Synopses & Reviews
From the stripes of a zebra and the spots on a leopard's back to the ripples on a sandy beach or desert dune, regular patterns arise everywhere in nature. The appearance and evolution of these phenomena have been a focus of recent research activity across several disciplines. This book provides an introduction to the range of mathematical theory and methods used to analyze and explain these often intricate and beautiful patterns. Bringing together several different approaches, from group theoretic methods to envelope equations and theory of patterns in large-aspect ratio-systems, the book also provides insight behind the selection of one pattern over another.
Synopsis
Mathematical guide to pattern formation. Exercises, examples and fully illustrated.
Synopsis
Fully illustrated mathematical guide to pattern formation. Includes instructive exercises and examples.
Synopsis
From the stripes of a zebra and the spots on a leopard's back to the ripples on a sandy beach or desert dune, regular patterns arise everywhere in nature. This book provides an introduction to the range of mathematical theory and methods used to analyse and explain these often intricate and beautiful patterns. Suitable as an upper-undergraduate textbook for mathematics students or as a fascinating, fully illustrated resource for readers in physics and biology. Rebecca Hoyle's book unifies a range of techniques used by active researchers in this growing field.
Synopsis
Upper undergraduate and graduate textbook. Exercises included with solutions available.
About the Author
'Rebecca Hoyle is a Senior Lecturer in Mathematics at the University of Surrey'
Table of Contents
'1. What are natural patterns?; 2. A bit of bifurcation theory?; 3. A bit of group theory?; 4. Bifurcations with symmetry; 5. Simple lattice patterns; 6. Superlattices, hidden symmetries and other complications; 7. Spatial modulation and envelope equations; 8. Instabilities of stripes and travelling plane waves; 9. More instabilities of patterns; 10. Spirals, defects and spiral defect chaos; 11. Large-aspect-ratio systems and the Cross-Newell equations.\n
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