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  • © 2009

Lectures on Topological Fluid Mechanics

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

Editors:

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
  2. Braids and Knots

    • Patrick D. Bangert
    Pages 1-73
  3. Tangles, Rational Knots and DNA

    • Louis H. Kauffman, Sofia Lambropoulou
    Pages 99-138
  4. Structural Complexity and Dynamical Systems

    • Renzo L. Ricca
    Pages 167-186
  5. Back Matter

    Pages 219-231

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.

Keywords

  • Braids
  • Fluid flows
  • Knot theory
  • Knots &amp
  • Links
  • Magnetohydrodynamics
  • Topological Fluid Mechanics
  • computational fluid dynamics
  • fluid dynamics
  • fluid mechanics

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

Bibliographic Information

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions