http://hdl.handle.net/1957/17264 2013-06-20T09:23:34Z 2013-06-20T09:23:34Z Hunt, Jonathan http://hdl.handle.net/1957/29452 2012-05-30T20:37:06Z 2012-05-30T00:00:00Z

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 McKenzie, Brian http://hdl.handle.net/1957/26650 2012-01-11T18:32:29Z 2012-01-06T00:00:00Z

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 Synhavsky, Paul http://hdl.handle.net/1957/26514 2012-01-06T17:53:42Z 2008-12-22T00:00:00Z

Effectiveness in Stallings' Proof of Grushko's Theorem Synhavsky, Paul Graduation date: 2009

2008-12-22T00:00:00Z Baker, Joel http://hdl.handle.net/1957/26215 2011-12-19T21:14:59Z 2011-12-16T00:00:00Z

De Bruijn graphs and their applications to fault tolerant networks Baker, Joel See paper for abstract. 2011

2011-12-16T00:00:00Z