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Knotting and Linking of Vortex Lines

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Analysis of Quantised Vortex Tangle

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

The vortices of our wave-chaotic systems always form closed loops, and therefore may be expected to be knotted or to link with one other; were the vortices formed of physical string, it would not always be possible to simplify them to separate planar circles without cutting the string or somehow passing it through itself. In wave chaos the vortices may reconnect under a change of parameters, potentially changing their knot type, but still must have a characteristic average statisical behaviour. We show in this Chapter that vortex curves do form knots and links, and suggest that this behaviour becomes generic for long vortices. These results are compared against the statistical behaviour of random walks, isolating some particular knotting statistics of the filamentary tangle, and demonstrating that topological quantities can be particularly sensitive to boundary conditions. We further discuss some specific topological problems that arise when considering how knotted structures may form.

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Authors and Affiliations

  1. H H Wills Physics Laboratory, University of Bristol, Bristol, UK

    Alexander John Taylor

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  1. Alexander John Taylor
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Correspondence to Alexander John Taylor .

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Taylor, A.J. (2017). Knotting and Linking of Vortex Lines. In: Analysis of Quantised Vortex Tangle. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-48556-0_5

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