Pattern Formation: An Introduction to Methods (Cambridge Texts in Applied Mathematics)
Cambridge University Press, 3/23/2006
EAN 9780521817509, ISBN10: 0521817501
Hardcover, 434 pages, 25.7 x 21.1 x 3 cm
Language: English
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 has 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 analyse 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. Suitable as an upper-undergraduate textbook for mathematics students or as a fascinating, engaging, and fully illustrated resource for readers in physics and biology, Rebecca Hoyle's book, using a non-partisan approach, unifies a range of techniques used by active researchers in this growing field.
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.
'Rebecca Hoyle's book is an invaluable graduate text for those who first enter the field of Pattern Formation. It has a remarkably lucid style and friendly exposition and very balanced level of detail through the book. An important strength is its rigorous mathematical approach which equips the reader with the underlying understanding of the mechanisms of pattern formation and enables one to confidently investigate novel problems ... I find it remarkable that a book presenting a field that has recently grown to such proportions, feels so light and approachable when you first take it in your hands. This is, I think, a much needed encouragement for the beginner. The uncluttered chapter structure and also the nice publisher design play a role in this.' UK Nonlinear News