Publication Date:
2022-05-25
Description:
Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in International Journal of Non-Linear Mechanics 43 (2008): 65-73, doi:10.1016/j.ijnonlinmec.2007.10.004.
Description:
Twisted marine cables on the sea floor can form highly contorted three-dimensional loops
that resemble tangles. Such tangles or ‘hockles’ are topologically equivalent to the
plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these
intertwined loops is studied herein using a computational rod model that explicitly
accounts for dynamic self-contact. Numerical solutions are presented for an illustrative
example of a long rod subjected to increasing twist at one end. The solutions reveal the
dynamic evolution of the rod from an initially straight state, through a buckled state in the
approximate form of a helix, through the dynamic collapse of this helix into a near-planar
loop with one site of self-contact, and the subsequent intertwining of this loop with
multiple sites of self-contact. This evolution is controlled by the dynamic conversion of
torsional strain energy to bending strain energy or, alternatively by the dynamic
conversion of twist (Tw) to writhe (Wr).
Description:
The authors (NCP and SG) gratefully acknowledge the research support provided by the
U.S. Office of Naval Research (grant N00014-00-1-0001), the Lawrence Livermore
25
National Laboratories (grant B 531085), and the U. S. National Science Foundation
(grants CMS 0439574 and CMS 0510266).
Keywords:
Rod dynamics
;
Self-contact
;
Intertwining
;
DNA Supercoiling
;
Cable hockling
Repository Name:
Woods Hole Open Access Server
Type:
Preprint
Format:
application/pdf
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