You are here
Search results
(1  20 of 124)
Pages
 Title
 A containerattachable inertial sensor for realtime hydration tracking
 Creator
 Griffith, Henry
 Date
 2019
 Collection
 Electronic Theses & Dissertations
 Description

The underconsumption of fluid is associated with multiple adverse health outcomes, including reduced cognitive function, obesity, and cancer. To aid individuals in maintaining adequate hydration, numerous sensing architectures for tracking fluid intake have been proposed. Amongst the various approaches considered, containerattachable inertial sensors offer a nonwearable solution capable of estimating aggregate consumption across multiple drinking containers. The research described herein...
Show moreThe underconsumption of fluid is associated with multiple adverse health outcomes, including reduced cognitive function, obesity, and cancer. To aid individuals in maintaining adequate hydration, numerous sensing architectures for tracking fluid intake have been proposed. Amongst the various approaches considered, containerattachable inertial sensors offer a nonwearable solution capable of estimating aggregate consumption across multiple drinking containers. The research described herein demonstrates techniques for improving the performance of these devices.A novel sip detection algorithm designed to accommodate the variable duration and sparse occurrence of drinking events is presented at the beginning of this dissertation. The proposed technique identifies drinks using a twostage segmentation and classification framework. Segmentation is performed using a dynamic partitioning algorithm which spots the characteristic inclination pattern of the container during drinking. Candidate drinks are then distinguished from handling activities with similar motion patterns using a support vector machine classifier. The algorithm is demonstrated to improve true positive detection rate from 75.1% to 98.8% versus a benchmark approach employing static segmentation. Multiple strategies for improving drink volume estimation performance are demonstrated in the latter portion of this dissertation. Proposed techniques are verified through a largescale data collection consisting of 1,908 drinks consumed by 84 individuals over 159 trials. Support vector machine regression models are shown to improve perdrink estimation accuracy versus the prior stateoftheart for a single inertial sensor, with mean absolute percentage error reduced by 11.1%. Aggregate consumption accuracy is also improved versus previously reported results for a containerattachable device.An approach for computing aggregate consumption using fill level estimates is also demonstrated. Fill level estimates are shown to exhibit superior accuracy with reduced intersubject variance versus volume models. A heuristic fusion technique for further improving these estimates is also introduced herein. Heuristic fusion is shown to reduce root mean square error versus direct estimates by over 30%. The dissertation concludes by demonstrating the ability of the sensor to operate across multiple containers.
Show less
 Title
 Effect of pavement structural response on rolling resistance and fuel economy
 Creator
 Balzarini, Danilo
 Date
 2019
 Collection
 Electronic Theses & Dissertations
 Description

The massive use of fuel required by road transportation is accountable for the exploitation of nonrenewable energy sources, is a major source of pollutants emission, and implies high economic costs. Rolling resistance is a factor affecting vehicles energy consumption; the structural rolling resistance (SRR) is the component of rolling resistance that occurs due to the deformation of the pavement structure. The present research presents an investigation on the SRR in order to identify its...
Show moreThe massive use of fuel required by road transportation is accountable for the exploitation of nonrenewable energy sources, is a major source of pollutants emission, and implies high economic costs. Rolling resistance is a factor affecting vehicles energy consumption; the structural rolling resistance (SRR) is the component of rolling resistance that occurs due to the deformation of the pavement structure. The present research presents an investigation on the SRR in order to identify its causes, characterize it and develop the instruments to predict its impact on fuel consumption for different road and traffic conditions.First the methods to calculate the SRR on asphalt and concrete pavements were developed. The structural rolling resistance is calculated as the resistance to motion caused by the uphill slope seen by the tires due to the pavement deformation. The SRR can be converted into fuel consumption using the calorific value of the fuel and the engine efficiency, and the greenhouse gas emissions associated with it can be calculated.Purely mechanistic models were used to determine the structural rolling resistance, and the fuel consumption associated with it, on 17 California pavement sections under different loading and environmental conditions. The results were used to develop simple and rapidtouse mechanistic empirical heuristic models to predict the energy dissipation associated with the structural rolling resistance on any asphalt or concrete pavement.The difference in terms of fuel consumption and pollutants emissions between different pavement structures can be significant and could be included in economic evaluations and life cycle assessment studies. For this purpose, a practical tool was createddeveloped, based on the heuristic models, that allows the calculation of the fuel consumption associated with the SRR for any given traffic and pavement section. Examples of applications of such a tool are presented and discussed.
Show less
 Title
 Recalibration of rigid pavement performance models and development of traffic inputs for PavementME design in Michigan
 Creator
 Musunuru, Gopi Krishna
 Date
 2019
 Collection
 Electronic Theses & Dissertations
 Description

