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The Mathematical Foundations of Mixing
The Linked Twist Map as a Paradigm in Applications: Micro to Macro, Fluids to Solids

$84.00 ( ) USD

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: November 2006
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511243547

$ 84.00 USD ( )
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About the Authors
  • Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions.

    • First book explaining new important ideas in our understanding of how fluids mix
    • Authors are well-known book writers and leading researchers
    • Starts with a broad, accessible and thought-provoking chapter, and ends with a collection of open problems
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    Reviews & endorsements

    "The material is presented in a style that should make it accessible to a wise audience, and especially to readers involved in practical aspects of mixing who wish to learn more about the mathematical problems underlying the physical phemonology."
    Mathematical Reviews

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    Product details

    • Date Published: November 2006
    • format: Adobe eBook Reader
    • isbn: 9780511243547
    • contains: 110 b/w illus. 17 colour illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    1. Mixing: physical issues
    2. Linked twist maps
    3. The ergodic hierarchy
    4. Existence of a horseshoe
    5. Hyperbolicity
    6. The ergodic partition for toral LTMs
    7. Ergodicity and Bernoulli for TLTMs
    8. Linked twist maps on the plane
    9. Further directions and open problems
    Bibliography
    Index.

  • Authors

    Rob Sturman, University of Bristol
    Rob Sturnan gained his PhD from University College London in 2000. He is currently carrying out research on mixing in microfluidics at the University of Bristol.

    Julio M. Ottino, Northwestern University, Illinois
    Julio M. Ottino is Dean of the R. R. McCormick School of Engineering and Applied Sciences, R. R. McCormick Institute Professor and Walter P. Murphy Professor of Chemical and Biological Engineering at Northwestern University.

    Stephen Wiggins, University of Bristol
    Stephen Wiggins is a Professor of Applied Mathematics and Head of the School of Mathematics at the University of Bristol.

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