Abstract Using a finite element package software DEFORMTM, this study simulated plastic deformation of the sheet at the roll-gap during sheet rolling processes. Rigid-plastic model of material is adopted. The rolls are assumed to be perfectly rigid and the sheets are isotropic. This study consists of three parts¡G(1) analysis of asymmetrical sheet rolling ; the effects of rolls speed ratios, roll radii ratios, friction factor ratios between sheet and rolls surface, upon the curvature of the rolled product and rolling force were systematically discussed. The larger the roll radius and the roll speed ratios are, the smaller the rolling force is and the larger the curvature of the sheet analytically. (2) Closing behavior, the deformation mechanism and stress-strain distributions around internal voids inside the sheet during sheet rolling was discussed numerically. The influences of various rolling conditions, such as the thickness reduction, the dimension of the internal void, friction factor, cross-sectional area of the void, etc., on the dimension of the void at the exit were discussed. The critical thickness reductions, over which the void would close completely, were also investigated. It is known that the critical reduction decreases with increasing roll radius. That is because the rolling pressure at the roll gap increases with increasing roll radius, accordingly, it takes smaller reductions to make the void closed completely. The critical thickness reduction decreases with increasing roll radius and decreasing voids dimension-thickness ratios. (3) The possibility of voids occurred at the front and back of the inclusion was investigated. The effects of various rolling conditions, such as the thickness reduction, the diameter of the inclusions, the roll diameter, friction factor, etc., on the generation and development of voids anticipated to occur in the front and rear of the inclusions were discussed. The critical thickness reductions under which void generation can be avoided were also examined. On the other hand, the effect of friction factor on between roll and sheet upon the void lengths in the front and rear of the inclusion is greater than that of friction factor on between inclusions and sheet. It is known that it decreases with increasing inclusions dimension, whereas the critical reduction decreases with decreasing roll radius. The analytical results showed a steady trend for 0.1mm< voids and inclusions dimension < 2.5mm. To verify the validity of the models, a series of experiments on the sheet rolling using aluminum (A1050, A6061) sheet as specimen were carried out. The experiments on sheet rolling with an internal void inside the sheet were conducted by micro-drill. The inclusions used ¡§SUS HSS¡¨ steel. The void length in the front of the inclusion is larger than that in the rear of the inclusion for both simulated and experimental results. The simulated results were compared with experimental results, and good agreement is found. Therefore, this numerical model using DEFORM software can offer useful knowledge for designing the pass-schedule in sheet rolling processes.

Thesis / Master of Engineering (MEngr)

Transmission lines are the basic building blocks of any RF and microwave circuits. The width of a microstripline increases as the characteristic impedance is lowered for a given substrate. Wide microstriplines suffer from spurious and higher order modes at higher frequencies and may not behave as transmission lines. This means the lower limitation for a realisable microstripline is about 10 ohm. In this project microstriplines with characteristic impedances of 7 ohm and 25 ohm at a frequency of 2 GHz were designed and realised using the artificial transmission lines (ATL) concept. Detailed theoretical analysis and circuit and EM simulations were used for the design and implementation of the ATLs. Taconic TLY-5 substrate was used for the PCB fabrication. The substrate thickness was 0.787 mm and the dielectric constant was 2.2. The measured results were de-embedded and compared with the simulation results. The detailed procedure of modelling and de-embedding of an SMA connector is also given. The 25 ohm ATL was realised using microstriplines only, where as microstriplines and chip capacitors were used in realising the 7 ohm ATL. The measured characteristic impedance of the 25 ohm ATL was 24.4 ohm and the measured electrical length of the 25 ohm ATL was 180 degrees at 2.1 GHz. To realise a 25 ohm ATL with 90 degrees electrical length, the half-wavelength 25 ohm ATL geometry was cut into half and one of the half geometries was EM simulated. The EM simulated electrical length of the 25 ohm ATL was 90 degrees at 1.9 GHz. The measured characteristic impedance of the 7 ohm ATL was 5.9 ohm and the measured electrical length of the 7 ohm ATL was 90 degrees at 1.8 GHz. The main advantage of an ATL is size reduction. A 25 ohm meandered microstrip line (substrate thickness = 0.787 mm, dielectric constant = 2.2) with 180 degrees electrical length at 2 GHz has a size of 34 mm x 15 mm. The 25 ohm ATL with 180 degrees electrical length at 2.1 GHz was realised in a size of 22 mm x 19 mm. The design of the 25 Ω ATL resulted in 18 percent reduction in area compared to the meander line. A 7 ohm conventional microstripline (substrate thickness = 0.787 mm, dielectric constant = 2.2) with 90 degrees electrical length at 1.8 GHz has a size of about 28 mm x 27 mm. The 7 ohm ATL with 90 degrees electrical length at 1.8 GHz was realised in a size of 7 mm x 8.4 mm which is only 8 percent of the conventional 7 ohm microstripline area. In general, a spacing of 3h where h is the substrate thickness is required between the adjacent microstriplines. In this project detailed investigations were done to see if the spacing can be reduced without any detrimental coupling affects and a spacing of 0.6 mm was used. This reduction in spacing has resulted in reduced size of the ATL. For an asymmetrical power splitter based on the Wilkinson topology, the power splitter output power split ratio depends on the square of the characteristic impedances of the quarter-wavelength arms. In this project an asymmetrical power splitter was designed and realised using a 7 ohm ATL and a 25 ohm ATL as the quarter-wavelength arms. The desired centre frequency of the power splitter was 2 GHz and the measured centre frequency was 1.6 GHz. At the centre frequency the phase difference between the output ports of the power splitter will be zero. The simulated power split ratio was 10.1 dB and the measured power split ratio was 13 dB. The power split ratio calculated using the measured characteristic impedances of the ATLs (24.4 ohm and 5.9 ohm) will be 12.4 dB which is very close to the measured power split ratio.