The mechanisticempirical pavement design guide (AASHTOWARE PavementME) incorporates mechanistic models to estimate stresses, strains, and deformations in pavement layers using sitespecific climatic, material, and traffic characteristics. These structural responses are used to predict pavement performance using empirical models (i.e., transfer functions). The transfer functions need to be calibrated to improve the accuracy of the performance predictions, reflecting the unique field...
Show moreThe mechanisticempirical pavement design guide (AASHTOWARE PavementME) incorporates mechanistic models to estimate stresses, strains, and deformations in pavement layers using sitespecific climatic, material, and traffic characteristics. These structural responses are used to predict pavement performance using empirical models (i.e., transfer functions). The transfer functions need to be calibrated to improve the accuracy of the performance predictions, reflecting the unique field conditions and design practices. The existing local calibrations of the performance models were performed by using version 2.0 of the PavementME software. However, AASHTO has released versions 2.2 and 2.3 of the software since the completion of the last study. In the revised versions of the software, several bugs were fixed.Consequently, some performance models were modified in the newer software versions. As a result, the concrete pavement IRI predictions and the resulting PCC slab thicknesses have been impacted. The performance predictions varied significantly from the observed structural and function distresses, and hence, the performance models were recalibrated to enhance the confidence in pavement designs. Linear and nonlinear mixedeffects models were used for calibration to account for the nonindependence among the data measured on the same sections over time. Also, climate data, material properties, and design parameters were used to develop a model for predicting permanent curl for each location to address some limitations of the PavementME. This model can be used at the design stage to estimate permanent curl for a given location in Michigan.PavementME also requires specific types of traffic data to design new or rehabilitated pavement structures. The traffic inputs include monthly adjustment factors (MAF), hourly distribution factors (HDF), vehicle class distributions (VCD), axle groups per vehicle (AGPV), and axle load distributions for different axle configurations. During the last seven years, new traffic data were collected, which reflect the recent economic growth, additional, and downgraded WIM sites. Hence it was appropriate to reevaluate the current traffic inputs and incorporate any changes. Weight and classification data were obtained from 41 WeighinMotion (WIM) sites located throughout the State of Michigan to develop Level 1 (sitespecific) traffic inputs. Cluster analyses were conducted to group sites for the development of Level 2A inputs. Classification models such as decision trees, random forests, and Naive Bayes classifier were developed to assign a new site to these clusters; however, this proved difficult. An alternative simplified method to develop Level 2B inputs by grouping sites with similar attributes was also adopted. The optimal set of attributes for developing these Level 2B inputs were identified by using an algorithm developed in this study. The effects of the developed hierarchical traffic inputs on the predicted performance of rigid and flexible pavements were investigated using the PavementME. Based on the statistical and practical significance of the life differences, appropriate levels were established for each traffic input. The methodology for developing traffic inputs is intuitive and practical for future updates. Also, there is a need to identify the change in traffic patterns to update the traffic inputs so that the pavement sections would not be overdesigned or underdesigned. Models were developed where the shortterm counts from the PTR sites can be used as inputs to check if the new traffic patterns cause any substantial differences in design life predictions.
Show less
 Title
 Investigation of the possibility of efficient Lband SRF cavities for mediumbeta heavy ion multichargestate beams
 Creator
 Shanab, Safwan
 Date
 2020
 Collection
 Electronic Theses & Dissertations
 Description

The possibility of using 1288 MHz (Lband) SRF elliptical cavities to accelerate heavy ion multichargestate (up to 5 charge states) beams is being investigated for accelerating energy higher than 200 MeV/u. This cavity can be a potential energy upgrade for heavy ions linac accelerators such as the Facility for Rare Isotope Beams (FRIB) in the United States of America and Rare Isotope Science Project (RISP) in Korea. One of possible disadvantages of the Lband frequency structure is its...
Show moreThe possibility of using 1288 MHz (Lband) SRF elliptical cavities to accelerate heavy ion multichargestate (up to 5 charge states) beams is being investigated for accelerating energy higher than 200 MeV/u. This cavity can be a potential energy upgrade for heavy ions linac accelerators such as the Facility for Rare Isotope Beams (FRIB) in the United States of America and Rare Isotope Science Project (RISP) in Korea. One of possible disadvantages of the Lband frequency structure is its small longitudinal acceptance. It should be sufficiently large for transporting the ions with the limited beam loss ensuring accelerator handson maintenance.A first simple analytic study was performed and it showed a promising result with 1288 MHz linac. In addition, from beam loss point of view, the study deduced that 1288 MHz linac frequency could be the limit for mediumbeta heavy ion up to five charge states beam accelerators. This work is the result of the detailed beam dynamics simulation for the linac performance using TRACK code to confirm the analytic result. The result shows that the longitudinal acceptance is large enough for mediumbeta heavy ion with five charge state beams. Usually accelerator upgrade projects have limitations such as environment, space, and cryogenic cooling plant. Thus, high frequency and high gradient cavity is demanded to resolve such limitations. Exploiting cavity nitrogen doping technology would be beneficial for efficient cryogenics.Nitrogen doping technology has shown that it is more beneficial for higher frequencies cavities. This impact on BCS surface resistance (RBCS). RBCS is proportional to the frequency squared, nitrogen doping technology benefit is larger in the higher frequencies. For instance, the benefit is larger at 1300 MHz cavity than low frequency cavities such as 650 MHz cavity. That is due to the fact that BCS surface resistance, RBCS (depends on temperature and electron mean free path of the niobium material) is higher than the residual surface resistance, Rres (Temperature independent) in higher frequencies. The Research and Development (R&D) of nitrogen doping technology is still on going. However our neon doping proposal to give us more insight on the physics of nitrogen doping of RF surfaces and confirm or refute the assumption that the interstitial nitrogen atoms play the role of improving the cavity intrinsic quality factor not the nitrogen nitride (NbN) chemical compositions hasn't been implemented yet, it is still an open question.
Show less
 Title
 I. amhb : (anti)aromaticitymodulated hydrogen bonding. ii. evaluation of implicit solvation models for predicting hydrogen bond free energies
 Creator
 Kakeshpour, Tayeb
 Date
 2019
 Collection
 Electronic Theses & Dissertations
 Description

