Pattern Formation

In this area, I am interested in;
  • Patterns in fluid dynamics: convection, Faraday wave and Taylor-Couette experiments
  • Quasipatterns and the small divisor problem
  • Quasicrystals in soft matter
  • Patterns with two length scales
  • Localised patterns
  • Spiral patterns
  • Spatiotemporal chaos
More details of PhD topics

Examples: two-dimensional and three-dimensional quasipatterns

Example of a two-dimensional approximate quasipattern
Example of an approximate quasipattern in a periodically forced PDE. Spatial Fourier transforms of quasipatterns observed in Faraday wave experiments suggest that the patterns are well represented by the sum of 8, 10 or 12 Fourier modes with wavevectors equally spaced around a circle. However, nonlinear interactions between these wavevectors generate new modes that come arbitrarily close to the original 8, 10 or 12 wavevectors, which leads to complications in the theory for these patterns.

See: Design of parametrically forced patterns and quasipatterns, by A.M. Rucklidge and M. Silber. SIAM J. Applied Dynamical Systems 8 (2009) 298-347. Link to pdf and doi:10.1137/080719066

Example of a three-dimensional icosahedral quasicrystal
Example of a three-dimensional icosahedral quasicrystal in a phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. See: Three-dimensional Icosahedral Phase Field Quasicrystal, by P. Subramanian, A.J. Archer, E. Knobloch and A.M. Rucklidge. Physical Review Letters 117 (2016) 075501. Link to pdf and doi:10.1103/PhysRevLett.117.075501