We propose a new framework for understanding block Krylov subspace methods, which hinges on a matrix-valued inner product. We can recast the ``classical" block Krylov methods, such as O'Leary's block conjugate gradients, global methods, and loop-interchange methods, within this framework. Leveraging the generality of the framework, we develop an efficient restart procedure and error bounds for the shifted block full orthogonalization method (Sh-BFOM(m)). Regarding BFOM as the prototypical block Krylov subspace method, we propose another formalism, which we call modified BFOM, and show that block GMRES and the new block Radau-Lanczos method can be regarded as modified BFOM. In analogy to Sh-BFOM(m), we develop an efficient restart procedure for shifted BGMRES with restarts (Sh-BGMRES(m)), as well as error bounds. Using this framework and shifted block Krylov methods with restarts as a foundation, we formulate block Krylov subspace methods with restarts for matrix functions acting on multiple vectors f(A)B. We obtain convergence bounds for \bfomfom (BFOM for Functions Of Matrices) and block harmonic methods (i.e., BGMRES-like methods) for matrix functions. With various numerical examples, we illustrate our theoretical results on Sh-BFOM and Sh-BGMRES. We also analyze the matrix polynomials associated to the residuals of these methods. Through a variety of real-life applications, we demonstrate the robustness and versatility of B(FOM)^2 and block harmonic methods for matrix functions. A particularly interesting example is the tensor t-function, our proposed definition for the function of a tensor in the tensor t-product formalism. Despite the lack of convergence theory, we also show that the block Radau-Lanczos modification can reduce the number of cycles required to converge for both linear systems and matrix functions. / Mathematics

No / Given only the traffic correlations of counts and intervals, a Batch Renewal Arrival Process (BRAP) is completely determined, as the least biased choice and thus, it provides the analytic means to construct suitable traffic models for the study of queueing systems independently of any other traffic characteristics. In this context, the BRAP and the Batch Markovian Arrival Process (BMAP) are employed in the continuous time domain towards the analysis of the stable BRAP/GE/1 and BMAP/GE/1 queues with infinite capacity, single servers and generalized exponential (GE) service times. Novel closed form expressions for the steady state probabilities of these queues are obtained, based on the embedded Markov chains (EMCs) technique and the matrix-geometric (M-G) method, respectively. Moreover, the stable GEsGGeo/GE/1 queue with GE-type service times and a GEsGGeo BRAP consisting of bursty GE-type batch interarrival times and a shifted generalized geometric (sGGeo) batch size distribution is adopted to assess analytically the combined adverse effects of varying degrees of correlation of intervals between individual arrivals and the burstiness of service times upon the typical quality of service (QoS) measure of the mean queue length (MQL). Moreover, a comprehensive experimental study is carried out to investigate numerically the relative impact of count and interval traffic correlations as well as other traffic characteristics upon the performance of stable BRAP/GE/1 and BMAP/GE/1 queues. It is suggested via a conjecture that the BRAP/GE/1 queue is likely to yield pessimistic performance metrics in comparison to those of the stable BMAP/GE/1 queues under the worst case scenario (i.e., a worst case scenario) of the same positive count and interval traffic correlations arising from long sojourn in each phase.