My doctoral research under Professor James E. Jackson focused on hydrogen bonding (Hbonding) using physical organic chemistry tools. In the first chapter, I present how I used quantum chemical simulations, synthetic organic chemistry, NMR spectroscopy, and Xray crystallography to provide robust theoretical and experimental evidence for an interplay between (anti)aromaticity and Hbond strength of heterocycles, a concept that we dubbed (Anti)aromaticityModulated Hydrogen Bonding (AMHB). In...
Show moreMy doctoral research under Professor James E. Jackson focused on hydrogen bonding (Hbonding) using physical organic chemistry tools. In the first chapter, I present how I used quantum chemical simulations, synthetic organic chemistry, NMR spectroscopy, and Xray crystallography to provide robust theoretical and experimental evidence for an interplay between (anti)aromaticity and Hbond strength of heterocycles, a concept that we dubbed (Anti)aromaticityModulated Hydrogen Bonding (AMHB). In the second chapter, I used accurately measured hydrogen bond energies for a range of substrates and solvents to evaluate the performance of implicit solvation models in combination with density functional methods for predicting solution phase hydrogen bond energies. This benchmark study provides useful guidelines for a priori modeling of hydrogen bondingbased designs.Coordinates of the optimized geometries and crystal structures are provided as supplementary materials.
Show less
 Title
 Ab initio molecular dynamics : applications to defective silicon nanocrystals and developments toward dense manifold systems
 Creator
 Peng, WeiTao
 Date
 2019
 Collection
 Electronic Theses & Dissertations
 Description

Ab initio molecular dynamics (AIMD) methods consider the nuclear motions under the potential generated by electronic wavefunctions which are determined from ab initio quantum mechanical calculations onthefly. AIMD methods allow researchers to investigate chemical processes without prior knowledge or assumptions about the shape of the potential energy surface (PES). In this thesis, we applied AIMD methods to study silicon nanocrystals with dangling bond defects (DBSiNCs). DB defects on...
Show moreAb initio molecular dynamics (AIMD) methods consider the nuclear motions under the potential generated by electronic wavefunctions which are determined from ab initio quantum mechanical calculations onthefly. AIMD methods allow researchers to investigate chemical processes without prior knowledge or assumptions about the shape of the potential energy surface (PES). In this thesis, we applied AIMD methods to study silicon nanocrystals with dangling bond defects (DBSiNCs). DB defects on SiNCs have been known as nonradiative (NR) decay centers. However, the atomistic mechanism for the decay process is unclear. Previously, researchers considered a pyramidalization mode surrounding the DB site involved in the process. Based on our AIMD calculations on the first excited state and the static analysis of the PESs of SiNC systems, we discovered that asymmetrical SiSi bond stretching modes surrounding DB sites are important, in addition to pyramidalization. Most importantly, we found a lowlying defectinduced conical intersection (DICI) in the neutral DB system. The minimum energy conical intersection (MECI) is estimated to be 1.74 eV above the ground state minimum energy geometry by application of multistate complete active space secondorder perturbation theory (MSCASPT2) to a small cluster model system. In addition, the roles of charged DBs on NR decay process are investigated. We found DICIs for both positively and negatively charged DB systems. The MECI energies are 2.10 eV and 2.65 eV respectively. The rationalization of the existence of conical intersections and detailed dynamics after excitation of these systems are discussed in the thesis. Additionally, to study the possible defectdefect interactions during the NR recombination process, we considered slab models with two DB defects at short (4 0303A) and long (100303 A) separations. According to our simulations, the NR recombination process is localized on a single DB site, regardless the defectdefect distances. However, energy transfer between defect sites with short separations is possible.For the defective SiNC systems, we demonstrated the power of the AIMD method to investigate the dynamics after excitations. However, the applications of AIMD to highlying states are much more challenging, due to the dense manifold of states that cause immense computational effort. In the thesis, we developed several methods toward the application to such systems. First, we developed a timedependent configuration interaction (TDCI) method that can simulate the electron dynamics under a strong field efficiently. The method is based on the direct scheme to form the vector, , which can be accelerated by a graphical processing unit. A TDCI calculation with 853776 determinants requires only 20.1 hours to propagate to 100 fs with 1 attosecond (1018 second) time steps. On the other hand, when the field is strong enough, the electrons can be driven to the boundary of the basis set, which would cause unphysical effects such as reflection. To account for this, we developed an analytical expression for a moleculecentered complex absorbing potential which can be evaluated efficiently to remove the unwanted effects. Finally, for the nuclear dynamics, we developed an Ehrenfest dynamics method based on the TDCI wavefunction. In this approach, the nuclear motions are propagated under the averaged potential generated by TDCI wave function, thus the approach is promising for application to systems with dense manifolds of states.
Show less
 Title
 Comparison of methods for detecting violations of measurement invariance with continuous construct indicators using latent variable modeling
 Creator
 Zhang, Mingcai (Graduate of Michigan State University)
 Date
 2020
 Collection
 Electronic Theses & Dissertations
 Description

