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Tubular-body theory for viscous flows

Cable-like bodies play a key role in many interdisciplinary systems but are hard to simulate. Asymptotic theories, called slender-body theories, are effective but apply in specific regimes and can be hard to extend beyond leading order. In this letter we develop an exact slender-body-like theory for the surface traction of cable-like bodies in viscous flow. This theory expresses the traction as a series of solutions to a well-behaved one-dimensional Fredholm integral equation of the second kind. This process can be simply generalised to other systems.