Non-invasive blood analysis devices that can measure characteristics less prominent than the oxygenation of hemoglobin are of interest in the medical community. An important step in creating these devices is to model the interaction of photons with human tissue in increasingly greater physiological detail. We have modeled, using a Monte Carlo technique, the interaction of photons through epidermis, blood and water arranged both in layers and in a homogeneous mixture. We confirm the expected linear relation between photon attenuation and material volumetric percentage in our two-layer models. We discovered that this relationship becomes non-linear in the homogeneously mixed models where volumetric percentage must be replaced with interaction volume percentage. These nonlinearities become significant when the values of the interaction coefficient, µt, differ by an order of magnitude or more and could prove crucial in accurately reading oxygenation or other constituents in the blood and also in modeling radiation delivered to a patient in photodynamic therapy.

This thesis is about modelling of the combustion and emissions of dual fuel HCCI engines for design of “engine combustion system”. For modelling the combustion first the laminar flamelet model and a hybrid Lagrangian / Eulerian method are developed and implemented to provide a framework for incorporating detailed chemical kinetics. This model can be applied to an engine for the validation of the chemical kinetic mechanism. The chemical kinetics, reaction rates and their equations lead to a certain formula for which the coefficients can be obtained from different sources, such as NASA polynomials [1]. This is followed by study of the simulation results and significant findings. Finally, for investigation of the knock phenomenon some characteristics such as compression ratio, fuel equivalence ratio, spark timing and their effects on the performance of an engine are examined and discussed. The OH radical concentration (which is the main factor for production of knock) is evaluated with regard to adjustment of the above mentioned characteristic parameters. In the second part of this work the specification of the sample engine is given and the results obtained from simulation are compared with experimental results for this sample engine, in order to validate the method applied in AVL Fire software. This method is used to investigate and optimize the effects of parameters such as inlet temperature, fuels ratio, diesel fuel injection timing, engine RPM and EGR on combustion in a dual fuel HCCI engine. For modelling the dual fuel HCCI engine AVL FIRE software is applied to simulate the combustion and study the optimization of a combustion chamber design. The findings for the dual fuel HCCI engine show that the mixture of methane and diesel fuel has a great influence on an engine's power and emissions. Inlet air temperature has also a significant role in the start of combustion so that inlet temperature is a factor in auto-ignition. With an increase of methane fuel, the burning process will be more rapid and oxidation becomes more complete. As a result, the amounts of CO and HC emissions decrease remarkably. With an increase of premixed ratio beyond a certain amount, NOX emissions decrease. With pressure increases markedly and at high RPM, knock phenomenon is observed in HCCI combustion.

Given a birational map among projective varieties, it is known that there exists a variety Z with a one-dimensional torus action such that the birational map is induced from two geometric quotients of Z. We proceed in the opposite direction: given a smooth projective variety X with a one-dimensional torus action, one can define a birational map associated to the action and study the properties of the map via the geometry of X. Rational homogeneous varieties admit natural torus actions, so they are a good class of example to test the general theory. In the thesis, we obtain and discuss some results about the birational maps associated to some one-dimensional torus actions on rational homogeneous varieties.

Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematic areas. Despite they have been studied for decades, several aspects of their geometry are still mysterious, among which identifiability and singularity of their points. In this thesis we study the secant varieties of lines of Grassmannians and of Spinor varieties. As first result, we completely determine their posets of orbits under the action of the groups SL and Spin, respectively. Then we solve the problems of identifiability and tangential-identifiability of points in the secant varieties of lines: as a consequence, we also determine the second Terracini locus to a Grassmannian and to a Spinor variety. Our main result concerns the singular locus of the secant variety of lines: we completely determine it for Grassmannians, and we give lower and upper bounds for Spinor varieties. Finally, we partially describe the poset of orbits in the secant variety of lines of any cominuscule variety.

The industrial revolution caused the release of carbon dioxide (CO2) into the atmosphere leading to a climate crisis. The impact of more CO2 in the atmosphere has been experienced by everybody. The summers are longer and hotter, while the winters are colder and shorter. The ocean water has become more acidic threatening the ocean life. There is an immediate need to reduce CO2 and switch to alternate energy for human survival. Electrochemical reduction of CO2 (ERC) is a promising technology capable of converting excess CO2 into valueded products. The process of recycling CO2 can address the problem of excess CO2 and is a sustainable solution until our dependence on fossil fuels is reduced. However, currently there are very few catalysts that can convert CO2 into valuable products with a low overpotential. The current research evaluates new catalysts for their ERC potential. [Ni(cyclam)]2+ is a well-known catalyst used to reduce CO2 homogeneously. Therefore, it was used as a standard to optimize the CO2 evaluation protocol. Two new catalysts developed in Dr. Hollis's laboratory, a Pt- pincer and a Fepincer molecule were assessed using this method. Cyclic voltammetry and bulkelectrolysis (BE) experiments were performed under Ar and CO2 environments. The gaseous products from BE were primarily CO and H2 and their quantitative measurement was performed using gas chromatography. Formate determination was performed using UV-Vis spectroscopy. Faradaic yields were calculated for CO, H2, and formate. The overpotentials were calculated for all the processes, and a comparison was made to determine the most efficient process. The turnover numbers (TON) and the turnover frequencies (TOF) of all the catalysts were calculated. Based on all the criteria, the Fepincer complex was determined to be the most promising catalyst for further optimization. Additionally, a Faradaic efficiency calculation spreadsheet was created to improve calculation efficiency. The protocol described here has been successfully applied to assess new catalysts and can prove to be an invaluable tool when numerous catalysts require evaluation.

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When a power system is subjected to a disturbance, the power flow changes, leading to deviations in the synchronous generator rotor angles. The rotor angle deviations propagate as electromechanical waves (EMWs) throughout the power system. These waves became observable since the development of synchrophasor measurement instruments. The speed of EMW propagation is hundreds of miles per second, much less than the electromagnetic wave propagation speed, which is the speed of light. Recently, with the development of renewable energy resources and a growth in using HVDC and FACTS devices, these waves are propagating slower, and their impacts are more considerable and complicated. The protection system needs a control system that can take suitable action based on local measurements to overcome the results of power system faults. Therefore, the dynamic behavior of power systems should be properly observed. The EMW propagation in the literature was studied using assumptions such as constant voltage throughout the entire power system and zero resistances and equal series reactances for the transmission lines. Although these assumptions help simplify the power system study model, the model cannot capture the entire power system's dynamic behaviors, since these assumptions are unrealistic. This research will develop an accurate model for EMW propagation when the system is facing a disturbance using a continuum model. The model includes a novel inertia distribution. It also investigates the impacts of voltage changes in the power system on EMW behaviors and when these impacts are negligible. Furthermore, the impacts of the internal reactances of synchronous generators and the resistances of transmission lines on EMW propagation are explored. / Doctor of Philosophy / Power systems, essential for electricity supply, undergo disturbances causing changes in power flow and synchronous generator behavior. These disturbances create electromechanical waves (EMWs) that influence system dynamics. Recent advancements, including renewable energy integration and new technologies, alter EMW behavior, posing challenges for control and protection systems. Existing studies simplify models, limiting their accuracy. This research aims to develop a realistic EMW propagation model considering factors like novel inertia distribution, voltage changes, and internal generator properties. This work addresses the evolving power landscape, enhancing our understanding of power system dynamics for improved control and reliability.