Measurement invariance (MI) refers to the fact that the measurement instrument measures the same concept in the same way in two or more groups. However, in educational and psychological testing practice, the assumption of MI is often violated due to the contamination by possible noninvariance in the measurement models. In the framework of Latent Variable Modeling (LVM), methodologists have developed different statistical methods to identify the noninvariant components. Among these methods,...
Show moreMeasurement invariance (MI) refers to the fact that the measurement instrument measures the same concept in the same way in two or more groups. However, in educational and psychological testing practice, the assumption of MI is often violated due to the contamination by possible noninvariance in the measurement models. In the framework of Latent Variable Modeling (LVM), methodologists have developed different statistical methods to identify the noninvariant components. Among these methods, the free baseline method (FR) is popularly employed, but this method is limited due to the necessity of choosing a truly invariant reference indicator (RI). Two other methods, namely, the BenjaminiHochberg method (BH) and the alignment method (AM) are exempt from the RI setting. The BH method applies the false discovery rate (FDR) procedure. The AM method aims to optimize the model estimates under the assumption of approximate invariance. The purpose of the present study is to address the problem of RI setting by comparing the BH method and the AM method with the traditional free baseline method through both a simulation study and an empirical data analysis. More specifically, the simulation study is designed to investigate the performances of the three methods through varying the sample sizes and the characteristics of noninvariance embedded in the measurement models. The characteristics of noninvariance are distinguished as the location of noninvariant parameters, the degree of noninvariant parameters, and the magnitude of model noninvariance. The performances of these three methods are also compared on an empirical dataset (Openness for Problem Solving Scale in PISA 2012) that is obtained from three countries (ShanghaiChina, Australia, and the United States).The simulation study finds that the wrong RI choice heavily impacts the FR method, which produces high type I error rates and low statistical power rates. Both the BH method and the AM method perform better than the FR method in this setting. Comparatively speaking, the benefit of the BH method is that it performs the best by achieving high powers for detecting noninvariance. The power rate increases with lowering the magnitude of model noninvariance, and with increasing sample size and degree of noninvariance. The AM method performs the best with respect to type I errors. The type I error rates estimated by the AM method are low under all simulation conditions. In the empirical study, both the BH method and the AM method perform similarly in estimating the invariance/noninvariance patterns among the three country pairs. However, the FR method, for which the RI is the first item by default, recovers a different invariance/noninvariance pattern. The results can help the methodologists gain a better understanding of the potential advantages of the BH method and the AM method over the traditional FR method. The study results also highlight the importance of correctly specifying the model noninvariance at the indicator level. Based on the characteristics of the noninvariant components, practitioners may consider deleting/modifying the noninvariant indicators or free the noninvariant components while building partial invariant models in order to improve the quality of crossgroup comparisons.
Show less
 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.
Show less
 Title
 Mathematical modeling and computation of molecular solvation and binding
 Creator
 Wang, Bao
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

This dissertation contains a couple of results on biophysics modeling and computation, ranging from solvated molecular conformation modeling to molecular solvation and binding modeling in the solvent environment.We study the solvent excluded surface in Eulerian representation, provide the surface area and enclosed volume calculation, the molecular topological analysis is also addressed. We further analyze the electrostatic for the solvated molecules with the Eulerian solvent excluded surface....
Show moreThis dissertation contains a couple of results on biophysics modeling and computation, ranging from solvated molecular conformation modeling to molecular solvation and binding modeling in the solvent environment.We study the solvent excluded surface in Eulerian representation, provide the surface area and enclosed volume calculation, the molecular topological analysis is also addressed. We further analyze the electrostatic for the solvated molecules with the Eulerian solvent excluded surface. We show that our surface is analytical without any numerical approximation.We study the coarse grid Poisson Boltzmann solver. Our software enables extremely accurate numerical solution to the Poisson Boltzmann equation even at very large grid spacing. As a consequence, our software provides a reliable electrostatic calculation for the solvation and protein ligand binding related problem.We study the blind solvation free energy prediction problem. A hybrid of physical and statistical protocol is proposed for highly accurate solvation free energy prediction. Furthermore, to mediate the force field parametrization influence on the solvation free energy prediction, we propose a learning to rank based solvation free energy prediction paradigm.We explore the protein ligand binding free energy prediction and docking scoring via the learning to rank approach. In which a learn to rank based scoring function is proposed for accurate protein ligand binding scoring.
Show less
 Title
 Kinetically modeling total ion chromatograms and extracted ion profiles to identify ignitable liquids for fire debris applications
 Creator
 Capistran, Briana Ashley
 Date
 2020
 Collection
 Electronic Theses & Dissertations
 Description

Identification of ignitable liquids in fire debris samples is typically conducted via comparison of total ion chromatograms (TICs) of such samples to reference collections containing chromatograms of common liquids. Due to the extent of liquid evaporation in fires, reference collections often contain TICs of ignitable liquids that have been experimentally evaporated to various levels; however, such evaporations can be time intensive. A kinetic model was developed to predict evaporation rate...
Show moreIdentification of ignitable liquids in fire debris samples is typically conducted via comparison of total ion chromatograms (TICs) of such samples to reference collections containing chromatograms of common liquids. Due to the extent of liquid evaporation in fires, reference collections often contain TICs of ignitable liquids that have been experimentally evaporated to various levels; however, such evaporations can be time intensive. A kinetic model was developed to predict evaporation rate constants of compounds as a function of GC retention index. The model can be applied to predict chromatograms of ignitable liquids at any evaporation level, alleviating the need to perform experimental evaporations. Previous work demonstrated good predictive accuracy of the model for petroleum distillate liquids and gasoline.In this work, the kinetic model was applied to ignitable liquids of the isoparaffinic, naphthenicparaffinic, and aromatic ASTM classes. Predicted extracted ion profiles (EIPs) were generated in addition to TICs for each liquid, and good predictive accuracy of the model was demonstrated with PPMC coefficients as high as 0.9983. Reference collections containing predicted TICs and EIPs were generated. The TICs and EIPs of singleblind samples and largescale burn samples were compared to the reference collections; in all cases, the correct ASTM liquid class was identified. Use of the EIP reference collection for the burn samples resulted in higher correlation compared to the TIC collection due to reduced substrate interferences. Overall, this work demonstrates the utility of a kinetic model for generating predicted reference collections as a tool in the identification of ignitable liquids for fire debris applications.
Show less
 Title
 Numerical methods for gravity inversion, synthetic aperture radar, and traveltime tomography
 Creator
 Gao, Qinfeng
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

