The Mathematical Foundations of Mixing

Erscheinungsjahr 2006
ISBN: 978-0-521-86813-6
Verlag: Cambridge University Press

Buch, Englisch, Band 22, 302 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 591 g

Reihe: Cambridge Monographs on Applied and Computational Mathematics

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.

Autoren/Hrsg.

Sturman, Rob

Ottino, Julio M.

Wiggins, Stephen

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre

Inhaltsverzeichnis

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.

Über Autor(innen)

Ottino, Julio M.
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.

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

Sturman, Rob
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.