Power converters used in high reliability radiation hardened space applications trail their commercial counterparts in terms of power density and efficiency. This is due to the additional challenges that arise in the design of space rated power converters from the harsh environment they need to operate in, to the limited availability of space qualified components and field demonstrated power converter topologies. New radiation hardened Gallium Nitride (GaN) Field Effect Transistors (FETs) with their inherent radiation tolerance and superior performance over Silicon Power Metal Oxide Semiconductor Field Effect Transistors (MOSFETs) are a promising alternative to improve power density and performance in space power converters. This thesis presents the considerations and design of a practical implementation of the Phase Shifted Full Bridge DC-DC Isolated converter with synchronous rectification for space applications. Recently released radiation hardened GaN FETs were used in the Full Bridge and synchronous rectifier power stages. A survey outlining the benefits of new radiation hardened GaN FETs for space power applications compared to current radiation hardened power MOSFETs is included. In addition, this work presents the overall design process followed to design the DC-DC converter power stage, as well as a comprehensive power loss analysis. Furthermore, this work includes details to implement a conventional hard-switched Full Bridge DC-DC converter for this application. An efficiency and component stress comparison was performed between the hard-switched Full Bridge design and the Phase Shifted Full Bridge DC-DC converter design. This comparison highlights the benefits of phase shift modulation (PSM) and zero voltage switching (ZVS) for GaN FET applications. Furthermore, different magnetic designs were characterized and compared for efficiency in both converters. The DC-DC converters implemented in this work regulate the output to a nominal 20 V, delivering 500 W from a nominal 100 V DC Bus input. Complete fault analysis and protection circuitry required for a space-qualified implementation is not addressed by this work. / MS / Recently released radiation-hardened Gallium Nitride (GaN) Field Effect Transistors (FETs) offer the opportunity to increase efficiency and power density of space DC-DC power converters. The current state of the art for space DC-DC power conversion trails their commercial counterparts in terms of power density and efficiency. This is mainly due to two factors. The first factor is related to the additional challenges that arise in the design of space rated power converters from the harsh environment they need to operate in, to the limited availability of space qualified components and field demonstrated converter topologies. The second factor lies in producing reliable radiation hardened power Metal Oxide Semiconductor Field Effect Transistors (MOSFETs). GaN FETs not only have better electrical performance than power MOSFETs, they have also demonstrated inherent tolerance to radiation. This results in less structural device changes needed to make GaN FETs operate reliably under high radiation compared to their MOSFETs counterparts. This work outlines the design implications of using newly released radiation hardened GaN FETs to implement a fixed frequency isolated Phase Shifted Full Bridge DC-DC converter while strictly abiding to the design constraints found in space-power converter applications. In addition, a one-to-one performance comparison was made between the soft-switched Phase Shift modulated Full Bridge and the conventional hard-switched Full Bridge DC-DC converter. Finally, different magnetic designs were evaluated in the laboratory to assess their impact on converter efficiency.

The battery charger plays an important role in the development of electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEVs).This thesis focuses on the DC-DC converter for high voltage battery charger and is divided into four chapters. The background related to EV battery charger is introduced, and the topologies of isolated DC-DC converter possibly applied in battery charge are sketched in Chapter 1. Since the EV battery charger is high voltage high power, the phase-shifted full bridge and LLC converters, which are popularly used in high power applications, are discussed in detail in Chapter 2. They are generally considered as high efficiency, high power density and high reliability, but their prominent features are also limited in certain range of operation. To make full use of the advantages and to avoid the limitation of the phase-shifted full bridge and LLC converters, a novel hybrid resonant and PWM converter combining resonant LLC half-bridge and phase shifted full-bridge topology is proposed and is described in Chapter 3. The converter achieves high efficiency and true soft switching for the entire operation range, which is very important for high voltage EV battery charger application. A 3.4 kW hardware prototype has been designed, implemented and tested to verify that the proposed hybrid converter truly avoids the disadvantages of LLC and phase-shifted full bridge converters while maintaining their advantages. In this proposed hybrid converter, the utilization efficiency of the auxiliary transformer is not that ideal. When the duty cycle is large, LLC converter charges one of the capacitors but the energy stored in the capacitor has no chance to be transferred to the output, resulting in the low utilization efficiency of the auxiliary transformer. To utilize the auxiliary transformer fully while keeping all the prominent features of the previous hybrid converter in Chapter 3, an improved hybrid resonant and PWM converter is proposed in Chapter 4. The idea has been verified with simulations. The last chapter is the conclusion which summaries the key features and findings of the two proposed hybrid converters. / Master of Science

Modern arc welding machines utilize controllable high frequency DC/DC power supply with high dynamic and steady state current regulation performance. In the design robustness, small size and low weight, low complexity, and high efficiency are the defining criteria. The most suitable approach for a 5 kW arc welding machine power supply application is the high frequency Full-Bridge Phase-Shifted Zero Voltage Switching (FB-PS-ZVS) DC/DC converter with an isolation transformer. This converter not only gives the advantage of zero voltage switching for a wide load current range, it also provides reduced Electromagnetic Interference (EMI) and reduced component stress compared to standard PWM converters. In this thesis a FB-PS-ZVS DC/DC converter with 5 kW power rating is designed for modern arc welding machine applications. IGBTs are utilized at 50 kHz switching frequency for high efficiency and control bandwidth. The output current of the DC/DC converter is controlled via a Digital Signal Processor (DSP) control platform. The performance of the designed DC/DC converter is evaluated via the computer simulations and the experimental study of the constructed prototype.