"Inverse problems have many applications. In this thesis, we focus on designing and implementing numerical methods for three inverse problems: gravity inversion, synthetic aperture radar, and traveltime tomography. We present extensive numerical examples to demonstrate that these algorithms are stable and efficient. In Chapter 2, lowrank approximation is incorporated into a local levelset method for gravity inversion. This change helps to reduce the computational time of the mismatch...
Show more"Inverse problems have many applications. In this thesis, we focus on designing and implementing numerical methods for three inverse problems: gravity inversion, synthetic aperture radar, and traveltime tomography. We present extensive numerical examples to demonstrate that these algorithms are stable and efficient. In Chapter 2, lowrank approximation is incorporated into a local levelset method for gravity inversion. This change helps to reduce the computational time of the mismatch gravity force term on the boundary, and reduces the computational complexity from O(N3 ) to O(N2 ) in 2D and from O(N5 ) to O(N4 ) in 3D. Many numerical results show that the locations of unknown objects are accurately captured by this lowrank levelset method. In Chapter 3, both the wave equation and Radon transform are carried out as an approach to the synthetic aperture radar problem. The waveequationbased method includes harmonic extension at terminal time, solving the wave equation backward using a perfectly matched layer, and Neumann iteration. These two methods provide comparable results and help to prove that a curved flight path is no better than a straight one. In Chapter 4, we implement the finite element method as a penalizationregularizationoperator splitting method for traveltime tomography based on the eikonal equation. Both the travel time and slowness are recovered with this algorithm in both 2D and 3D. Finally, Chapter 5 contains our conclusions."Page ii.
Show less
 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.
Show less
 Title
 Simulation of amorphous silicon anode in lithiumion batteries
 Creator
 Wang, Miao (Graduate of Michigan State University)
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

"The energy density of the current generation of Liion batteries (LIBs) is only about 1% of that of gasoline. Improving the energy density of the LIBs is critical for vehicle electrification. Employing high capacity electrode materials is a key factor in this endeavor. Silicon (Si) is one of the high capacity anode materials for LIBs. However, Si experiences large volume variation (up to 300%) during battery cycling, which affects the structural integrity of battery and results in rapid...
Show more"The energy density of the current generation of Liion batteries (LIBs) is only about 1% of that of gasoline. Improving the energy density of the LIBs is critical for vehicle electrification. Employing high capacity electrode materials is a key factor in this endeavor. Silicon (Si) is one of the high capacity anode materials for LIBs. However, Si experiences large volume variation (up to 300%) during battery cycling, which affects the structural integrity of battery and results in rapid capacity fading. It has been shown that the cycle life of Si anode can be improved greatly through novel electrode designs. So far, such work is conducted through experiments. Numerical simulations have the potentials for design optimization of LIBs, as demonstrated in multiphysics models for LIBs with graphite anode. This research extends a previously developed microstructureresolved multiphysics (MRM) model to LIBs with amorphous Si anode. The MRM model considers the electrochemical reactions, Li transport in electrodes and electrolyte, lithiation induced volume change, mechanical strains and stresses, material property evolution with lithiation, and the chemomechanical coupling. The model is solved using finite element package COMSOL Multiphysics. The major challenges in this work are the large deformation of the Si, and the uncertainty in parameters and the coupling relation. To simulate the large deformation of Si, a large strain based formulation for the concentration induced volume expansion was used. The electrolyte was modeled as fluid. A method to simulate the galvanostatic charge/discharge of a finite deformation electrode with moving boundary was developed. Important model parameters were determined one by one by correlating the simulation to appropriate experiments. For example, the Li diffusivity in Si reported in literature varies from 1013 to 1019 m2 /s. To estimate this parameter, the insitu transmission electron microscope experiment of twophase lithiation of aSi nanospheres was simulated. The diffusivity was found at the order of 2×1017m2 /s for the lithium poor phase in first lithiation and 2×1015 m2 /s for lithium rich phase and in subsequent cycles. The reaction rate constant and the apparent transfer coefficient are determined in a similar way using different experiments. In literature, different forms of chemomechanical coupling theories have been proposed for Li diffusion in Si. The coupling relationship and parameters were often derived based on one type of experiment even though the process is highly coupled. In this work, the chemomechanical coupling was investigated by simulations of two geometries: a thin film and a sphere. A strong asymmetric rate behavior between lithiation and delithiation has been observed in thin film aSi anode but not in other geometries. The results reveal that the rate behavior is affected by the geometry and the constraint of the electrode, the chemomechanical coupling, and the prior process. A substrateconstrained film has a relatively low surface/volume ratio and a constant surface area. Its lithiation has a great tendency to be hindered by surface limitation. The chemomechanical coupling plays an important role in the specific rate behavior of a geometry. Finally, an MRM model was built for a half cell with aSi nanowalls as anode. The specific and volumetric capacities of the cell as a function of size, length/size ratio, spacing of the nanostructure, and the Li+ concentration in electrolyte were investigated. The results show that the factors reducing the concentration polarization can enhance the maximum achievable SOC of the cell. However, the cell with the highest SOC does not necessarily lead to the highest capacity."Page iiiii.
Show less
 Title
 Brain connectivity analysis using information theory and statistical signal processing
 Creator
 Wang, Zhe (Software engineer)
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

