Theses and Dissertations at Montana State University (MSU)
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Item Crystal pressure of pharmaceuticals in nanoscale pores(Montana State University - Bozeman, College of Engineering, 2017) Berglund, Emily Anne; Chairperson, Graduate Committee: James WilkingMany pharmaceutical compounds are poorly soluble in water. This is problematic because most pharmaceuticals are delivered orally and must dissolve in the gastrointestinal fluid to be absorbed by the body. Drug dissolution rate is proportional to surface area, so a common formulation strategy is to structure drugs as small as possible to maximize surface area. A simple approach to create very small particles is to structure the compounds within the nanoscale pore space of a colloidal packing. The resulting composite undergoes rapid disintegration in water and the exposed drug exhibits dramatically improved dissolution rates. We hypothesize that composite breakup is driven by the growth of nanoscale crystals, which exert a pressure on the walls of the confining pores. To test this hypothesis, we systematically vary the amount of water permitted into the composite and use calorimetry to monitor the evolution of the crystal size distribution as a function of water content. To exert sufficient pressure to overcome the tensile yield stress of the composite, the crystals must be fed by a supersaturated phase. Our results suggest that differences in crystal curvature due to crystal confinement and crystal size polydispersity generate the necessary supersaturation. These results are relevant not just for drug formulations, but for understanding physical processes such as salt damage to buildings and road damage due to frost heave.Item Emergence of cooperative behavior in microbial consortia(Montana State University - Bozeman, College of Letters & Science, 2018) Schepens, Diana Ruth; Chairperson, Graduate Committee: Tomas GedeonCooperative microbial communities and their impact are ubiquitous in nature. The complexities of the cross-feeding interactions within such communities invite the application of mathematical models as a tool which can be used to investigate key influences in the emergence of cooperative behavior and increased productivity of the community. In this work, we develop and investigate a differential equation model of competition within a chemostat between four microbial strains utilizing a substrate to produce two necessary metabolites. The population of our chemostat includes a wild type strain that generalizes in producing both metabolites, two cross-feeding cooperator strains that each specialize in producing one of the two metabolites, and a cheater strain that produces neither metabolite. Using numerical methods we consider three key characteristics of the microorganisms and investigate the impact on the emergence of mutual cross-feeding in the community. First, we investigate the impact that substrate input concentration and the rate and type (active vs. passive) of metabolite transport between cells has on the emergence of cooperation and multi-stabilities resulting from the competition. Second, we investigate the role that resource allocation within metabolic pathways plays in the results of the competition between cells with different metabolite production strategies. Introducing metabolite production cost into the model leads to new outcomes of the competition, including stable coexistence between different strains. Lastly, we examine the effect that an initial population of a non-cooperative cheater strain has on the outcome of competition. Our results show that the emergence of a cross-feeding consortia relies on the availability and efficient use of resources, ease of transport of metabolites between cells, and limited existence of cheaters.Item Distribution of the sample range for parent populations associated with Pearson's differential equation(Montana State University - Bozeman, College of Letters & Science, 1954) Ingram, Glenn R.Item Comparison of numerical approximation methods for the solution of first order differential equations(Montana State University - Bozeman, College of Letters & Science, 1952) Rouge, Leon J. D.Item Iterative procedure for a nonlinear circuit(Montana State University - Bozeman, College of Letters & Science, 1963) Peterson, Marcia M.Item Existence, comparison and oscillation results for some functional differential equations(Montana State University - Bozeman, College of Letters & Science, 1972) True, Ernest DeCarteteretItem Existence and oscillation of solutions of certain functional differential equations(Montana State University - Bozeman, College of Letters & Science, 1971) Grefsrud, Gary WayneItem Approximation of eigenvalues of Sturm-Liouville differential equations by the sinc-collocation method(Montana State University - Bozeman, College of Letters & Science, 1987) Jarratt, Mary KatherineItem An Alternating-Direction Sinc-Galerkin method for elliptic problems on finite and infinite domains(Montana State University - Bozeman, College of Letters & Science, 2009) Alonso, Nicomedes, III; Chairperson, Graduate Committee: Kenneth L. BowersAlternating-Direction Implicit (ADI) schemes are a class of very efficient algorithms for the numerical solution of differential equations. Sinc-Galerkin schemes employ a sinc basis to produce exponentially accurate approximate solutions to differential equations even in the presence of singularities. In this dissertation we begin with a broad overview of sinc methods for problems posed on both finite and infinite, one- and two-dimensional domains. We then present a variety of finite difference methods that lead to the introduction of a new Alternating-Direction Sinc-Galerkin scheme based on the classic ADI scheme for a linear matrix system. We note that when a Sinc-Galerkin method is used to solve a Poisson equation, the resulting matrix system is a Sylvester equation. We discuss ADI model problems in general and then prove that when a symmetric Sinc-Galerkin method is employed, the resulting Sylvester equation can be classified as an ADI model problem. Finally, we derive our Alternating-Direction Sinc-Galerkin (ADSG) method to solve this resulting Sylvester equation, specifying the use of a constant iteration parameter to avoid costly eigen-value computations. We end by applying ADSG to a variety of problems, comparing its performance to the standard technique that uses the Kronecker product, the Kronecker sum, and the concatenation operator.