Quasipatterns in surface waves

Alastair Rucklidge

Applied Maths Department, University of Leeds

Spatially quasiperiodic patterns have been observed in the Faraday surface wave experiment, in which a container of fluid is subjected to vertical vibrations. Spatial Fourier transforms of these quasipatterns suggest that the patterns are well represented by the sum of 8, 10 or 12 Fourier modes with wavevectors equally spaced around a circle. This representation has been used many times as the starting point for standard perturbative methods of computing the weakly nonlinear dependence of the pattern amplitude on parameters. We discuss some of the difficulties caused by small divisors, implicit in this approach.

Reference:

Convergence properties of the 8, 10 and 12 mode representations of

quasipatterns, by A.M. Rucklidge and W.J.Rucklidge. Physica D 178 (2003)

62-82. http://dx.doi.org/10.1016/S0167-2789(02)00792-3