1.2 Applications

Ginzburg-Landau equations have been used to model a wide variety of physical systems. This page simply lists a few of the possible applications, although no details are given. The interested reader is encouraged to consult Aranson and Kramer (2002) for the appropriate references.

1.2.1 The Real Ginzburg-Landau equation

Physical systems which undergo an instability described by the RGLE include

• Rayleigh-Benárd convection
• Taylor-Couette flow
• Flames stabilized on a burner

In more than one dimension, the system must be anisotropic (eg., electroconvection and convection in an inclined layer) for the RGLE to be applicable. On the other hand, in isotropic systems, the Laplacian operator must be replaced.

1.2.2 The Complex Ginzburg-Landau equation

Physical systems which undergo an instability described by the CGLE include:

• Rayleigh-Benárd convection in binary mixtures
• The instability of rolls in low-Prandtl number Rayleigh-Benárd convection (this is a secondary instability)
• Hydrothermal waves
• Electroconvection in nematic liquid crystals