Esta dissertação tem como objetivo o estudo da distribuição ``slash\'\', considerando seus casos simétrico e assimétrico univariados. Serão apresentadas propriedades probabilísticas e inferenciais dessa distribuição, assim como peculiaridades e problemas. Para serem feitas inferências será considerado o enfoque clássico através do uso dos métodos dos momentos e máxima verossimilhança. São apresentados também os cálculos para a obtenção destes estimadores. Nos casos onde estes estimadores não podem ser obtidos algebricamente foram utilizados métodos computacionais, através da implementação do algoritmo EM. Para isto, foi utilizado o software R e os comandos estão no apêndice. No caso dos estimadores de máxima verossimilhança será implementado o método de Louis para estimar os elementos da matriz de informação de Fisher. Foram realizados estudos de simulação e aplicações para dados reais. Nas aplicações foi analisado o modelo de regressão linear simples, onde foi considerado que os erros seguem distribuição slash assimétrica. / This dissertation aims at studying the ``slash\'\' distribution considering its symmetric and asymmetric versions. We present probabilistic as well as inferential aspects of this distribution, including peculiarities and problems related to model fitting. The classical approach based on maximum likelihood estimation is used. Moments estimation is also considered as starting values for the maximum likelihood estimation. The implementation of the EM algorithm is developed for the implementation of the likelihood approach. For this implementation software R was used and codes required are presented in the Appendix. As a byproduct of the EM algorithm, Louis method is considered for estimating the Fisher information matrix which can be used for computing large sample intervals for model parameters. Extensions for a simple regression model is considered. Simulation studies are presented illustrating the performance of the estimation approach considered. Results of real data analysis indicate that the methodology can perform well in applied scenarios.

Esta dissertação tem como objetivo o estudo da distribuição ``slash\'\', considerando seus casos simétrico e assimétrico univariados. Serão apresentadas propriedades probabilísticas e inferenciais dessa distribuição, assim como peculiaridades e problemas. Para serem feitas inferências será considerado o enfoque clássico através do uso dos métodos dos momentos e máxima verossimilhança. São apresentados também os cálculos para a obtenção destes estimadores. Nos casos onde estes estimadores não podem ser obtidos algebricamente foram utilizados métodos computacionais, através da implementação do algoritmo EM. Para isto, foi utilizado o software R e os comandos estão no apêndice. No caso dos estimadores de máxima verossimilhança será implementado o método de Louis para estimar os elementos da matriz de informação de Fisher. Foram realizados estudos de simulação e aplicações para dados reais. Nas aplicações foi analisado o modelo de regressão linear simples, onde foi considerado que os erros seguem distribuição slash assimétrica. / This dissertation aims at studying the ``slash\'\' distribution considering its symmetric and asymmetric versions. We present probabilistic as well as inferential aspects of this distribution, including peculiarities and problems related to model fitting. The classical approach based on maximum likelihood estimation is used. Moments estimation is also considered as starting values for the maximum likelihood estimation. The implementation of the EM algorithm is developed for the implementation of the likelihood approach. For this implementation software R was used and codes required are presented in the Appendix. As a byproduct of the EM algorithm, Louis method is considered for estimating the Fisher information matrix which can be used for computing large sample intervals for model parameters. Extensions for a simple regression model is considered. Simulation studies are presented illustrating the performance of the estimation approach considered. Results of real data analysis indicate that the methodology can perform well in applied scenarios.