Connectivity between different brain regions generates our minds. Existing work on brain network analysis has mainly been focused on the characterization of connections between the regions in terms of connectivity and causality. Connectivity measures the dependence between regional brain activities, and causality analysis aims to determine the directionality of information flow among the functionally connected brain regions, and find the relationship between causes and effects.Traditionally,...
Show moreConnectivity between different brain regions generates our minds. Existing work on brain network analysis has mainly been focused on the characterization of connections between the regions in terms of connectivity and causality. Connectivity measures the dependence between regional brain activities, and causality analysis aims to determine the directionality of information flow among the functionally connected brain regions, and find the relationship between causes and effects.Traditionally, the study on connectivity and causality has largely been limited to linear relationships. In this dissertation, as an effort to achieve more accurate characterization of connections between brain regions, we aim to go beyond the linear model, and develop innovative techniques for both nondirectional and directional connectivity analysis. Note that due to variability in the brain connectivity of each individual, the connectivity between two brain regions alone may not be sufficient for brain function analysis, in this research, we also conduct network connectivity pattern analysis, so as to reveal more indepth information.First, we characterize nondirectional connectivity using mutual information (MI). In recent years, MI has gradually appeared as an alternative metric for brain connectivity, since it measures both linear and nonlinear dependence between two brain regions, while the traditional Pearson correlation only measures the linear dependence. We develop an innovative approach to estimate the MI between two functionally connected brain regions and apply it to brain functional magnetic resonance imaging (fMRI) data. It is shown that: on average, cognitively normal subjects show larger mutual information between critical regions than Alzheimer's disease (AD) patients.Second, we develop new methodologies for brain causality analysis based on directed information (DI). Traditionally, brain causality is based on the wellknown Granger Causality (GC) analysis. The validity of GC has been widely recognized. However, it has also been noticed that GC relies heavily on the linear prediction method. When there exists strong nonlinear interactions between two regions, GC analysis may lead to invalid results. In this research, (i) we develop an innovative framework for causality analysis based on directed information (DI), which reflects the information flow from one region to another, and has no modeling constraints on the data. It is shown that DI based causality analysis is effective in capturing both linear and nonlinear causal relationships. (ii) We show the conditional equivalence between the DI Framework and Friston's dynamic causal modeling (DCM), and reveal the relationship between directional information transfer and cognitive state change within the brain. Finally, based on brain network connectivity pattern analysis, we develop a robust method for the AD, mild cognitive impairment (MCI) and normal control (NC) subject classification under size limited fMRI data samples. First, we calculate the Pearson correlation coefficients between all possible ROI pairs in the selected subnetwork and use them to form a feature vector for each subject. Second, we develop a regularized linear discriminant analysis (LDA) approach to reduce the noise effect. The feature vectors are then projected onto a subspace using the proposed regularized LDA, where the differences between AD, MCI and NC subjects are maximized. Finally, a multiclass AdaBoost Classifier is applied to carry out the classification task. Numerical analysis demonstrates that the combination of regularized LDA and the AdaBoost classifier can increase the classification accuracy significantly.
Show less
 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.
Show less
 Title
 Dynamics of horizontal axis wind turbines and systems with parametric stiffness
 Creator
 Acar, Gizem Dilber
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

"The dynamics of a wind turbine blade under bendbendtwist coupled vibrations is investigated. The potential and kinetic energy expressions for a straight nonuniform blade are written in terms of beam parameters. Then, the energies are expressed in terms of modal coordinates by using the assumed modes method, and the equations of motion are found by applying Lagrange's formula. The bendbendtwist equations are coupled with each other, and have stiffness variations due to centrifugal effects...
Show more"The dynamics of a wind turbine blade under bendbendtwist coupled vibrations is investigated. The potential and kinetic energy expressions for a straight nonuniform blade are written in terms of beam parameters. Then, the energies are expressed in terms of modal coordinates by using the assumed modes method, and the equations of motion are found by applying Lagrange's formula. The bendbendtwist equations are coupled with each other, and have stiffness variations due to centrifugal effects and gravitational parametric terms which vary cyclicly with the hub angle. To determine the natural frequencies and mode shapes of the system, a modal analysis is applied on the linearized coupled equations of constant angle snapshots of a blade with effects of constant speed rotation. Lower modes of the coupled bendbendtwist model are dominantly inplane or outofplane modes. To investigate the parametric effects, several blade models are analyzed at different angular positions. The stiffness terms involving centrifugal and gravitational effects can be significant for long blades. To further see the effect of blade length on relative parametric stiffness change, the blade models are scaled in size, and analyzed at constant rotational speeds, at horizontal and vertical orientations. Bladehub dynamics of a horizontalaxis wind turbine is also studied. Blade equations are coupled through the hub equation, and have parametric terms due to cyclic aerodynamic forces, centrifugal effects and gravitational forces. The modal inertia of a single blade is defined by the linear mass density times the square of transverse displacements from blade's undeflected axis. For reasonable transverse displacements, the modal inertia of a blade is usually small compared to the rotor inertia which is the combined inertia of the hub plus all three blades about the shaft. This enables us to treat the effect of blade motion as a perturbation on the rotor motion. The rotor speed is not constant, and the cyclic variations cannot be expressed as explicit functions of time. By casting the rotor angle as the independent variable, and assuming small variations in rotor speed, the leading order blade equations are decoupled from the rotor equation. The interdependent blade equations constitute a threedegreeoffreedom system with periodic parametric and direct excitation. The response is analyzed by using the method of multiple scales. The system has superharmonic and subharmonic resonances due to direct and parametric effects introduced by gravity. Amplitudefrequency relations and stabilities of these resonances are studied. The Mathieu equation represents the transient dynamics of a singlemode blade model. Approximate solutions to the linear unforced Mathieu equation, and their stabilities, are investigated. Floquet theory shows that the solution can be written as a product between an exponential part and a periodic part at the same frequency or half the frequency of excitation. An approach combining Floquet theory with the harmonic balance method is investigated. A Floquet solution having an exponential part with an unknown exponential argument and a periodic part consisting of a truncated series of harmonics is assumed. Then, performing harmonic balance, the Floquet exponents and and harmonic coefficients are found. From this frequencies of the response and stability of the solution are determined. The truncated solution is consistent with an existing infinite series solution for the undamped case. The truncated solution is then applied to the damped Mathieu equation and to parametric excitation with two harmonics. Solutions and stability of multidegreeoffreedom Mathieutype systems are also investigated. A procedure similar to the one applied for the Mathieu equation is used to find the initial conditions response, frequency content, and stability characteristics. The approach is applied to two and threedegreesoffreedom examples. For a few parameter sets, the results obtained from this method are compared to the numerical solutions. This study provides a framework for a transient analysis of threeblade turbine equations."Pages iiiii.
Show less
 Title
 Design and simulation of singlecrystal diamond diodes for high voltage, high power and high temperature applications
 Creator
 Suwanmonkha, Nutthamon
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