In this thesis a two-stage AC/DC/DC power converter is designed and implemented. The AC/DC input stage of the converter consists of the two&amp / #8211 / phase interleaved boost topology employing the average current mode control principle. The output stage consists of a zero voltage switching phase shifted full bridge (ZVS&amp / #8211 / PS&amp / #8211 / FB) DC/DC converter. For the input stage, main design goals are obtaining high input power factor, low input current distortion, and well regulated output dc voltage, and obtaining these attributes in a power converter with high power density. For the input stage, the interleaved structure has been chosen in order to obtain reduced line current ripple and EMI, reduced power component stresses, and improved power density. The control of the pre&amp / #8211 / regulator is provided by utilizing a new commercial monolithic integrated circuit, which provides interleaved continuous conduction mode power factor correction (PFC). The output stage is formed by utilizing the available prototype hardware of a ZVS&amp / #8211 / PS&amp / #8211 / FB DC/DC converter and mainly the system integration and controller design and implementation studies have been conducted. The converter small signal model is derived and utilizing its transfer function and employing voltage loop control, the output voltage regulator has been designed. The output voltage controller is implemented utilizing a digital signal processor (DSP). Integrating the AC/DC preregulator and DC/DC converter, a laboratory AC/DC/DC converter system with high overall performance has been obtained. The overall system performance has been verified via computer simulations and experimental results obtained from laboratory prototype.

Bi-directional DC-DC converters are used for applications that require a flow of energy in two directions, while a wide range converter offer efficient operation over a wide range of input and output voltages. However, an efficient technology that is both bi-directional and Wide Input Wide Output (WIWO), currently, does not currently exist.   To find a suitable topology, the work began by surveying the existing literature and when a potentially suitable solution was identified, it was evaluated via simulation.   Using a wide range, unidirectional topology as the starting point, a converter topology was designed, capable of reconfiguring its transformer ratios by controlling the synchronization of its switches.   By aiming to use soft switching in simulation, this topology was improved to reach 92\% efficiency in the forward mode and 95\% in the reverse mode of operation. Furthermore, a prototype of this converter was developed that reached 82\% efficiency. While this prototype requires a better controller, hardware optimization and testing for optimal performance, the proposed technology was verified via simulation to work as a WIWO converter that is also bi-directional.

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No description available.

Resilin is a disordered elastomeric protein and can be found in specialized regions of insect cuticles. Its protein sequence, functions and dynamic mechanical properties vary substantially across the species. Resilin can operate across the frequency range from 5 Hz for locomotion to 13 kHz for sound production. To understand the functions of different exons of resilin, we synthesize recombinant resilin-like hydrogels from different exons, and investigate the water content and dynamic mechanical properties, along with estimating surface energies relevant for adhesion. The recombinant resilin-like hydrogel has 80wt% water and does not show any sign of tack even though it satisfies the Dahlquist criterion. Finally, doubly shifted dynamic moduli master curves are developed by applying the time-temperature concentration superposition principle (TTCSP), and compared to results obtained with natural resilin from locusts, dragonflies and cockroaches. The resulting master curves show that the synthetic resilin undergoes a prominent transition, though the responsible mechanism is unclear. Possible explanations for the significant increase in modulus include the formation of intramolecular hydrogen bonds, altered structural organization, or passing through a glass transition, all of which have been reported in the literature for polymeric materials. Results show that in nature, resilin operates at a much lower frequency than this glass transition frequency at room temperature. Moreover, recombinant resilins from different clones have comparable resilience with natural resilin, though the modulus is around 1.5 decades lower. Results from the clones with and without chitin binding domains (ChBD) indicate that the transition for the clone without ChBD occurs at lower frequencies than for those with the ChBD, perhaps due to the disordered nature of the clone without ChBD. Atomistic molecular modeling is applied on the repetitive motifs of resilin and different elastomeric proteins to better understand the relationship between elastomeric behavior and amino acid sequences. Results show that the motifs form a favorable bent conformation, likely enabled by glycine's lack of steric hindrance and held in place through intramolecular hydrogen bonds. During Steered Molecular Dynamic (SMD) pulling of these motifs, the hydrogen bonds break and they reform again when the peptides are released to move freely, returning to similar bent conformations. The transition seen in the master curves of recombinant resilins might be due to either these intramolecular hydrogen bonds or to glass transition behavior, though evidence indicates that the transition probably due to the glass transition. What we learned from the synthesized recombinant resilin and simulating the repetitive motifs of resilin may be applicable to the biology and mechanics of other elastomeric biomaterials, and may provide deeper understanding of their unique properties. / Ph. D.