Taylor, CI; (2015) Interacting Elastic Rods. Doctoral thesis , UCL (University College London).

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Abstract

This study presents a general theory of interacting elastic curves in two dimen-sions before moving into a more general model of interacting elastic rods in three dimensions. It begins by looking at methods of modelling a single continuous two dimensional curve, before making a first attempt at modelling interactions between such curves. Finding that a discrete model would be more appropriate, the theory of two dimensional discrete curves is introduced along with a definition of discrete curvature. This model is shown to provide a good approximation to the continuous case. With promising results in the case of a single curve we model the interac¬tion between several discrete curves with great success. The general equations are then applied to a variety of interacting curve models, providing physically realistic results. Continuous space curves, curve framing, and the general theory of elastic rods is introduced in order to build discrete analogies to each, before moving on to build a discrete model of an elastic curve deforming in three dimensions. This study provides the basis to support the eventual modelling of interacting elastic rods in three dimensions. Such a model can be applied to many bundle models, including but not limited to collagen type 1 fibrils.

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