Patterns, Nonlinear Dynamics and Applications - PANDA
Fourth meeting: Friday 18th October 2002, DAMTP, Cambridge
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.