An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns

This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial dimensions, where it can be replaced by a scaling phenomenology. The Ginzburg-Landau formalism can then be used to justify the phenomenological theory using the renormalization group, which elucidates the physical and mathematical mechanism for universality. In the second part of the paper it is shown how near pattern forming linear instabilities of dynamical systems, a formally similar Ginzburg-Landau theory can be derived for nonequilibrium macroscopic phenomena. The real and complex Ginzburg-Landau equations thus obtained yield nontrivial solutions of the original dynamical system, valid near the linear instability. Examples of such solutions are plane waves, defects such as dislocations or spirals, and states of temporal or spatiotemporal (extensive) chaos

Orientational transition in nematic liquid crystals under oscillatory Poiseuille flow

We investigate the orientational behaviour of a homeotropically aligned nematic liquid crystal subjected to an oscillatory plane Poiseuille flow produced by an alternating pressure gradient. For small pressure amplitudes the director oscillates within the flow plane around the initial homeotropic position, whereas for higher amplitudes a spatially homogeneous transition to out-of-plane director motion was observed for the first time. The orientational transition was found to be supercritical and the measured frequency dependence of the critical pressure amplitude in the range between 2 and 20 Hz was in quantitative agreement with a recent theory.Comment: 11 pages, 4 figures, submitted to Europhys. Let