Forced periodic and quasi-periodic patterns in anisotropic systems

We investigate pattern formation in two-dimensional anisotropic systems under an external spatially periodic modulation force. Electrohydrodynamic convection or Rayleigh-Bénard convection of nematic liquid crystals are typical examples of anisotropic pattern forming systems. We are especially interested in the situation where the wave vector of the convection rolls and the wave vector of the external modulation force are not parallel to each other. On the basis of descriptions using amplitude equations we find various two-dimensional periodic and quasi-periodic patterns, such as rectangular pattern, skewed varicose pattern, undulations and their quasi-periodic generalizations. Temporal evolutions of a few patterns obtained by numerical simulations as well as a possible experiment are described.