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Pattern formation in large domains

Rucklidge, A.M. (2003) Pattern formation in large domains. Philosophical Transactions Of The Royal Society Of London Series A - Mathematical Physical and Engineering Sciences, 361 (1813). pp. 2649-2664. ISSN 1471-2962

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Pattern formation is a phenomenon that arises in a wide variety of physical, chemical and biological situations. A great deal of theoretical progress has been made in understanding the universal aspects of pattern formation in terms of amplitudes of the modes that make up the pattern. Much of the theory has sound mathematical justification, but experiments and numerical simulations over the last decade have revealed complex two-dimensional patterns that do not have a satisfactory theoretical explanation. This paper focuses on quasi-patterns, where the appearance of small divisors causes the standard theoretical method to fail, and ends with a discussion of other outstanding problems in the theory of two-dimensional pattern formation in large domains.

Item Type: Article
Copyright, Publisher and Additional Information: © 2003 The Royal Society
Keywords: pattern formation; quasi-patterns; small divisors
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: A. M. Rucklidge
Date Deposited: 05 Nov 2004
Last Modified: 05 Jun 2014 07:09
Published Version: http://www.journals.royalsoc.ac.uk/openurl.asp?gen...
Status: Published
Refereed: Yes
Identification Number: 10.1098/rsta.2003.1267
URI: http://eprints.whiterose.ac.uk/id/eprint/176

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