Theory of Supercoiled Elastic Rings with SelfContact and Its Application to DNA Plasmids
 Bernard D. Coleman,
 David Swigon
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Methods are presented for obtaining exact analytical representations of supercoiled equilibrium configurations of impenetrable elastic rods of circular crosssection that have been pretwisted and closed to form rings, and a discussion is given of applications in the theory of the elastic rod model for DNA. When, as here, selfcontact is taken into account, and the rod is assumed to be inextensible, intrinsically straight, transversely isotropic, and homogeneous, the important parameters in the theory are the excess link Δℒ (a measure of the amount the rod was twisted before its ends were joined), the ratio ω of the coefficients of torsional and flexural rigidity, and the ratio d of crosssectional diameter to the length of the axial curve C. Solutions of the equations of equilibrium are given for cases in which selfcontact occurs at isolated points and along intervals. Bifurcation diagrams are presented as graphs of Δℒ versus the writhe of C and are employed for analysis of the stability of equilibrium configurations. It is shown that, in addition to primary, secondary, and tertiary branches that arise by successive bifurcations from the trivial branch made up of configurations for which the axial curve is a circle, there are families of equilibrium configurations that are isolas in the sense that they are not connected to bifurcation branches by paths of equilibrium configurations compatible with the assumed impenetrability of the rod. Each of the isolas found to date is connected to a bifurcation branch by a path which, although made up of solutions of the governing equations, contains regions on which the condition of impenetrability does not hold.
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 Title
 Theory of Supercoiled Elastic Rings with SelfContact and Its Application to DNA Plasmids
 Journal

Journal of elasticity and the physical science of solids
Volume 60, Issue 3 , pp 173221
 Cover Date
 20000601
 DOI
 10.1023/A:1010911113919
 Print ISSN
 03743535
 Online ISSN
 15732681
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 contact problems for elastic rods
 DNA topology
 Industry Sectors
 Authors

 Bernard D. Coleman ^{(1)}
 David Swigon ^{(1)}
 Author Affiliations

 1. Department of Mechanics and Materials Science, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, NJ, 088548058, U.S.A.