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The Resource Analysis of Quantised Vortex Tangle

Analysis of Quantised Vortex Tangle

Label
Analysis of Quantised Vortex Tangle
Title
Analysis of Quantised Vortex Tangle
Creator
Subject
Language
eng
Member of
Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Springer Theses Ser
Analysis of Quantised Vortex Tangle
Label
Analysis of Quantised Vortex Tangle
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4748065
Publication
Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Supervisor's Foreword -- Abstract -- Acknowledgements -- Contents -- 1 Introduction -- 1.1 General Introduction -- 1.2 What Does It Mean to Be Tangled? -- 1.3 Phase Singularities in Two and Three Dimensions -- 1.4 Random Waves and Vortex Tangle -- 1.5 Knotting and Linking as a Statistical Tool -- 1.6 Other Random Tangles and Random Walks -- 1.7 Variations on Random Waves -- 1.7.1 The 3-Torus (Periodic Boundary Conditions) -- 1.7.2 The 3-Sphere -- 1.7.3 The Quantum Harmonic Oscillator -- 1.8 Thesis Outline -- References -- 2 Numerical Methods -- 2.1 Numerically Locating Vortices -- 2.2 Tracking Vortices with a Resampling Algorithm -- 2.3 Vortex Tracking in Different Systems -- 2.4 Geometrical Details in Different Systems -- 2.4.1 The 3-Torus -- 2.4.2 The 3-Sphere -- 2.4.3 The Quantum Harmonic Oscillator -- 2.5 Summary of Numerical Results -- 2.5.1 The 3-Torus -- 2.5.2 The 3-Sphere -- 2.5.3 The Quantum Harmonic Oscillator -- References -- 3 Geometry and Scaling of Vortex Lines -- 3.1 Introduction to Geometrical Statistics -- 3.2 Local Geometry of Random Wave Vortices -- 3.3 Statistics of Curvature and Torsion -- 3.4 Geometric Correlations -- 3.5 Three Measures of Fractality -- 3.6 Scaling Relations of Random Tangle -- 3.7 Crossing Number and Writhe of Vortex Loops -- 3.8 Discussion -- References -- 4 Topological Methods -- 4.1 A Practical Introduction to Knot Theory -- 4.2 Calculating Invariants -- 4.2.1 The Alexander Polynomial -- 4.2.2 The Determinant and Roots of the Alexander Polynomial -- 4.2.3 The Jones and HOMFLY-PT Polynomials -- 4.2.4 Hyperbolic Volume -- 4.2.5 Minimal Crossing Number -- 4.2.6 The Linking Number -- 4.2.7 The Fary-Milnor Theorem -- 4.3 Simplifying Space Curves -- 4.4 Topological Complexity -- References -- 5 Knotting and Linking of Vortex Lines -- 5.1 Finding Knots -- 5.1.1 The 3-torus -- 5.1.2 The 3-sphere
  • 5.1.3 The Quantum Harmonic Oscillator -- 5.2 Probabilities of Knotting -- 5.3 Comparison of Knot Type Statistics -- 5.4 Finding Links -- 5.4.1 The 3-torus -- 5.4.2 The 3-sphere -- 5.4.3 The Quantum Harmonic Oscillator -- 5.5 Probabilities of Linking -- 5.6 Knotting in Lines with Non-trivial Homology -- 5.7 Postselection Relations -- 5.8 The Smallest Knot -- 5.9 Discussion -- References -- 6 Conclusions -- Appendices
http://library.link/vocab/cover_art
https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9783319485560&userID=ebsco-test&password=ebsco-test
Dimensions
unknown
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b4414220'}
Extent
1 online resource (206 pages)
Form of item
online
Isbn
9783319485560
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
unknown sound
Specific material designation
remote

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