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Details of Grant 

EPSRC Reference: EP/C010396/1
Title: WORKSHOP: Theoretical Aspects of Pattern Formation
Principal Investigator: Rucklidge, Professor A M
Other Investigators:
Melbourne, Professor I Sandstede, Professor B
Researcher Co-Investigators:
Project Partners:
Department: Applied Mathematics
Organisation: University of Leeds
Scheme: Standard Research (Pre-FEC)
Starts: 02 November 2005 Ends: 01 April 2006 Value (£): 5,126
EPSRC Research Topic Classifications:
Non-linear Systems Mathematics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
Many physical, chemical and biological systems are capable of forming patterns. One of the great successes of the theory of pattern formation has been the realisation that, in spite of the different details of each of these systems, the pattern formation process is universal, and can be described by simple equations for the amplitudes of the waves that make up the pattern. In one dimension (rolls), there is a well established rigorous theory, and the relevant amplitude equation is the Ginzburg-Landau equation when the size of the domain is large compared to the characteristic lengthscale of the pattern. In two dimensions (squares, hexagons or more complex patterns), the theory is rigorous in the cases where the pattern is strictly periodic in space, or where the size of the domain is of the same order as the lengthscale of the pattern. Modulation equations have been developed to describe the large-scale evolution of some of the simpler patterns (rolls and hexagons), but these equations are based on asymptotics techniques and do not have a sound theoretical basis, partly because of the rotational degeneracy that is inherent in two-dimensional pattern formation, and partly because of the formation of defects, which violate the assumptions made in the derivation.The main thrust of our proposal is to bring together pure and applied mathematicians working in this area, as well as experimentalists whose work consistently challenges theory, to see what rigorous progress can be made in understanding the nature of two-dimensional patterns.
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Project URL: http://www.newton.ac.uk/programmes/PFD/pfdw03.html
Further Information:  
Organisation Website: http://www.leeds.ac.uk