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Two problems in the study of elastic filaments are considered. First, a reliable numerical algorithm is developed that can determine the shape of a static elastic rod under a variety of conditions. In this algorithm the governing equations are written entirely in terms of local coordinates and are discretized using finite differences. The algorithm is seen to have significant advantages. In the second problem a model is presented describing the dynamics of an elastic tube conveying a fluid. A study into the effect of the fluid on the twist-to- writhe instability is given. A linear stability analysis demonstrates that for an infinite rod the twist-to-writhe threshold is lowered by the presence of a fluid flow. It is shown that for finite length tubes the bifurcation threshold depends delicately on the length of the tube and that it can be either raised or lowered relative to the fluid-free case.

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Dr. Beauregard earned his doctorate in Applied Mathematics minoring in Aerospace and Mechanical Engineering in the Program in Applied Mathematics at the University of Arizona. He has held academic positions at the University of Arizona, Kaplan University, and Baylor University. His interests are in numerical pdes and elasticity theory.

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