The Dynamics of Patterns

By M.I. Rabinovich, A.B. Ezersky and P.D. Weidman

Reviewed by Rebecca Hoyle

World Scientific, 2001
ISBN 9810240554 64 (Hardback)
ISBN 9810240562 33 (Paperback)

This beautifully illustrated book brings together a remarkable array of pattern-forming phenomena. The early chapters concentrate on model equations from Swift-Hohenberg to Ginzburg-Landau. The authors then move through tesselating `crystals' to quasicrystals, defects, localized phenomena and spirals. The latter part of the book focuses on areas of the authors' particular expertise such as patterns in soap films, colonies of microorganisms (guest-written by L. Tsimring) and chaotic media. The final chapter, musing on the way forward for the nonlinear theory of pattern formation in neural networks and living systems more generally, contains an enjoyable account of the theory of visual hallucinations. Two appendices give an overview of nonlinear dynamics and key experiments.

This is very much the physicist's perspective on pattern formation, replete with phenomenological models and exquisite experiments. It's a good read, whipping along at lightning pace past a dazzling parade of surely the best-looking physics around. The authors have assembled an impressive collection of striking photographs and computer-generated images, and the book would be worth buying for this alone.

The mathematical exposition increases in detail as the book progresses. Thus the early chapters each summarise briefly a collection of models, while the middle chapters fill in some steps on the path to each solution and the final chapters are detailed accounts of pattern formation in specific systems.

The middle portion of the book was for me the most engaging: the chapters on quasicrystals, the breaking of order and spirals give a concise overview of each topic with enough detail to allow the nonspecialist reader to follow the arguments. The later chapters on soap films and self-organizing microorganisms, both fascinating subjects, are much more detailed review articles suitable for researchers. I particularly enjoyed learning about slime moulds, but others will find the soap films, or perhaps the chapters on spatial disorder and chaotic media, more appealing.

I found myself in two minds about the first few chapters. Here the authors provide a comprehensive outline of a multitude of phenomena from the Rayleigh-Taylor instability to nerve membrane excitation as modelled by the Complex Ginzburg-Landau equation. Perhaps unavoidably then, the mathematical arguments are only sketched, which might make hard reading for those new to the subject. The short guide to nonlinear dynamics, which forms an appendix, is a great whirlwind tour, but again a little short on detail. These parts of the book are the most naturally appropriate for graduates and postgraduate students - who, along with researchers new to the field, make up the target audience - and I think they might struggle without a more elementary text to hand. On the other hand, those already working in pattern formation and nonlinear dynamics may well appreciate the quick overview provided of each topic and the drawing together of so many models.

Saving the best for last, the appendix describing key experiments is a highlight. Here the authors outline the historical development of experiments in parametrically-excited patterns, thermal convection and diffusive chemical reactions. I thoroughly enjoyed the charming account of Faraday's original observations of the crispations now named after him, and the ensuing controversy over discrepancies with Matthiesson's work where Lord Rayleigh weighed in. In its fundamentals the world of science seems little changed since the 1830s, except that they had a better turn of phrase - Faraday talked of the "preferableness" of "quadrangular arrangements" - and, judging from the excerpt from Faraday's diary reproduced here, we have better graphics.

A listing of books reviewed in UK Nonlinear News is available.

UK Nonlinear News would like to thank World Scientific for providing the review copy.

 


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