The Lead-Acid battery has become the power source of several electron product. The major drawback is that it requires long charging time. This thesis is to design a programmable rapid charger and energy recovery scheme with DSP. Furthermore zero-voltage-switching(ZVS) capability of the adopted asymmetrical half-bridge topology enhances the power density of the charger. The energy recovery cell stores the negative pulse energy into DC bus capacitor temporarily to avoid unnecessary energy consumption in conventional schemes. This thesis is experimentally verified on 12V/7.5Ah nonspillable sealed-lead assembled batteries. According to experimental results, the charger can achieve the goal of rapid charge within 1 hour. Because of using the rapid charge algorithm, it can give different charging section depends on temperature and voltage of battery, and it can adjust the over-temperature and the over-voltage of battery to guarantee the battery be charged safely. In this thesis, a prototype module is implemented with mature protection condition. Some experiments are shown to verify the feasibility of the proposed scheme.

This thesis presents the design and implementation of a single-stage with high power factor asymmetrical half-bridge converter. The main structure combines a boost converter with an asymmetrical half-bridge. An Asymmetrical half-bridge converter has many advantages such as soft-switching properties and fewer components. Therefore it is suitable for DC/DC cell. The boost converter is used in a PFC cell that operating in discontinuous condition mode have innate ability of power factor correction without additional controller. In this thesis, the complete analysis of operation principle and design of controller for the equivalent circuits of a single-stage AC/DC converter in every operating stage have been described in detail. Finally, we construct the single-stage circuit and experimental result show that it can reach the expected goal for power-factor correction.

Asymmetrical dispersal is when dispersal rates differ in opposite directions. This is expected to be common in natural populations. This work aims to study the symmetrical and asymmetrical dispersal through the use of a simulation program, simuPOP. The main questions were (i) "what are the differences between asymmetrical and symmetrical dispersal in relation to genetic differentiation and equilibrium?" and (ii) "Is it possible to identify asymmetrical dispersal structure from observed patterns of genetic differentiation between populations, and variation within populations?". To address these questions, simulations were conducted with two and three subpopulations subject by three different dispersal rate contrasts and several spatial patterns of dispersal. Variables were estimated at drift-dispersal equilibrium included genetic differentiation between subpopulations (θ) and heterozygosity. With pairwise θ for three subpopulations it was possible to determine whether the metapopulations were subject to symmetrical or asymmetrical dispersal and sometimes to identify the structure of dispersal. Equilibrium heterozygosities did not aid diagnosis of asymmetrical dispersal patterns. I also checked the applicability of two predictions originally made for symmetrical dispersal: Wright's expectations for θ at equilibrium, and Whitlock's expectations fro time to half of equilibrium θ. In most cases these expectations were not applicable. Study of asymmetrical dispersal on living organisms is strongly encouraged.

Asymmetrical dispersal is when dispersal rates differ in opposite directions. This is expected to be common in natural populations. This work aims to study the symmetrical and asymmetrical dispersal through the use of a simulation program, simuPOP. The main questions were (i) "what are the differences between asymmetrical and symmetrical dispersal in relation to genetic differentiation and equilibrium?" and (ii) "Is it possible to identify asymmetrical dispersal structure from observed patterns of genetic differentiation between populations, and variation within populations?". To address these questions, simulations were conducted with two and three subpopulations subject by three different dispersal rate contrasts and several spatial patterns of dispersal. Variables were estimated at drift-dispersal equilibrium included genetic differentiation between subpopulations (θ) and heterozygosity. With pairwise θ for three subpopulations it was possible to determine whether the metapopulations were subject to symmetrical or asymmetrical dispersal and sometimes to identify the structure of dispersal. Equilibrium heterozygosities did not aid diagnosis of asymmetrical dispersal patterns. I also checked the applicability of two predictions originally made for symmetrical dispersal: Wright's expectations for θ at equilibrium, and Whitlock's expectations fro time to half of equilibrium θ. In most cases these expectations were not applicable. Study of asymmetrical dispersal on living organisms is strongly encouraged.

