DIMENSION REDUCTION FOR POWER SYSTEM MODELING USING PCA METHODS CONSIDERING INCOMPLETE DATA READINGS

Principal Component Analysis (PCA) is a popular method for dimension reduction that can be used in many fields including data compression, image processing, exploratory data analysis, etc. However, traditional PCA method has several drawbacks, since the traditional PCA method is not efficient for dealing with high dimensional data and cannot be effectively applied to compute accurate enough principal components when handling relatively large portion of missing data. In this report, we propose to use EM-PCA method for dimension reduction of power system measurement with missing data, and provide a comparative study of traditional PCA and EM-PCA methods. Our extensive experimental results show that EM-PCA method is more effective and more accurate for dimension reduction of power system measurement data than traditional PCA method when dealing with large portion of missing data set.

Three dimensional finite element simulation of polymer melting and flow in a single-screw extruder : optimization of screw channel geometry

Single-screw extrusion is one of the widely used processing methods in plastics industry, which was the third largest manufacturing industry in the United States in 2007 [5]. In order to optimize the single-screw extrusion process, tremendous efforts have been devoted for development of accurate models in the last fifty years, especially for polymer melting in screw extruders. This has led to a good qualitative understanding of the melting process; however, quantitative predictions of melting from various models often have a large error in comparison to the experimental data. Thus, even nowadays, process parameters and the geometry of the extruder channel for the single-screw extrusion are determined by trial and error. Since new polymers are developed frequently, finding the optimum parameters to extrude these polymers by trial and error is costly and time consuming. In order to reduce the time and experimental work required for optimizing the process parameters and the geometry of the extruder channel for a given polymer, the main goal of this research was to perform a coordinated experimental and numerical investigation of melting in screw extrusion. In this work, a full three-dimensional finite element simulation of the two-phase flow in the melting and metering zones of a single-screw extruder was performed by solving the conservation equations for mass, momentum, and energy. The only attempt for such a three-dimensional simulation of melting in screw extruder was more than twenty years back. However, that work had only a limited success because of the capability of computers and mathematical algorithms available at that time. The dramatic improvement of computational power and mathematical knowledge now make it possible to run full 3-D simulations of two-phase flow in single-screw extruders on a desktop PC. In order to verify the numerical predictions from the full 3-D simulations of two-phase flow in single-screw extruders, a detailed experimental study was performed. This experimental study included Maddock screw-freezing experiments, Screw Simulator experiments and material characterization experiments. Maddock screw-freezing experiments were performed in order to visualize the melting profile along the single-screw extruder channel with different screw geometry configurations. These melting profiles were compared with the simulation results. Screw Simulator experiments were performed to collect the shear stress and melting flux data for various polymers. Cone and plate viscometer experiments were performed to obtain the shear viscosity data which is needed in the simulations. An optimization code was developed to optimize two screw geometry parameters, namely, screw lead (pitch) and depth in the metering section of a single-screw extruder, such that the output rate of the extruder was maximized without exceeding the maximum temperature value specified at the exit of the extruder. This optimization code used a mesh partitioning technique in order to obtain the flow domain. The simulations in this flow domain was performed using the code developed to simulate the two-phase flow in single-screw extruders.

In-situ electrical, mechanical and electrochemical characterizations of one-dimensional nanostructures

One-dimensional nanostructures initiated new aspects to the materials applications due to their superior properties compared to the bulk materials. Properties of nanostructures have been characterized by many techniques and used for various device applications. However, simultaneous correlation between the physical and structural properties of these nanomaterials has not been widely investigated. Therefore, it is necessary to perform in-situ study on the physical and structural properties of nanomaterials to understand their relation. In this work, we will use a unique instrument to perform real time atomic force microscopy (AFM) and scanning tunneling microscopy (STM) of nanomaterials inside a transmission electron microscopy (TEM) system. This AFM/STM-TEM system is used to investigate the mechanical, electrical, and electrochemical properties of boron nitride nanotubes (BNNTs) and Silicon nanorods (SiNRs). BNNTs are one of the subjects of this PhD research due to their comparable, and in some cases superior, properties compared to carbon nanotubes. Therefore, to further develop their applications, it is required to investigate these characteristics in atomic level. In this research, the mechanical properties of multi-walled BNNTs were first studied. Several tests were designed to study and characterize their real-time deformation behavior to the applied force. Observations revealed that BNNTs possess highly flexible structures under applied force. Detailed studies were then conducted to understand the bending mechanism of the BNNTs. Formations of reversible ripples were observed and described in terms of thermodynamic energy of the system. Fracture failure of BNNTs were initiated at the outermost walls and characterized to be brittle. Second, the electrical properties of individual BNNTs were studied. Results showed that the bandgap and electronic properties of BNNTs can be engineered by means of applied strain. It was found that the conductivity, electron concentration and carrier mobility of BNNTs can be tuned as a function of applied stress. Although, BNNTs are considered to be candidate for field emission applications, observations revealed that their properties degrade upon cycles of emissions. Results showed that due to the high emission current density, the temperature of the sample was increased and reached to the decomposition temperature at which the B-N bonds start to break. In addition to BNNTs, we have also performed in-situ study on the electrochemical properties of silicon nanorods (SiNRs). Specifically, lithiation and delithiation of SiNRs were studied by our STM-TEM system. Our observations showed the direct formation of Li22Si5 phases as a result of lithium intercalation. Radial expansion of the anode materials were observed and characterized in terms of size-scale. Later, the formation and growth of the lithium fibers on the surface of the anode materials were observed and studied. Results revealed the formation of lithium islands inside the ionic liquid electrolyte which then grew as Li dendrite toward the cathode material.

