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Lectures on Topological Fluid Mechanics

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 2 - 10, 2001

  • Book
  • © 2009

Overview

Authors:
  1. Mitchell A. Berger

    1. Dept. Mathematics, University of Exeter, Exeter, United Kingdom

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  2. Louis H. Kauffman

    1. Dept. Mathematics, Statistics &, Computer Science, University of Illinois, Chicago, Chicago, U.S.A.

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  3. Boris Khesin

    1. Dept. Mathematics, University of Toronto, Toronto, Canada

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  4. H. Keith Moffatt

    1. Ctr. Mathematical Sciences, Dept. Applied Mathematics &, University Cambridge, Cambridge, United Kingdom

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  5. Renzo L. Ricca

    1. Dipto. Matematica e Applicazioni, Università Milano-Bicocca, Milano, Italy

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  6. De Witt Sumners

    1. Dept. Mathematics, Florida State University, Tallahassee, USA

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Editors:
  1. Renzo L. Ricca

    1. Dipto. Matematica e Applicazioni, Università Milano-Bicocca, Milano, Italy

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1973)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (7 chapters)

  1. Front Matter

    Pages 1-12
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  2. Braids and Knots

    • Patrick D. Bangert
    Pages 1-73

  3. Topological Quantities: Calculating Winding, Writhing, Linking, and Higher Order Invariants

    • Mitchell A. Berger
    Pages 75-97

  4. Tangles, Rational Knots and DNA

    • Louis H. Kauffman, Sofia Lambropoulou
    Pages 99-138

  5. The Group and Hamiltonian Descriptions of Hydrodynamical Systems

    • Boris Khesin
    Pages 139-155

  6. Singularities in Fluid Dynamics and their Resolution

    • H. K. Moffatt
    Pages 157-166

  7. Structural Complexity and Dynamical Systems

    • Renzo L. Ricca
    Pages 167-186

  8. Random Knotting: Theorems, Simulations and Applications

    • De Witt Sumners
    Pages 187-217

  9. Back Matter

    Pages 219-231
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Keywords

About this book

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other.

This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.

Authors, Editors and Affiliations

  • Dipto. Matematica e Applicazioni, Università Milano-Bicocca, Milano, Italy

    Renzo L. Ricca, Renzo L. Ricca

  • Dept. Mathematics, University of Exeter, Exeter, United Kingdom

    Mitchell A. Berger

  • Dept. Mathematics, Statistics &, Computer Science, University of Illinois, Chicago, Chicago, U.S.A.

    Louis H. Kauffman

  • Dept. Mathematics, University of Toronto, Toronto, Canada

    Boris Khesin

  • Ctr. Mathematical Sciences, Dept. Applied Mathematics &, University Cambridge, Cambridge, United Kingdom

    H. Keith Moffatt

  • Dept. Mathematics, Florida State University, Tallahassee, USA

    De Witt Sumners

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