Publications

Results from a Differential Equation Model for Cell Motion with Random Switching Show that the Model Cell Velocity is Asymptotically Independent of Force, Journal of Differential Equations, 268, (2019), 301-317, with J. C. Dallon, Emily J. Evans, and W. V. Smith.
A Continuous-time Model of Centrally Coordinated Motion with Random Switching, Journal of Mathematical Biology, 74 (2017), 727-753, with J. C. Dallon, Lynnae C. Despain, Emily J. Evans, and W. V. Smith.
Cell Speed is Independent of Force in a Mathematical Model of Amoeboidal Cell Motion with Random Switching Terms, Mathematical Biosciences, 246 (2013), 1-7, with J. C. Dallon, E. J. Evans, and W. V. Smith.
A Sharkovsky Theorem for Non-Locally Connected Spaces, Discrete and Continuous Dynamical Systems - Series A, 32 (2012), 3485-3499, with Gregory R. Conner and Mark H. Meilstrup.
Resistance and Conductance in Structured Zermelo Tournaments, Advances in Applied Mathematics, 44 (2010), 37-52, with Gregory R. Conner and Benjamin Z. Webb.
Neighborhood Monotonicity, the Extended Zermelo Model, and Symmetric Knockout Tournaments, Discrete Mathematics, 309 (2009), 3998-4010, with Gregory R. Conner.
The Rasch Model & Additive Conjoint Measurement, Advances in Rasch Measurement, Volume One, 2006, with Van A. Newby, Gregory R. Conner, and C. Victor Bunderson.
Blowup in a Mass-Conserving Convection-Diffusion Equation with Superquadratic Nonlinearity, Proceedings of the American Mathematical Society, 129 (2001), 3353-3362, with Todd L. Fisher.
Grain Sizes in the Discrete Allen-Cahn and Cahn-Hilliard Equations, Discrete and Continuous Dynamical Systems, 7 (2001) 127-146.
Superabundance of Stationary Solutions for the Discrete Allen-Cahn Equation, Dynamics of Continuous, Discrete, & Impulsive Systems, 8B (2001) 71-92.
An Extension of Zermelo's Model for Ranking by Paired Comparisons, European Journal of Applied Mathematics, 11 (2000) 225-247, with Gregory R. Conner.
Interior Blowup in a Convection-Diffusion Equation, SIAM Journal on Mathematical Analysis, 29 (1998) 1447-1458.
Asymptotics of Blowup for a Convection-Diffusion Equation with Conservation, Differential and Integral Equations 9 (1996) 719-728, with Gregory R. Conner.
Slowly-Migrating Transition Layers for the Discrete Allen-Cahn and Cahn-Hilliard Equations, Nonlinearity 8 (1995) 861-876, with Erik Van Vleck.
Slow Motion in One-Dimensional Cahn-Morral Systems, SIAM Journal on Mathematical Analysis 26 (1995) 21-34.
Spinodal Decomposition for the Cahn-Hilliard Equation, Communications in Partial Differential Equations 18 (1993) 453-490.
The Dynamics of Pattern Selection for the Cahn-Hilliard Equation, Ph.D. Dissertation, University of Utah, August 1991.
A Property of Two Dimensions, Solution to Advanced Problem 6593, American Mathematical Monthly 98 (1991) 65-67, with Michel Balazard.
Blow Up for a Diffusion-Advection Equation, Proceedings of the Royal Society of Edinburgh 113A (1989) 181-190, with Nicholas Alikakos and Peter Bates.
Stabilization and Blow-up of Solutions of a Nonlinear Parabolic Equation, M.S. Thesis, BYU, December 1988.