Planar magneto-photonic and gradient-photonic structures : crystals and metamaterials.

In the field of photonics, two new types of material structures, photonic crystals and metamaterials, are presently of great interest. Both are studied in the present work, which focus on planar magnetic materials in the former and planar gradient metamaterials in the latter. These planar periodic structures are easy to handle and integrate into optical systems. The applications are promising field for future optical telecommunication systems and give rise to new optical, microwave and radio technologies. The photonic crystal part emphasizes the utilization of magnetic material based photonic crystals due to its remarkable magneto-optical characteristics. Bandgaps tuning by magnetic field in bismuth-gadolinium-substituted lutetium iron garnet (Bi0.8 Gd0.2 Lu2.0 Fe5 O12) based one- dimensional photonic crystals are investigated and demonstrated in this work. Magnetic optical switches are fabricated and tested. Waveguide formulation for band structure in magneto photonic crystals is developed. We also for the first time demonstrate and test two- dimensional magneto photonic crystals optical. We observe multi-stopbands in two- dimensional photonic waveguide system and study the origin of multi-stopbands. The second part focus on studying photonic metamaterials and planar gradient photonic metamaterial design. We systematically study the effects of varying the geometry of the fishnet unit cell on the refractive index in optical frequency. It is the first time to design and demonstrate the planar gradient structure in the high optical frequency. Optical beam bending using planar gradient photonic metamaterials is observed. The technologies needed for the fabrication of the planar gradient photonic metamaterials are investigated. Beam steering devices, shifter, gradient optical lenses and etc. can be derived from this design.

Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

Optical hysteresis of ridge waveguide magnetic garnet films and cavities in two-dimensional magneto-photonic crystal slabs

Magnetic iron garnets as well as magnetic photonic crystals are of great interests in magneto-optic applications such as isolators, current captors, circulators, TE-TM mode conversion, wavelength accordable filters, optical sensors and switches, all of which provide a promising platform for future integrated optical circuits. In the present work, two topics are studied based on magnetic iron garnet films. In the first part, the characteristics of the magnetization are investigated for ridge waveguides fabricated on (100) oriented iron garnet thin films. The magnetic response in magneto-optic waveguides patterned on epitaxial magnetic garnet films depends on the crystallographic orientation of the waveguides and the magnetic anisotropy of the material. These can be studied by polarization rotation hysteresis loops, which are related to the component of magnetization parallel to the light propagation direction and the linear birefringence. Polarization rotation hysteresis loops for low birefringence waveguides with different orientations are experimentally investigated. Asymmetric stepped curves are obtained from waveguides along, due to the large magnetocrystalline anisotropy in the plane. A model based on the free energy density is developed to demonstrate the motion of the magnetization and can be used in the design of magneto-optic devices. The second part of this thesis focuses on the design and fabrication of high-Q cavities in two-dimensional magneto-photonic crystal slabs. The device consists of a layer of silicon and a layer of iron garnet thin film. Triangular lattice elliptical air holes are patterned in the slab. The fundamental TM band gap overlaps with the first-order TE band gap from 0374~0.431(a/λ) showing that both TE and TM polarization light can be confined in the photonic crystals. A nanocavity is designed to obtain both TE and TM defect modes in the band gaps. Additional work is needed to overlap the TE and TM defect modes and obtain a high-Q cavity so as to develop miniaturized Faraday rotators.

