Worm structure in the modified Swift-Hohenberg equation for electroconvection
Abstract
An anisotropic complex Swift-Hohenberg equation is proposed to study pattern formation in electroconvection. In the subcritical regime, a localized state is found in two dimensions, which resembles the ``worm'' state observed in recent experiment by M. Dennin et al. [Phys. Rev. Lett. 77, 2475 (1996); Science 272, 388 (1996)]. In the corresponding one-dimensional model, a stationary pulse state is discovered, due to a nonadiabatic effect, and it is shown to explain the localization of the ``worm'' state in the two-dimensional model. Based on these results, we believe that the initial bifurcation should be subcritical where the ``worm'' state is observed, and further experiment is suggested to test this scenario.
- Publication:
-
Physical Review E
- Pub Date:
- October 1997
- DOI:
- 10.1103/PhysRevE.56.R3765
- arXiv:
- arXiv:patt-sol/9701001
- Bibcode:
- 1997PhRvE..56.3765T
- Keywords:
-
- 47.54.+r;
- 02.60.Cb;
- 47.20.Ky;
- Numerical simulation;
- solution of equations;
- Nonlinearity bifurcation and symmetry breaking;
- Nonlinear Sciences - Pattern Formation and Solitons
- E-Print:
- doi:10.1103/PhysRevE.56.R3765