DOI: 10.1051/jp2:1996183
J. Phys. II France 6 (1996) 305-328

Forced Periodic and Quasi-Periodic Patterns in Anisotropic Systems

Atsushi Ogawa^{1, 2}, Walter Zimmermann^{2, 3}, Kyozi Kawasaki^{2, 3} and Toshihiro Kawakatsu<sup>4, 2, 3

1</sup>  Department of Applied Physics, Faculty of Engineering, Fukui University Bunkyo 3-9-1, Fukui 910, Japan
²  Department of Physics, Faculty of Science, Kyushu University 33, Fukuoka 812, Japan
³  IFF, Forschungszentrum Jülich, 52425 Jülich, Germany
⁴  Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-03, Japan

(Received 14 November 1994, revised 27 September 1995, accepted 18 October 1995)

Abstract
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.

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