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EPSRC Reference: GR/A00515/02
Title: AF: NONLINEAR SPATIO-TEMPORAL BEHAVIOUR OF PATTERN-FOR MING PDES
Principal Investigator: Rucklidge, Professor A M
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Department: Applied Mathematics
Organisation: University of Leeds
Scheme: Advanced Fellowship (Pre-FEC)
Starts: 01 October 2000 Ends: 30 September 2003 Value (£): 102,702
EPSRC Research Topic Classifications:
Light-Matter Interactions
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Summary on Grant Application Form
My research interests include developing new ideas in nonlinear dynamics and bifurcation theory; using these ideas to analyse complicated behaviour in fluid dynamical systems; and direct numerical modelling of problems of astrophysical importance. My strength lies in my ability to use the methods of bifurcation theory (developing new methods where necessary) to understand complicated behaviour in PDEs that are relevant to real physical problems. I propose three threads of research into the nonlinear spatio-temporal behaviour of pattern-forming PDEs. First, I shall develop the theory of bifurcations from nontrivial solutions of PDEs, paying particular attention to analysing the transition to increasingly complicated spatial and spatio-temporal structures that break the spatial periodicity of the original pattern. Second, I shall investigate the interplay of symmetries with global dynamics in PDEs, ODEs and maps, examining the issue of the loss of stability of structurally stable heteroclinic cycles between chaotic sets, the influence of noise on the stability of heteroclinic cycles, and global bifurcations in situations where the symmetries imply an increase in the dimension of the map required to model the dynamics near the global bifurcation. Third, I shall pursue my astrophysical work on the problems of the internal structure of sunspots, in particular, the filamentary spatial structure, and of chaotic magnetic fields in the solar corona.
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Organisation Website: http://www.leeds.ac.uk