness of peaks is correlated with the fitness of peaks within their neighborhood, and that the size of peaks' basins of attraction tends to be proportional to the heights of the peaks. Finally, I visualize local dynamics and perform a detailed comparison between the space of what evolutionary trajectories are technically possible from a single starting point and the results of actual evolving populations.
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 Title
 Strategic behavior in single issue collective choice settings an experimental analysis with application to millage issue elections
 Creator
 Stengel, Daniel B.
 Date
 1984
 Collection
 Electronic Theses & Dissertations
 Title
 Stochastic modeling of routing protocols for cognitive radio networks
 Creator
 Soltani, Soroor
 Date
 2013
 Collection
 Electronic Theses & Dissertations
 Description

Cognitive radios are expected torevolutionize wireless networking because of their ability tosense, manage and share the mobile available spectrum.Efficient utilization of the available spectrum could be significantly improved by incorporating different cognitive radio based networks. Challenges are involved in utilizing the cognitive radios in a network, most of which rise from the dynamic nature of available spectrum that is not present in traditional wireless networks. The set of available...
Show moreCognitive radios are expected torevolutionize wireless networking because of their ability tosense, manage and share the mobile available spectrum.Efficient utilization of the available spectrum could be significantly improved by incorporating different cognitive radio based networks. Challenges are involved in utilizing the cognitive radios in a network, most of which rise from the dynamic nature of available spectrum that is not present in traditional wireless networks. The set of available spectrum blocks(channels) changes randomly with the arrival and departure of the users licensed to a specific spectrum band. These users are known as primary users. If a band is used by aprimary user, the cognitive radio alters its transmission power level ormodulation scheme to change its transmission range and switches to another channel.In traditional wireless networks, a link is stable if it is less prone to interference. In cognitive radio networks, however, a link that is interference free might break due to the arrival of its primary user. Therefore, links' stability forms a stochastic process with OFF and ON states; ON, if the primary user is absent. Evidently, traditional network protocols fail in this environment. New sets of protocols are needed in each layer to cope with the stochastic dynamics of cognitive radio networks.In this dissertation we present a comprehensive stochastic framework and a decision theory based model for the problem of routing packets from a source to a destination in a cognitive radio network. We begin by introducing two probability distributions called ArgMax and ArgMin for probabilistic channel selection mechanisms, routing, and MAC protocols. The ArgMax probability distribution locates the most stable link from a set of available links. Conversely, ArgMin identifies the least stable link. ArgMax and ArgMin together provide valuable information on the diversity of the stability of available links in a spectrum band. Next, considering the stochastic arrival of primary users, we model the transition of packets from one hop to the other by a SemiMarkov process and develop a Primary Spread Aware Routing Protocol (PSARP) that learns the dynamics of the environment and adapts its routing decision accordingly. Further, we use a decision theory framework. A utility function is designed to capture the effect of spectrum measurement, fluctuation of bandwidth availability and path quality. A node cognitively decides its best candidate among its neighbors by utilizing a decision tree. Each branch of the tree is quantified by the utility function and a posterior probability distribution, constructed using ArgMax probability distribution, which predicts the suitability of available neighbors. In DTCR (Decision Tree Cognitive Routing), nodes learn their operational environment and adapt their decision making accordingly. We extend the Decision tree modeling to translate video routing in a dynamic cognitive radio network into a decision theory problem. Then terminal analysis backward induction is used to produce our routing scheme that improves the peak signaltonoise ratio of the received video.We show through this dissertation that by acknowledging the stochastic property of the cognitive radio networks' environment and constructing strategies using the statistical and mathematical tools that deal with such uncertainties, the utilization of these networks will greatly improve.
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 Title
 Statistical properties of some almost Anosov systems
 Creator
 Zhang, Xu
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

