Significance of Knotted Structures for Function of Proteins and Nucleic Acids
Poster Session II
45 – POS
Board 17
Knotted Defect Tangles in Three-dimensional Random Waves
Alexander Taylor
, Mark R. Dennis.
University of Bristol, Bristol, Bristol, United Kingdom.
Many physical 3D space filling processes can be understood in terms of complex filamentary
tangles. These include polymer strands in a dense melt, as well as disclinations in liquid crystals,
and the topological defects in quantum condensed matter systems and optical fields. On large
scales these systems appear statistically random, but certain properties appear universal despite
the physically different origins of complexity.
We track the tangle of topological defects in numerical simulations of a random wave model [1].
These are the lines of zero intensity in the wavefield, and despite the linear input conditions form
a dense filamentary tangle with nonlinear features that encompass the complexity of the field. As
with other systems, the small scale conformations of the lines are described with a simple local
model, but on global scales the tangling becomes random.
We observe that while many standard quantities reveal only a common statistical scaling on the
large scale [2], the topology – particularly the occurrence of knots in vortex loops - discriminates
between tangles with different origins. In fact, knotting is somewhat less common than in
standard random walk models, though highly complex knots do occur.
[1] M V Berry and M R Dennis
. Proc R Soc A
456, 2059-79 (2000)
[2] A J Taylor and M R Dennis. Geometry and scaling of tangled vortex lines in three-
dimensional random wave fields, in preparation.
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