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Analysis of Quantised Vortex Tangle

  • Book
  • © 2017

Overview

Authors:
  1. Alexander John Taylor

    1. H H Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom

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  • Nominated as an outstanding PhD thesis by the University of Bristol, UK
  • Presents a detailed introduction to an unusual and comparatively new kind of analysis for tangled systems
  • Introduces readers to wave chaos as a generic model for statistics expressed in many different physical systems
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction

    • Alexander John Taylor
    Pages 1-43

  3. Numerical Methods

    • Alexander John Taylor
    Pages 45-73

  4. Geometry and Scaling of Vortex Lines

    • Alexander John Taylor
    Pages 75-108

  5. Topological Methods

    • Alexander John Taylor
    Pages 109-141

  6. Knotting and Linking of Vortex Lines

    • Alexander John Taylor
    Pages 143-187

  7. Conclusions

    • Alexander John Taylor
    Pages 189-192

  8. Back Matter

    Pages 193-197
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Keywords

About this book

In this thesis, the author develops numerical techniques for tracking and characterising the convoluted nodal lines in three-dimensional space, analysing their geometry on the small scale, as well as their global fractality and topological complexity---including knotting---on the large scale.  The work is highly visual, and illustrated with many beautiful diagrams revealing this unanticipated aspect of the physics of waves. Linear superpositions of waves create interference patterns, which means in some places they strengthen one another, while in others they completely cancel each other out. This latter phenomenon occurs on 'vortex lines' in three dimensions.  In general wave superpositions modelling e.g. chaotic cavity modes, these vortex lines form dense tangles that have never been visualised on the large scale before, and cannot be analysed mathematically by any known techniques. 

Authors and Affiliations

  • H H Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom

    Alexander John Taylor

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