We investigate the polynomial lower and upper bounds for decay of correlations of a class of twodimensional almost Anosov diffeomorphisms with respect to their SinaiRuelleBowen measures (SRB measures), where the almost Anosov diffeomorphism is a system which is hyperbolic everywhere except for one point. At the indifferent fixed point, the Jacobian matrix is an identity matrix. The degrees of the bounds are determined by the expansion and contraction rates as the orbits approach the...
Show moreWe investigate the polynomial lower and upper bounds for decay of correlations of a class of twodimensional almost Anosov diffeomorphisms with respect to their SinaiRuelleBowen measures (SRB measures), where the almost Anosov diffeomorphism is a system which is hyperbolic everywhere except for one point. At the indifferent fixed point, the Jacobian matrix is an identity matrix. The degrees of the bounds are determined by the expansion and contraction rates as the orbits approach the indifferent fixed point, and can be expressed by using coefficients of the third order terms in the Taylor expansions of the diffeomorphisms at the indifferent fixed points.We discuss the relationship between the existence of SRB measures and the differentia bility of some almost Anosov diffeomorphisms near the indifferent fixed points in dimensions bigger than one. The eigenvalue of Jacobian matrix at the indifferent fixed point along the onedimensional contraction subspace is less than one, while the other eigenvalues along the expansion subspaces are equal to one. As a consequence, there are twicedifferentiable al most Anosov diffeomorphisms that admit infinite SRB measures in two or threedimensional spaces; there exist twicedifferentiable almost Anosov diffeomorphisms with SRB measures in dimensions bigger than three. Further, we obtain the polynomial lower and upper bounds for the correlation functions of these almost Anosov maps that admit SRB measures.
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 Title
 Starquakes, heating anomalies, and nuclear reactions in the neutron star crust
 Creator
 Deibel, Alex Thomas
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

"When the most massive stars perish, their cores may remain intact in the form of extremely dense and compact stars. These stellar remnants, called neutron stars, are on the cusp of becoming black holes and reach mass densities greater than an atomic nucleus in their centers. Although the interiors of neutron stars were difficult to investigate at the time of their discovery, the advent of modern spacebased telescopes (e.g., Chandra Xray Observatory) has pushed our understanding of the...
Show more"When the most massive stars perish, their cores may remain intact in the form of extremely dense and compact stars. These stellar remnants, called neutron stars, are on the cusp of becoming black holes and reach mass densities greater than an atomic nucleus in their centers. Although the interiors of neutron stars were difficult to investigate at the time of their discovery, the advent of modern spacebased telescopes (e.g., Chandra Xray Observatory) has pushed our understanding of the neutron star interior into exciting new realms. It has been shown that the neutron star interior spans an enormous range of densities and contains many phases of matter, and further theoretical progress must rely on numerical calculations of neutron star phenomena built with detailed nuclear physics input. To further investigate the properties of the neutron star interior, this dissertation constructs numerical models of neutron stars, applies models to various observations of neutron star highenergy phenomena, and draws new conclusions about the neutron star interior from these analyses. In particular, we model the neutron star's outermost 2248 1 km that encompasses the neutron star's envelope, ocean, and crust. The model must implement detailed nuclear physics to properly simulate the hydrostatic and thermal structure of the neutron star. We then apply our model to phenomena that occur in these layers, such as: thermonuclear bursts in the envelope, gmodes in the ocean, torsional oscillations of the crust, and crust cooling of neutron star transients. A comparison of models to observations provides new insights on the properties of dense matter that are often difficult to probe through terrestrial experiments. For example, models of the quiescent cooling of neutron stars, such as the accreting transient MAXI J0556332, at late times into quiescence probe the thermal transport properties of the deep neutron star crust. This modeling provides independent data from astronomical observations on the nature of neutron superfluidity and the thermal conductivity of nuclear pasta. Our neutron star modeling efforts also pose new questions. For instance, reaction networks find that neutrino emission from cycling nuclear reactions is present in the neutron star ocean and crust, and potentially cools an accreting neutron star. This is a theory we attempt to verify using observations of neutron star transients and thermonuclear bursts, although it remains unclear if this cooling occurs. Furthermore, on some accreting neutron stars, more heat than supplied by nuclear reactions is needed to explain their high temperatures at the outset of quiescence. Although the presence of heating anomalies seems common, the source of extra heating is difficult to determine."Pages iiiii.
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