Planar graphs have a rich history that dates back to the 18th Century. They form one of the core concepts of graph theory. In computational graph theory, they offer broad advantages to algorithm design and many groundbreaking results are based on them. Formally, a given graph is either planar or non-planar. However, there exists a diverse set of established measures to estimate how far away from being planar any given graph is. In this thesis, we aim at evaluating and improving algorithms to compute these measures of non-planarity. Particularly, we study (1) the problem of finding a maximum planar subgraph, i.e., a planar subgraph with the least number of edges removed; (2) the problem of embedding a graph on a lowest possible genus surface; and finally (3) the problem of drawing a graph such that there are as few edge crossings as possible. These problems constitute classical questions studied in graph drawing and each of them is NP-hard. Still, exact (exponential time) algorithms for them are of high interest and have been subject to study for decades. We propose novel mathematical programming models, based on different planarity criteria, to compute maximum planar subgraphs and low-genus embeddings. The key aspect of our most successful new models is that they carefully describe also the relation between embedded (sub-)graphs and their duals. Based on these models, we design algorithms that beat the respective state-of-the-art by orders of magnitude. We back these claims by extensive computational studies and rigorously show the theoretical advantages of our new models. Besides exact algorithms, we consider heuristic and approximate approaches to the maximum planar subgraph problem. Furthermore, in the realm of crossing numbers, we present an automated proof extraction to easily verify the crossing number of any given graph; a new hardness result for a subproblem that arises, e.g., when enumerating simple drawings; and resolve a conjecture regarding high node degree in minimal obstructions for low crossing number.

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The primary motivation behind this research was to determine whether 3D printed lenses printed out using the non-planar technique can help achieve better beam intensity for a 60 GHz printed-circuit-board based radar and consequently improve radar efficiency. Non-planar printing is a new development in the 3D printing industry. In the non-planar printing method, the printer is moving simultaneously in all X, Y and Z-axis. This process prints with curved layers, which helps achieve a smoother surface. For this, a newly developed version of the Slic3r, specifically called non-planar Slic3r, was used. The modelled lens was imported into this Slic3r software. The G-Code was generated, and using it, non-planar lenses were printed along with planar lenses for comparison purpose. The lenses printed out using the non-planar technique were not perfectly smooth as was thought initially. Both planar and non-planar lenses measurements were taken in a watchful environment, and the measurements were later compared. The comparison of measurements showed that the non-planar lens did not show any noticeable gain in the intensity over planar lenses. The conclusion, however, is limited to the frequency range around 60 GHz, and in the case of higher frequencies, the result may change

This thesis introduces two ortho-planar MEMS devices that can be used to position microcomponents: the XZ Micropositioning Mechanism and the XYZ Micromanipulator. The displacement and force relationships are presented. The devices were fabricated using surface micromachining processes and the resulting mechanisms were tested. A compliant XYZ Micromanipulator was also designed to reduce backlash and binding. In addition, several other MEMS positioners were fabricated and tested: the Micropositioning Platform Mechanism (MPM), the Ortho-planar Twisting Micromechanism (OTM), and the Ortho-planar Spring Micromechanism (OSM).

This dissertation presents the fabrication of hollow optical waveguides integrated on planar substrates. Similar in principle to Bragg waveguides and other photonic crystal waveguides, the antiresonant reflecting optical waveguide (ARROW) is used to guide light in hollow cores filled with liquids or gases. Waveguides with liquid or gas cores are an important new building block for integrated optical sensors. The fabrication method developed for hollow ARROW waveguides makes use of standard microfabrication processes and materials. Dielectric layers are deposited on a silicon wafer using plasma-enhanced chemical vapor deposition (PECVD) to form the bottom layers of the ARROW waveguide. A sacrificial core material is then deposited and patterned. Core materials used include aluminum, SU-8 and reflowed photoresist, each resulting in a different core geometry. Additional dielectric layers are then deposited, forming the top and sides of the waveguide. The sacrificial core is then removed in an acid solution, resulting in a hollow ARROW waveguide. Experiments investigating the mechanical strength of the hollow waveguides and the etching characteristics of the sacrificial core suggest design rules for the different core types. Integration of solid-core waveguides is accomplished by etching a ridge into the top dielectric layer of the ARROW structure. Improved optical performance can be obtained by forming the waveguides on top of a raised pedestal on the silicon substrate. Loss measurements on hollow ARROW waveguides fabricated in this manner gave loss coefficients of 0.26 cm-1 for liquid-core waveguides and 2.6 cm-1 for air-core waveguides. Fluorescence measurements in liquid-core ARROW waveguides have achieved single-molecule detection sensitivity. Integrated optical filters based on ARROW waveguides were fabricated, and preliminary results of a capillary electrophoresis separation device using a hollow ARROW indicate the feasibility of such devices for future investigation.

