title: Spatiotemporal complexity of electroconvection patterns in nematic liquid crystals.
abstract: We investigate a number of complex patterns driven by the electroconvection instability in a planarly aligned layer of a nematic liquid crystal. They are traced back to various secondary instabilities of the ideal roll patterns bifurcating at onset of convection, whereby the basic nematohydrodynamic equations are solved by common Galerkin expansion methods. Alternatively these equations are systematically approximated by a set of coupled amplitude equations. They describe slow modulations of the convection roll amplitudes, which are coupled to a flow field component with finite vorticity perpendicular to the layer and to a quasihomogeneous in-plane rotation of the director. It is demonstrated that the Galerkin stability diagram of the convection rolls is well reproduced by the corresponding one based on the amplitude equations. The main purpose of the paper is, however, to demonstrate that their direct numerical simulations match surprisingly well new experiments, which serves as a convincing test of our theoretical approach.
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.
authors.forename: Alexei
authors.initials: A
authors.lastname: Krekhov
authors.affiliation: Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany.
authors.forename: Bernd
authors.initials: B
authors.lastname: Dressel
authors.affiliation: Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany.
authors.forename: Werner
authors.initials: W
authors.lastname: Pesch
authors.affiliation: Institute of Molecule and Crystal Physics, Ufa Research Center, Russian Academy of Sciences, 450075 Ufa, Russia.
authors.forename: Vladimir
authors.initials: V
authors.lastname: Delev
authors.affiliation: Institute of Molecule and Crystal Physics, Ufa Research Center, Russian Academy of Sciences, 450075 Ufa, Russia.
authors.forename: Eduard
authors.initials: E
authors.lastname: Batyrshin