A twist localizes three-dimensional patterns

Abstract

A mechanism for the localization of spatially periodic, self-organized patterns in anisotropic media which requires systems extended in all three spatial dimensions is presented: When the anisotropy axis is twisted the pattern becomes localized in planes parallel to the anisotropy axis. An analytic description of the effect is developed and used to interpret recent experiments in the high-frequency regime of electroconvection by Bohatsch and Stannarius [Phys. Rev. E {\bf 60}, 5591 (1999)]. The localization width is found to be of the order of magnitude of the geometrical average of pattern wavelength and the inverse twist.