Patterns, Nonlinear Dynamics and Applications - PANDA

Fourth meeting: Friday 18th October 2002, DAMTP, Cambridge

Paul Matthews Pattern formation on a sphere
Abstract: Pattern formation on the surface of a sphere is described by equations involving interactions of spherical harmonics of degree l. When l is even, the leading-order equations are determined uniquely by the symmetry, regardless of the physical context. New general results are derived regarding the existence of solutions with dihedral symmetry and the stability of the axisymmetric state. Existence and stability results are found for even l up to l=12. Using either a variational or eigenvalue criterion, the preferred solution has icosahedral symmetry for l=6, l=10 and l=12.