The mixing performance of multiple transverse jets has been evaluated experimentally. Measurement techniques included laser Doppler velocimetry and planar laser induced fluorescence. Basic findings are consistent with results presented in literature for single jet mixing behavior. Mixing performance has been compared to literature for the single jet case and the Holdeman parameter has been re-evaluated for effectiveness at low jet numbers. A single jet in a confined crossflow was found to have a local minimum at B(d⁄D) = 0.721. Results for two jets indicate monotonically decreasing unmixedness for the range of conditions tested, with no local optimum apparent. Data for three jets indicate a local optimum at B(d⁄D) = 0.87and relatively flat range of mixing performance in the range of 0.75 < B(d⁄D) < 1.5. Six jets indicate a minimum unmixedness near B(d⁄D) = 0.5, but exhibited poorer mixing performance than all other configurations at the highest values of B(d⁄D)tested. The most optimum configuration tested was six jets at B(d⁄D) = 0.5, resulting in an unmixedness of 0.0192. This value was 76% lower than the next lowest configuration (three jets) at the same B(d⁄D).Total momentum was found to collapse the data well, as configurations more closely matched a historical correlation for second moment of a single confined jet more closely.

To achieve higher power density, converters and components must be able to handle higher voltage and current ratings at higher percentages of efficiency while also maintaining low cost and a compact footprint. To meet such demands, medium-voltage resonant converters have been favored by researchers for their ability to operate at higher switching frequencies. High frequency (HF) operation enables soft switching which, when achieved, reduces switching losses via either zero voltage switching (ZVS) or zero current switching (ZCS) depending on the converter topology. In addition to lower switching losses, the converter operates with low harmonic waveforms which produce less EMI compared to their hard switching counterparts. Finally, these resonant converters can be more compact because higher switching frequencies imply decreased volume of passive components. The passive component which benefits the most from this increased switching frequency is the transformer. The objective of this work is to design a >400 kHz, 100 kW transformer which will provide galvanic isolation in a Solid-State Transformer (SST) based PEBBs while maintaining high efficiency, high power density, and reduced size. This work aims to present a simplified design process for high frequency transformers, highlighting the trade-offs between co-dependent resonant converter and transformer parameters and how to balance them during the design process. This work will also demonstrate a novel high frequency transformer insulation design to achieve a partial discharge inception voltage (PDIV) of >10 kV. / Master of Science / As the world's population expands and countries progress, the demand for electricity that is high-powered, highly efficient, and dependable has increased exponentially. Further, it is integral to the longevity of global life that this development occurs in a fashion that mitigates environmental consequences. The power and technology sectors have been challenged to address the state of global environmental affairs, specifically regarding climate change, carbon dioxide emissions, and resource depletion. To move away from carbon emitting, non-renewable energy sources and processes, renewable energy sources and electric power systems must be integrated into the power grid. However, the challenge lies in the fact that there is not an easy way to interface between these renewable sources and the existing power grid. Such challenges have undermined the widespread adoption of renewable energy systems that are needed to address environmental issues in a timely manner. Recent developments in power electronics have enabled the practical application of the solid-state transformer (SST). The SST aims to replace the current, widespread form of power transformation: the line frequency transformer (50/60 Hz). This transformer is bulky, expensive, and requires a significant amount of additional circuitry to interface with renewable energy sources and electric power systems. The SST overcomes these drawbacks through high frequency operation (>200 kHz) which enables higher power at a reduced size by capitalizing on the indirect proportionality between the two parameters. The realization of the SST and its implementation has the ability to greatly advance the electrification of the transportation industry which is a top contributor to carbon emissions. This work aims to demonstrate a >400 kHz, 100 kW SST with a novel magnetic design and insulation structure suited for electric ship applications.