INVESTIGATING THE ROLE OF THE CONTACT LINE IN HETEROGENEOUS NUCLEATION WITH HIGH SPEED IMAGING

While nucleation of solids in supercooled liquids is ubiquitous [15, 65, 66], surface crystallization, the tendency for freezing to begin preferentially at the liquid-gas interface, has remained puzzling [74, 18, 68, 69, 51, 64, 72, 16]. Here we employ high-speed imaging of supercooled water drops to study the phenomenon of heterogeneous surface crystallization. Our geometry avoids the "point-like contact" of prior experiments by providing a simple, symmetric contact line (triple line defined by the substrate-liquid-air interface) for a drop resting on a homogeneous silicon substrate. We examine three possible mechanisms that might explain these laboratory observations: (i) Line Tension at the triple line, (ii) Thermal Gradients within the droplets and (iii) Surface Texture. In our first study we record nearly perfect spatial uniformity in the immersed (liquid-substrate) region and, thereby, no preference for nucleation at the triple line. In our second study, no influence of thermal gradients on the preference for freezing at the triple line was observed. Motivated by the conjectured importance of line tension (τ) [1, 66] for heterogeneous nucleation, we also searched for evidence of a transition to surface crystallization at length scales on the order of δ ∼ τ/σ, where σ is the surface tension [14]; poorly constrained τ [49] leads to δ ranging from microns to nanometers. We demonstrate that nano-scale texture causes a shift in the nucleation to the three-phase contact line, while micro-scale texture does not. The possibility of a critical length scale has implications for the effectiveness of nucleation catalysts, including formation of ice in atmospheric clouds [7].

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Benson's Theorem for Partial Geometries

In 1970 Clark Benson published a theorem in the Journal of Algebra stating a congruence for generalized quadrangles. Since then this theorem has been expanded to other specific geometries. In this thesis the theorem for partial geometries is extended to develop new divisibility conditions for the existence of a partial geometry in Chapter 2. Then in Chapter 3 the theorem is applied to higher dimensional arcs resulting in parameter restrictions on geometries derived from these structures. In Chapter 4 we look at extending previous work with partial geometries with α = 2 to uncover potential partial geometries with higher values of α. Finally the theorem is extended to strongly regular graphs in Chapter 5. In addition we obtain expressions for the multiplicities of the eigenvalues of matrices related to the adjacency matrices of these graphs. Finally, a four lesson high school level enrichment unit is included to provide students at this level with an introduction to partial geometries, strongly regular graphs, and an opportunity to develop proof skills in this new context.

IN-SITU ELECTRICAL, MECHANICAL AND ELECTROCHEMICAL CHARACTERIZATIONS OF ONE-DIMENSIONAL NANOSTRUCTURES

One-dimensional nanostructures initiated new aspects to the materials applications due to their superior properties compared to the bulk materials. Properties of nanostructures have been characterized by many techniques and used for various device applications. However, simultaneous correlation between the physical and structural properties of these nanomaterials has not been widely investigated. Therefore, it is necessary to perform in-situ study on the physical and structural properties of nanomaterials to understand their relation. In this work, we will use a unique instrument to perform real time atomic force microscopy (AFM) and scanning tunneling microscopy (STM) of nanomaterials inside a transmission electron microscopy (TEM) system. This AFM/STM-TEM system is used to investigate the mechanical, electrical, and electrochemical properties of boron nitride nanotubes (BNNTs) and Silicon nanorods (SiNRs). BNNTs are one of the subjects of this PhD research due to their comparable, and in some cases superior, properties compared to carbon nanotubes. Therefore, to further develop their applications, it is required to investigate these characteristics in atomic level. In this research, the mechanical properties of multi-walled BNNTs were first studied. Several tests were designed to study and characterize their real-time deformation behavior to the applied force. Observations revealed that BNNTs possess highly flexible structures under applied force. Detailed studies were then conducted to understand the bending mechanism of the BNNTs. Formations of reversible ripples were observed and described in terms of thermodynamic energy of the system. Fracture failure of BNNTs were initiated at the outermost walls and characterized to be brittle. Second, the electrical properties of individual BNNTs were studied. Results showed that the bandgap and electronic properties of BNNTs can be engineered by means of applied strain. It was found that the conductivity, electron concentration and carrier mobility of BNNTs can be tuned as a function of applied stress. Although, BNNTs are considered to be candidate for field emission applications, observations revealed that their properties degrade upon cycles of emissions. Results showed that due to the high emission current density, the temperature of the sample was increased and reached to the decomposition temperature at which the B-N bonds start to break. In addition to BNNTs, we have also performed in-situ study on the electrochemical properties of silicon nanorods (SiNRs). Specifically, lithiation and delithiation of SiNRs were studied by our STM-TEM system. Our observations showed the direct formation of Li22Si5 phases as a result of lithium intercalation. Radial expansion of the anode materials were observed and characterized in terms of size-scale. Later, the formation and growth of the lithium fibers on the surface of the anode materials were observed and studied. Results revealed the formation of lithium islands inside the ionic liquid electrolyte which then grew as Li dendrite toward the cathode material.

