66 research outputs found
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
- …