The Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications: Micro to Macro, Fluids to Solids: 22 (Cambridge Monographs ... Computational Mathematics, Series Number 22)
Cambridge University Press
Edition: Illustrated, 9/21/2006
EAN 9780521868136, ISBN10: 0521868130
Hardcover, 302 pages, 23.3 x 15.4 x 1.9 cm
Language: English
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.
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.
"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