ABSTRACTDESIGN AND SIMULATION OF SINGLECRYSTAL DIAMOND DIODES FOR HIGH VOLTAGE, HIGH POWER AND HIGH TEMPERATURE APPLICATIONSByNutthamon SuwanmonkhaDiamond has exceptional properties and great potentials for making highpower semiconducting electronic devices that surpass the capabilities of other common semiconductors including silicon. The superior properties of diamond include wide bandgap, high thermal conductivity, large electric breakdown field and fast carrier mobilities. All of these...
Show moreABSTRACTDESIGN AND SIMULATION OF SINGLECRYSTAL DIAMOND DIODES FOR HIGH VOLTAGE, HIGH POWER AND HIGH TEMPERATURE APPLICATIONSByNutthamon SuwanmonkhaDiamond has exceptional properties and great potentials for making highpower semiconducting electronic devices that surpass the capabilities of other common semiconductors including silicon. The superior properties of diamond include wide bandgap, high thermal conductivity, large electric breakdown field and fast carrier mobilities. All of these properties are crucial for a semiconductor that is used to make electronic devices that can operate at high power levels, high voltage and high temperature.Twodimensional semiconductor device simulation software such as Medici assists engineers to design device structures that allow the performance requirements of device applications to be met. Most physical material parameters of the wellknown semiconductors are already compiled and embedded in Medici. However, diamond is not one of them. Material parameters of diamond, which include the models for incomplete ionization, temperatureandimpuritydependent mobility, and impact ionization, are not readily available in software such as Medici. Models and data for diamond semiconductor material have been developed for Medici in the work based on results measured in the research literature and in the experimental work at Michigan State University. After equipping Medici with diamond material parameters, simulations of various diamond diodes including Schottky, PNjunction and merged Schottky/PNjunction diode structures are reported. Diodes are simulated versus changes in doping concentration, drift layer thickness and operating temperature. In particular, the diode performance metrics studied include the breakdown voltage, turnon voltage, and specific onresistance. The goal is to find the designs which yield low power loss and provide high voltage blocking capability. Simulation results are presented that provide insight for the design of diamond diodes using the various diode structures. Results are also reported on the use of field plate structures in the simulations to control the electric field and increase the breakdown voltage.
Show less
 Title
 Semiparametric models for mouthlevel indices in caries research
 Creator
 Yang, Yifan
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

For nonnegative count responses in health services research, a large proportion of zero counts are frequently encountered. For such data, the frequency of zero counts is typically larger than its expected counterpart under the classical parametric models, such as Poisson or negative binomial model. In this thesis, a semiparametric zeroinflated regression model is proposed for count data that directly relates covariates to the marginal mean response representing the desired target of...
Show moreFor nonnegative count responses in health services research, a large proportion of zero counts are frequently encountered. For such data, the frequency of zero counts is typically larger than its expected counterpart under the classical parametric models, such as Poisson or negative binomial model. In this thesis, a semiparametric zeroinflated regression model is proposed for count data that directly relates covariates to the marginal mean response representing the desired target of inference. The model specifically assumes two semiparametric forms: the loglinear form for the marginal mean and the logisticlinear form for the susceptible probability, in which the fully linear models are replaced with partially linear link functions. A splinebased estimation is proposed for the nonparametric components of the model. Asymptotic properties are discussed for the estimators of the parametric and nonparametric components of the models. Specifically, the estimators are shown to be strong consistent and asymptotically efficient under mild regularity conditions. A bootstrap hypothesis test is performed to evaluate difference involving the nonparametric component. Simulation studies are conducted to evaluate the finite sample performance of the model. Finally, the model is applied to dental caries indices in low income AfricanAmerican children to evaluate the nonlinear effects of sugar intake on caries development. The conclusion shows that the effect of sugar intake on caries indices is nonlinear, especially among young children under the age of 2. And children whose caregivers are unemployed and have poor oral healthy exhibit higher dental caries rates.
Show less
 Title
 Merging activespace and renormalized coupledcluster methods via the CC(P;Q) formalism, with applications to chemical reaction profiles and singlettriplet gaps
 Creator
 Bauman, Nicholas P.
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

