Pattern Formation
An Introduction to Methods

Fully illustrated mathematical guide to pattern formation. Includes instructive exercises and examples.

Rebecca Hoyle (Author)

9780521817509, Cambridge University Press

Hardback, published 17 March 2006

434 pages, 130 b/w illus. 20 colour illus. 9 tables 50 exercises
25.7 x 21.1 x 3 cm, 1.11 kg

' … a very useful guide to this topic area, presented in a clear and logical fashion and written with style and panache.' Mathematics Today

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.

Subject Areas: Nonlinear science [PBWR], Mathematical modelling [PBWH], Applied mathematics [PBW]