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Analysis of Quantised Vortex Tangle

  • Alexander John┬áTaylor

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Alexander John Taylor
    Pages 1-43
  3. Alexander John Taylor
    Pages 45-73
  4. Alexander John Taylor
    Pages 75-108
  5. Alexander John Taylor
    Pages 109-141
  6. Alexander John Taylor
    Pages 143-187
  7. Alexander John Taylor
    Pages 189-192
  8. Back Matter
    Pages 193-197

About this book

Introduction

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. 

Keywords

Filamentary Tangle Wave Chaos Knot Statistics Statistical Geometry Statistical Topology Quantum Chaos Chaotic Modes of Cavity

Authors and affiliations

  • Alexander John┬áTaylor
    • 1
  1. 1.H H Wills Physics LaboratoryUniversity of BristolBristolUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-48556-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-48555-3
  • Online ISBN 978-3-319-48556-0
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site