The development of accurate and computationally efficient wave function methods that can capture and balance dynamical and nondynamical manyelectron correlation effects to describe multireference problems, such as potential energy surfaces involving bond breaking, biradicals, and excited states characterized by dominant manyelectron excitations, is one of the main goals of quantum chemistry. Among the promising approaches in this endeavor are the completely renormalized and activespace...
Show moreThe development of accurate and computationally efficient wave function methods that can capture and balance dynamical and nondynamical manyelectron correlation effects to describe multireference problems, such as potential energy surfaces involving bond breaking, biradicals, and excited states characterized by dominant manyelectron excitations, is one of the main goals of quantum chemistry. Among the promising approaches in this endeavor are the completely renormalized and activespace coupledcluster (CC) and equationofmotion (EOM) CC methods. While the completely renormalized and activespace CC and EOMCC approaches have been very successful in many applications, there are some cases where they do not capture the dynamical or nondynamical manyelectron correlation effects in a satisfactory manner. In this dissertation, we introduce the CC(P;Q) formalism, which alleviates this concern by combining the completely renormalized and activespace together. The CC(P;Q) scheme provides a systematic approach to correcting energies obtained in the activespace CC and EOMCC calculations that recover much of the nondynamical and some dynamical manyelectron correlation effects for the remaining, mostly dynamical, correlation effects missing in the activespace CC and EOMCC considerations. We discuss the development of the CC(t;3), CC(t,q;3), CC(t,q;3,4), and CC(q;4) methods, which use the CC(P,Q) formalism to correct energies obtained with the CC and EOMCC approaches with singles, doubles, and activespace triples (CCSDt/EOMCCSDt) for missing triple excitations (CC(t;3)), or to correct energies obtained with the CC and EOMCC approaches with singles, doubles, and activespace triples and quadruples (CCSDtq/EOMCCSDtq) for missing triples (CC(t,q;3)) or missing triples and quadruples (CC(t,q;3,4)), or even to correct energies obtained with the CC and EOMCC approaches with singles, doubles, triples, and activespace quadruples (CCSDTq/EOMCCSDTq) for correlation effects due to the missing quadruple excitations (CC(q;4)). By examining the double dissociation of water, the Be + H2 > HBeH insertion, and the singlettriplet gaps in the strongly biradical (HFH) system and the BN molecule, we demonstrate that the CC(t;3), CC(t,q;3), and CC(t,q;3,4) methods reproduce the total and relative energies obtained with the parent full CC/EOMCC approaches with singles, doubles, and triples or singles, doubles, triples, and quadruples to within fractions of a millihartree at the tiny fraction of the computer cost, even when the electronic quasidegeneracies become substantial.The CC(P;Q) formulation prompted the development of efficient CCSDt, CCSDtq, and CCSDTq programs. In this dissertation, we describe the technique of spinintegration for both closed and open shells, and how the resulting equations for CCSDTQ were automatically derived and implemented in a factorized form. We also discuss how the efficiency of the code was improved by removing unnecessary operations through, in particular, the reorganization of the relevant loops. Finally, we explain how the CCSDTQ code was transformed to obtain the activespace CCSDtq and CCSDTq approaches, which are the most essential parts of the CC(t,q;3), CC(t,q;3,4), and CC(q;4) calculations.
Show less
 Title
 Multiscale Gaussianbeam method for highfrequency wave propagation and inverse problems
 Creator
 Song, Chao
 Date
 2018
 Collection
 Electronic Theses & Dissertations
 Description

The existence of Gaussian beam solution to hyperbolic PDEs has been known to the pure mathematics community since sometime in the 1960s [3]. It enjoys popularity afterwards due to its ability to resolve the caustics problem and its efficiency [49, 28, 31]. In this thesis, we will focus on the extension of the multiscale Gaussian beam method and its application to seismic wave modeling and inversion. In the first part of thesis, we discuss the application of the multiscale Gaussian beam...
Show moreThe existence of Gaussian beam solution to hyperbolic PDEs has been known to the pure mathematics community since sometime in the 1960s [3]. It enjoys popularity afterwards due to its ability to resolve the caustics problem and its efficiency [49, 28, 31]. In this thesis, we will focus on the extension of the multiscale Gaussian beam method and its application to seismic wave modeling and inversion. In the first part of thesis, we discuss the application of the multiscale Gaussian beam method to the inverse problem. A new multiscale Gaussian beam method is introduced for carrying out trueamplitude prestack migration of acoustic waves. After applying the Born approximation, the migration process is considered as shooting two beams simultaneously from the subsurface point which we want to image. The Multiscale Gaussian Wavepacket transform provides an efficient and accurate way for both decomposing the perturbation field and initializing Gaussian beam solution. Moreover, we can prescribe both the region of imaging and the range of dipping angles by shooting beams from a subsurface point in the region of imaging. We prove the imaging condition equation rigorously and conduct error analysis. Some numerical approximations are derived to improve the efficiency further. Numerical results in the twodimensional space demonstrate the performance of the proposed migration algorithm. In the second part of thesis, we propose a new multiscale Gaussian beam method with reinitialization to solve the elastic wave equation in the high frequency regime with different boundary conditions. A novel multiscale transform is proposed to decompose any arbitrary vectorvalued function to multiple Gaussian wavepackets with various resolution. After the step of initializing, we derive various rules corresponding to different types of reflection cases. To improve the efficiency and accuracy, we develop a new reinitialization strategy based on the stationary phase approximation method to sharpen each single beam ansatz. This is especially useful and necessary in some reflection cases. Numerical examples with various parameters demonstrate the correctness and robustness of the whole method. There are two boundary conditions considered here, the periodic and the Dirichlet boundary condition. In the end, we show that the convergence rate of the proposed multiscale Gaussian beam method follows the convergence rate of the classical Gaussian beam solution.
Show less