HIGH VOLTAGE ELECTROPHORETIC DEPOSITION FOR ELECTROCHEMICAL ENERGY STORAGE AND OTHER APPLICATIONS

High voltage electrophoretic deposition (HVEPD) has been developed as a novel technique to obtain vertically aligned forests of one-dimensional nanomaterials for efficient energy storage. The ability to control and manipulate nanomaterials is critical for their effective usage in a variety of applications. Oriented structures of one-dimensional nanomaterials provide a unique opportunity to take full advantage of their excellent mechanical and electrochemical properties. However, it is still a significant challenge to obtain such oriented structures with great process flexibility, ease of processing under mild conditions and the capability to scale up, especially in context of efficient device fabrication and system packaging. This work presents HVEPD as a simple, versatile and generic technique to obtain vertically aligned forests of different one-dimensional nanomaterials on flexible, transparent and scalable substrates. Improvements on material chemistry and reduction of contact resistance have enabled the fabrication of high power supercapacitor electrodes using the HVEPD method. The investigations have also paved the way for further enhancements of performance by employing hybrid material systems and AC/DC pulsed deposition. Multi-walled carbon nanotubes (MWCNTs) were used as the starting material to demonstrate the HVEPD technique. A comprehensive study of the key parameters was conducted to better understand the working mechanism of the HVEPD process. It has been confirmed that HVEPD was enabled by three key factors: high deposition voltage for alignment, low dispersion concentration to avoid aggregation and simultaneous formation of holding layer by electrodeposition for reinforcement of nanoforests. A set of suitable parameters were found to obtain vertically aligned forests of MWCNTs. Compared with their randomly oriented counterparts, the aligned MWCNT forests showed better electrochemical performance, lower electrical resistance and a capability to achieve superhydrophpbicity, indicating their potential in a broad range of applications. The versatile and generic nature of the HVEPD process has been demonstrated by achieving deposition on flexible and transparent substrates, as well as aligned forests of manganese dioxide (MnO2) nanorods. A continuous roll-printing HVEPD approach was then developed to obtain aligned MWCNT forest with low contact resistance on large, flexible substrates. Such large-scale electrodes showed no deterioration in electrochemical performance and paved the way for practical device fabrication. The effect of a holding layer on the contact resistance between aligned MWCNT forests and the substrate was studied to improve electrochemical performance of such electrodes. It was found that a suitable precursor salt like nickel chloride could be used to achieve a conductive holding layer which helped to significantly reduce the contact resistance. This in turn enhanced the electrochemical performance of the electrodes. High-power scalable redox capacitors were then prepared using HVEPD. Very high power/energy densities and excellent cyclability have been achieved by synergistically combining hydrothermally synthesized, highly crystalline α-MnO2 nanorods, vertically aligned forests and reduced contact resistance. To further improve the performance, hybrid electrodes have been prepared in the form of vertically aligned forest of MWCNTs with branches of α-MnO2 nanorods on them. Large- scale electrodes with such hybrid structures were manufactured using continuous HVEPD and characterized, showing further improved power and energy densities. The alignment quality and density of MWCNT forests were also improved by using an AC/DC pulsed deposition technique. In this case, AC voltage was first used to align the MWCNTs, followed by immediate DC voltage to deposit the aligned MWCNTs along with the conductive holding layer. Decoupling of alignment from deposition was proven to result in better alignment quality and higher electrochemical performance.

DEVELOPMENT OF A 2-DIMENSIONAL FINITE VOLUME MODEL TO ASSESS HYDRODYNAMIC AND MICROBIAL CONTROLS ON DNAPL DISSOLUTION AND DETOXIFICATION

Tetrachloroethene (PCE) and trichloroethene (TCE) form dense non-aqueous phase liquids (DNAPLs), which are persistent groundwater contaminants. DNAPL dissolution can be "bioenhanced" via dissolved contaminant biodegradation at the DNAPL-water interface. This research hypothesized that: (1) competitive interactions between different dehalorespiring strains can significantly impact the bioenhancement effect, and extent of PCE dechlorination; and (2) hydrodynamics will affect the outcome of competition and the potential for bioenhancement and detoxification. A two-dimensional coupled flowtransport model was developed, with a DNAPL pool source and multiple microbial species. In the scenario presented, Dehalococcoides mccartyi 195 competes with Desulfuromonas michiganensis for the electron acceptors PCE and TCE. Simulations under biostimulation and low velocity (vx) conditions suggest that the bioenhancement with Dsm. michiganensis alone was modestly increased by Dhc. mccartyi 195. However, the presence of Dhc. mccartyi 195 enhanced the extent of PCE transformation. Hydrodynamic conditions impacted the results by changing the dominant population under low and high vx conditions.