Helical configurations of elastic rods in the presence of a long-range interaction potential

de Lillo, Silvana, Lupo, Gaia and Sommacal, Matteo (2010) Helical configurations of elastic rods in the presence of a long-range interaction potential. Journal of Physics A: Mathematical and Theoretical, 43 (8). 085214. ISSN 1751-8113

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Abstract

Recently, the integrability of the stationary Kirchhoff equations describing an elastic rod folded in the shape of a circular helix was proven. In this paper we explicitly work out the solutions to the stationary Kirchhoff equations in the presence of a long-range potential which describes the average constant force due to a Morse-type interaction acting among the points of the rod. The average constant force results to be parallel to the normal vector to the central line of the folded rod; this condition remarkably permits to preserve the integrability (indeed the solvability) of the corresponding Kirchhoff equations if the elastic rod features constant or periodic stiffnesses and vanishing intrinsic twist. Furthermore, we discuss the elastic energy density with respect to the radius and pitch of the helix, showing the existence of stationary points, namely stable and unstable configurations, for plausible choices of the featured parameters corresponding to a real bio-polymer.

Item Type:	Article
Uncontrolled Keywords:	Soft matter, liquids and polymers, biological physics, condensed matter, chemical physics, physical chemistry
Subjects:	F300 Physics G100 Mathematics
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Ellen Cole
Date Deposited:	09 May 2012 11:23
Last Modified:	13 Oct 2019 00:30
URI:	http://nrl.northumbria.ac.uk/id/eprint/6869

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