The third quadrant (3rd-quad) conduction (or reverse conduction) of power transistors is critical for synchronous power converters. For power metal-oxide-semiconductor field-effect-transistors (MOSFETs), there are two current paths in the 3rd-quad conduction, namely the MOS channel path and the body diode path. It is well known that, for 1.2 kV silicon carbide (SiC) planar MOSFETs, the conduction loss in the 3rd-quad is reduced by turning on the MOS channel with a positive gate bias (VGS) and keeping the dead time as small as possible. Under this scenario, the current is conducted through both paths, allowing the device to take advantage of the zero 3rd-quad forward voltage drop (VF3rd) of the MOS channel path and the small differential resistance of the body diode path. However, in this thesis work, this popular belief is found to be invalid for power MOSFETs with higher voltage ratings (e.g., 3.3 kV and 10 kV), particularly at high temperatures and current levels. The aforementioned MOS channel and body diode paths compete in the device’s 3rd-quad conduction, and their competition is affected by VGS and device structure. This thesis work presents a comparative study on the 3rd-quad behavior of 1.2 kV to 10 kV SiC planar MOSFET through a combination of device characterization, TCAD simulation and analytical modeling. It is revealed that, once the MOS channel turns on, it changes the potential distribution within the device, which further makes the body diode turn on at a source-to-drain voltage (VSD) much higher than the built-in potential of the pn junction. In 10 kV SiC MOSFETs, with the MOS channel on, the body diode does not turn on over the entire practical VSD range. As a result, the positive VGS leads to a completely unipolar conduction via the MOS channel, which could induce a higher VF3rd than the bipolar body diode at high temperatures. Circuit test is performed, which validates that a negative VGS control provides the smallest 3rd-quad voltage drop and conduction loss at high temperatures in 10 kV SiC planar MOSFET. The study is also extended to the trench MOSFET, another major structure of commercial SiC MOSFETs. Based on the revealed physics for planar MOSFETs, the optimal VGS control for the 3rd-quad conduction in different types of commercial trench MOSFETs is discussed, which provides insights for the design of high-voltage trench MOSFETs. These results provide key guidelines for the circuit applications of medium-voltage SiC power MOSFETs. / M.S. / Recent years, the prosperity of power electronics applications such as electric vehicle and smart grid has led to a rapid increase in the adoption of wide bandgap (WBG) power devices. Silicon Carbide (SiC) metal-oxide-semiconductor field-effect transistor (MOSFET) is one of the most attractive candidates in WBG devices, owing to its good tradeoff between breakdown voltage and on resistance, capability of operation at high temperatures, and superior device robustness over other WBG power devices. In most power converters, power device is required to conduct current in its third quadrant (3rd-quad) (i.e., conduct reverse current) either for handling current during the dead time or acting as a commutation switch. In a SiC MOSFET, there are two current paths in the 3rd-quad conduction, namely the MOS channel path and the body diode path. It is widely accepted that by turning on the MOS channel with a positive gate-to-source bias (VGS), both paths are turned on in parallel such that the 3rd-quad conduction loss can be reduced. In this thesis work, it is shown that this long-held opinion does not hold for SiC MOSFETs with high voltage ratings (e.g., 3.3 kV and 10 kV). Through a combination of device characterization, TCAD simulation, and analytical modeling, this thesis work unveils the competing current sharing between the MOS channel and the body diode. Once the MOS channel turns on, it delays the turn-on of the body diode and suppresses the diode current. This effect is more pronounced in MOSFETs with higher voltage ratings. In 10 kV SiC MOSFETs, with the MOS channel on, the body diode does not turn on in the practical operation conditions. At high temperatures, as the bipolar diode path possesses the conductivity modulation, which can significantly lower the voltage drop and is absent in the MOS channel, it would be optimal to turn off the MOS channel. Circuit test is also performed to validate these device findings and evaluate their impact on device applications. Finally, the study is also extended to the commercial SiC trench MOSFET, the other mainstream type of SiC power MOSFETs. These results provide key guidelines for the circuit applications of medium-voltage SiC power MOSFETs.

<p dir="ltr">Examination of gaseous detonation flow-fields represents a unique experimental challenge. High-speed shock interaction within a reactive mixture manifests combustion modes across a range of spatial-temporal scales. While the kinetics along the leading front are often characterized by adiabatic compression, simultaneously strong shear induces turbulent mixing in downstream portions of the flow. This all occurs within a wave structure typically traveling near 2000 m/s. To advance fundamental understanding, high-resolution diagnostics are required to make quantitative, time-resolved measurements of the unsteady detonation propagation.</p><p dir="ltr">In this work, detonations are experimentally studied in a single-shot, narrow channel using non-intrusive optical diagnostics. The change in wave structure between mixtures fueled by methane and natural gas was characterized using 175 kHz schlieren and CH* chemiluminescence imaging. The effect of the higher order alkanes in natural gas is speed up the reaction kinetics and produce a wave structure with smaller spatial scales and in which reaction occurs closer to the leading shock front.</p><p dir="ltr">A schlieren system operating at a rate of 5 MHz is then implemented to resolve the spatial-temporal oscillation of the leading shock front. These images are used to compute the lead shock normal speed, which enables a statistical analysis of the oscillating shock velocity. The moments of distribution are compared with computed instability levels of sixteen mixtures and a positive correlation is found. Simultaneous chemiluminescence is used to create joint distribution of shock speed and chemical length scale, which are then compared with the quasi-steady reaction zone solution.</p><p dir="ltr">Experiments are performed with highly nitrogen diluted mixtures of methane and oxygen to examine specific flow features. Different regimes of transverse wave reactivity are observed, from nonreactive to detonative. The transverse detonation wave structure is modeled using oblique shock relations and good agreement is found. The chemical length scales within the configuration are compared to the relevant expansion scales to explain the observed near-steady propagation. Distinct reactive processes following transverse wave collision are also captured. In one instance an explosion immediately occurs, while in the other a reactive gas jet grows from the point of collision. An unsteady reaction zone model is applied to understand the reaction mode within the jet.</p><p dir="ltr">Lastly, 300 kHz OH PLIF is performed to study small scale and weak reaction structures within the flow. The evolution of deflagrative burning mechanisms becomes resolvable using this technique, which highlights the benefit of its use.</p>

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