Journal articles:

• Interlacing and non-orthogonality of spectral polynomials for the Lamé operator. With A. Bourget and A. Vargas. In review, Proc. Amer. Math. Soc. [.pdf]
• Nonlinear muscles, passive viscoelasticity and body taper conspire to create curvature waves in anguilliform swimmers. T. McMillen, T. Williams and P. Holmes. PLOS Comput. Biol. 4(8): e1000157 doi:10.1371/journal.pcbi.1000157 (2008) [.html, .pdf].
• On the zeros of complex Van Vleck polynomials. T. McMillen, A. Bourget and A. Agnew. In press, J. Comput. Appl. Math. [.html, .pdf]
• An elastic rod model for anguilliform swimming. T. McMillen and P. Holmes. J. Math. Biol. Vol. 53, no. 5: pp 843-886 (2006) [.pdf]
• The dynamics of choice among multiple alternatives. T. McMillen and P. Holmes. J. Math. Psych. Vol. 50: pp 30-57 (2006) [.pdf]
• Whip waves. T. McMillen and A. Goriely. Phys. D. Vol. 184: pp 192-225 (2003) [.pdf]
• The shape of a cracking whip. A. Goriely and T. McMillen. Phys. Rev. Lett. Vol. 88, no. 244301 (2002) [.pdf]
• Tendril perversion in intrinsically curved rods. T. McMillen and A. Goriely. J. Nonlinear Sci. Vol. 12: pp 241-281 (2002) [.pdf]
• Connecting a chemotactic model for mass action to a rapid integro-difference emulation strategy. J. Powell, T. McMillen, and P. White. SIAM J. App. Math. Vol. 59, no. 2: pp 547-572 (1999) [.pdf]

Other papers:

• On the effects of signal acuity in a connectionist model of decision making. Princeton Univ. CSBMB Technical Report #06-03 (2006) [.pdf]
• On the falling (or not) of the folded inextensible string. (2005) [.pdf]
• The shape and dynamics of the Rikitake attractor. The Nonlinear Journal: The Student Journal of Nonlinear Sciences (1999) [.pdf]

Dissertation: Perversions and whips: Static and dynamic problems of elastic filaments. University of Arizona (2003) [.pdf]

Selected presentations:

• Phase coupling between activation and curvature in lamprey swimming. With T. Williams and P. Holmes. Mathematical Biosciences Institute workshop on Neuromechanics of Locomotion, March 31 – April 4, 2008. Streaming real video (My talk starts at 1:24)
• Nonlinear muscles, viscoelasticity and body taper conspire in the creation of curvature waves. SIAM Conference on the Analysis of PDEs, Dec 10, 2007. [.pdf, .ppt]
• Mathematical problems of decision making. CSUF Math Department colloquium, April 25, 2007. [.ppt]

Swimming rod animations:

Rods traveling in a straight line, and making a turn
Rods with prescribed shape and preferred curvature in inertial and moving frames