Scholarship & Research
Permanent URI for this communityhttps://scholarworks.montana.edu/handle/1/1
Browse
8 results
Search Results
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.