http://hdl.handle.net/1957/17264 2013-05-22T08:47:32Z http://hdl.handle.net/1957/29452 Percolation and the bilevel lattice Hunt, Jonathan The paper reviews percolation and some of its important properties, particularly on the 2-D square lattice. A bilevel lattice is introduced, with a percolation model representing the spread of a forest fire according to characteristics of the forest. It is proven that the value of the laddering probability may determine whether a fire fizzles out or spreads without bound, and a programmed simulation assists in determining a critical laddering probability. 2012-05-30T00:00:00Z http://hdl.handle.net/1957/26650 Polynomial Chaos Expansions for Random Ordinary Differential Equations McKenzie, Brian We consider numerical methods for finding approximate solutions to Ordinary Differential Equations (ODEs) with parameters distributed with some probability by the Generalized Polynomial Chaos (GPC) approach. In particular, we consider those with forcing functions that have a random parameter in both the scalar and vector case. We then consider linear systems of ODEs with deterministic forcing and randomness in the matrix of the systems and conclude with a method of approximating solutions to the case where the system involves a nonlinear function of a matrix and a random variable. 2012-01-06T00:00:00Z http://hdl.handle.net/1957/26514 Effectiveness in Stallings' Proof of Grushko's Theorem Synhavsky, Paul Graduation date: 2009 2008-12-22T00:00:00Z http://hdl.handle.net/1957/26215 De Bruijn graphs and their applications to fault tolerant networks Baker, Joel See paper for abstract. 2011 2011-12-16T00:00:00Z