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Pattern formation in large domains

By A.M. Rucklidge

Abstract

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

Year: 2003
OAI identifier: oai:eprints.whiterose.ac.uk:176

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