Experimental studies have shown that the protein abundance in living cells varies from few tens to several thousands molecules per species. Molecular fluctuations roughly scale as the inverse square root of the number of molecules due to the random timing of reactions. It is hence expected that intrinsic noise plays an important role in the dynamics of biochemical networks. The Chemical Master Equation is the accepted description of these systems under well-mixed conditions. Because analytical solutions to this equation are available only for simple systems, one often has to resort to approximation methods. A popular technique is an expansion in the inverse volume to which the reactants are confined, called van Kampen's system size expansion. Its leading order terms are given by the phenomenological rate equations and the linear noise approximation that quantify the mean concentrations and the Gaussian fluctuations about them, respectively. While these approximations are valid in the limit of large molecule numbers, it is known that physiological conditions often imply low molecule numbers. We here develop systematic approximation methods based on higher terms in the system size expansion for general biochemical networks. We present an asymptotic series for the moments of the Chemical Master Equation that can be computed to arbitrary precision in the system size expansion. We then derive an analytical approximation of the corresponding time-dependent probability distribution. Finally, we devise a diagrammatic technique based on the path-integral method that allows to compute time-correlation functions. We show through the use of biological examples that the first few terms of the expansion yield accurate approximations even for low number of molecules. The theory is hence expected to closely resemble the outcomes of single cell experiments.

Photovoltaic solar power is an increasing source of energy and part of the renewable energy generation which is needed in the near future to achieve the set climate goals. When planning new photovoltaic installations, parameters which affect the design are both local conditions (e.g. weather) and system parameters such as tilt and azimuth angles. Commercial areas often have high loads during the day when solar power is available and are therefore interesting for photovoltaic installations. In order make a quick estimation of photovoltaic power potential in an area, a simulation tool which handles load profiles from multiple buildings would be desirable. The aim of this thesis project is therefore to create a tool which can simulate multiple photovoltaic systems and for each of them estimate system sizes, grid interactions, and area requirements. The simulation tool is based on Python programming with the aid of System Advisor Model, a simulation software for photovoltaic and other renewable energy tech-nologies. Optimization of orientation angles was made for clear sky with the goal of high load-generation match. Different system sizes were estimated and simulated based on different degrees of self-sufficiency, net-zero consumption, and the existing transfer capacity of the building in question. When the simulation result was compared to a detailed photovoltaic design project, some agreements between the results were found, as well as further development needs such as refining area estimation. To further develop the usability of the tool, a more user-friendly interface is needed. Other improvements could be to enable simulations of multiple direction systems and integration of the local grid structure and limitations.

The purpose of this study was to determine if there was a relationship between level of funding and achievement of school systems in Tennessee based on the standards of the No Child Left Behind Act (NCLB) of 2001. This study focused on Tennessee school systems and their adequate yearly progress (AYP) status of "targeted" or "good standing" from 2007 through 2009. Federal, state, and local funding, as well as per-pupil expenditure, average teacher salary, and number of students, were used as variables. All data were gathered from the Tennessee Department of Education website. The researcher performed 6 independent samples t-tests and one chi square analysis. The study showed significant differences in the means of federal, state, and local funding levels between targeted systems and systems in good standing. Targeted systems received more federal, state, and local funding than systems in good standing from 2007 through 2009. The study showed no significant difference in mean per-pupil expenditures between targeted systems and systems in good standing. The study showed a significant difference in the mean teacher salaries. Targeted systems had higher teacher salaries than systems in good standing from 2007 through 2009. The study also showed a significant difference in the mean number of students between targeted systems and systems in good standing. Targeted systems had more students than systems in good standing. The findings indicate that targeted systems are receiving as much funding as systems in good standing. To help control for the number of students in each system, the two groups (targeted and in good standing) were compared using per-pupil federal, state and local dollars. The analysis indicated no significant difference between targeted systems and systems in good standing for federal money. The analysis did indicate a significant difference between the two groups for state and local money. However, for state money systems in good standing had the higher mean and for local money, targeted systems had the higher mean. Mean per-pupil expenditures were relatively equal between targeted systems and systems in good standing. System size, based on the number of students, showed a significant relationship with the NCLB status of a system. The mean number of students in targeted systems was more than 3 times as large as systems in good standing (17,656 to 5,284). Also, a group of systems with over 4,445 students had over 5 times the number of targeted systems than a group of systems with fewer than 2,094 students.

Potential parameters that can handle multi-component oxide glass systems especially boron oxide are very limited in literature. One of the main goals of my dissertation is to develop empirical potentials to simulate multi-component oxide glass systems with boron oxide. Two approaches, both by introducing the composition dependent parameter feature, were taken and both led to successful potentials for boron containing glass systems after extensive testing and fitting. Both potential sets can produce reasonable glass structures of the multi-component oxide glass systems, with structure and properties in good agreement with experimental data. Furthermore, we have tested the simulation settings such as system size and cooling rate effects on the results of structures and properties of MD simulated borosilicate glasses. It was found that increase four-coordinated boron with decreasing cooling rate and system size above 1000 atoms is necessary to produce converged structure. Another application of the potentials is to simulate a six-component nuclear waste glass, international simple glass (ISG), which was for first time simulated using the newly developed parameters. Structural features obtained from simulations agree well with the experimental results. In addition, two series of sodium borosilicate and boroaluminosilicate glasses were simulated with the two sets of potentials to compare and evaluate their applicability and deficiency. Various analyses on the structures and properties such as pair distribution function, total correlation function, coordination number analysis, Qn distribution function, ring size distribution function, vibrational density of states and mechanical properties were performed. This work highlights the challenge of MD simulations of boron containing glasses and the capability of the new potential parameters that enable simulations of wide range of mixed former glasses to investigate new structure features and design of new glass compositions for various applications.