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From:
B. Audoly, N. Clauvelin, and S. Neukirch, “Elastic knots”, Physical Review Letters, 99(16):164301, 2007
ABSTRACT: We study the mechanical response of elastic rods bent into open knots, focusing on the case of trefoil and cinquefoil topologies. The limit of a weak applied tensile force is studied both analytically and experimentally: the Kirchhoff equations with self-contact are solved by means of matched asymptotic expansions; predictions on both the geometrical and mechanical properties of the elastic equilibrium are compared to experiments. The extension of the theory to tight knots is discussed.
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