Caulobacter crescentus goes through a classic dimorphic cell division cycle to adapt to the stringent environment and reduce intraspecific competition. Caulobacter mother cell gives rise to two progenies with distinct morphology - a motile swarmer cell equipped with a flagellum and a sessile stalked cell equipped with a stalk. Because of the nature of dimorphic lifestyle, Caulobacter becomes a model bacterium to study the cell differentiation, signalling transduction, stress response, and asymmetry development of prokaryotes. The dimorphic cell cycle of Caulobacter is driven by the elaborate spatiotemporal organization of regulatory molecules through regulations of synthesis, degradation, phosphorelay, and localization. There is a wealth of experimental observations about gene/protein interactions and localizations accumulated in recent decades, while several mathematical models have been proposed to study the cell cycle progression in Caulobacter. However, the specific control mechanisms of stress response and spatial asymmetry establishment are yet clearly elucidated, while these mechanisms are of fundamental importance to understanding the bacterial survival strategy and developing the microbial industry. Here we utilize mathematical modeling to study the regulatory network of cell cycle control in C. crescentus, focusing on the stress response and asymmetry development. First, we investigate the starvation response of Caulobacter through the connection of phosphotransferase systems (PTS) and guanine nucleotide-based second messenger system. We have developed a mathematical model to capture the temporal dynamics of vital regulatory second messengers, c-di-GMP (cdG) and guanosine pentaphosphate or tetraphosphate (pppGpp or ppGpp), under normal and stressful conditions. This research suggests that the RelA-SpoT homolog enzymes have the potential to effectively influence the cell cycle in response to nutrition changes by regulating cdG and (p)ppGpp levels. We further integrate the second messenger network into a temporal cell cycle model to investigate molecular mechanisms underlying responses of Caulobacter to nutrition starvation. Our model suggests that the cdG-relevant starvation signal is essential but not sufficient to robustly arrest the cell cycle of Caulobacter. We also demonstrate that there may be unknown pathway(s) reducing CtrA under starvation conditions, which results in delayed cytokinesis in starved stalked cells. The cell cycle development of Caulobacter is determined by the periodical activation and deactivation of the master regulator CtrA. cdG is an essential component of the ClpXP pro- tease complex, which is specifically responsible for the degradation of CtrA. We propose a mathematical model for the hierarchical assembly of ClpXP complexes, together with modeling DNA replication, transcription, and protein interactions, to characterize the Caulobacter cell cycle. Our model suggests that the ClpXP-based proteolysis system contributes to the timing and robustness of the cell cycle progression. Furthermore, we construct a spatiotemporal model with Turing-pattern mechanism to study the morphogenesis and asymmetry establishment during the cell cycle of Caulobacter. We apply reaction-diffusion equations to capture the spatial dynamics of scaffolding proteins PodJ, PopZ, and SpmX, which organize two distinct poles of Caulobacter. The spatial regulations influence the activity and distribution of key cell cycle regulators, governing the dimorphic lifestyle of Caulobacter. Our model captures major spatiotemporal experimental observations of wild-type and mutant cells. It provides predictions of novel mutant strains and explains the spatial regulatory mechanisms of bacterial cell cycle progression. / Doctor of Philosophy / Cell is the basic unit of life that undergoes a process called 'cell cycle' consisting of DNA replication and cell division to exhibit various functions, abilities, and behaviors. The cell cycle is well organized by complex regulations in time and space that determine when and where changes take place. The regulations behind cell cycle development play important roles for living organisms but are not fully understood. In this dissertation, we utilize mathematical models and focus on a model bacterium, Caulobacter crescentus, to capture characteristics of cell cycle and study the underlying regulations. Caulobacter is widely distributed in freshwater, including environments with poor nutrients. It divides asymmetrically, generating a pair of daughter cells with different appearances and replicative potentials. Therefore, Caulobacter population has the flexibility to save energy by halting DNA replication and to reduce the competition with siblings by settling into different places. We utilize the nature of the asymmetrical division of Caulobacter to quantitatively investigate the control mechanisms of cell cycle development, including how cells detect and respond to external cues and develop different organelles at specific times and locations.