Pattern Formation: An Introduction to Methods

ISBN-13: 9780521817509 / Angielski / Twarda / 2006 / 434 str.

Rebecca B. Hoyle

Opis

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.

Recenzje

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

Spis treści

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.