Phil. Trans. R. Soc. Lond. A
361 (2003) 2649-2664.
doi:10.1098/rsta.2003.1267
Pattern formation in large domains
A.M. Rucklidge
Department of Applied Mathematics,
University of Leeds, Leeds, LS2 9JT, UK
Abstract.
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
quasipatterns, 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.
Keywords: Pattern formation; quasipatterns; small divisors
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