(
2007-10)
Goyal, Sachin; Perkins, N. C.; Lee, Christopher L.
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).
