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The European Physical Journal B
ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)
Abstract Volume 5 Issue 2 (1998) pp 265-281
Spatio-temporal patterns in the thermoconvection of a planar nematic layer: I. Weakly nonlinear models
E. Plaut (a), R. Ribotta
Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay Cedex, France
Received: 1st December 1997 / Revised: 25 May 1998 / Accepted: 2 June 1998
Abstract: We study theoretically the formation of convection patterns in a laterally extended planar nematic layer heated from below, in the linear and weakly nonlinear regimes. By reformulating the viscous coupling terms of the basic nematohydrodynamic equations, a simple interpretation of the flow effects on the director dynamics can be proposed. A detailed linear analysis of the problem is presented. A systematic method to investigate nonlinear mechanisms is developed, and exemplified by the study of the nonlinear saturation in rolls. The extension of the roll amplitude equation with the envelope formalism is used to characterize the dynamics of the roll modulations near threshold. Coupled envelope equations are shown to describe the structure of the point defects in zig-zags observed experimentally. Finally the bifurcation to the bimodal varicose is studied. The secondary wavevector in the bimodal appears to be selected by a rotation of the director in the horizontal plane. Quantitative predictions concerning the amplitude of this rotation are given.
PACS. 47.20.Ky Nonlinearity (including bifurcation theory) - 47.20.Bp Buoyancy-driven instability - 42.70.Dr Surface-tensio-driven instability
(a) email: plaut@theo-phy.uni-bayreuth.de
Article in PDF-Format (574 KB)
Present address: Physikalisches Institut der Universität Bayreuth, 95440 Bayreuth, Germany.
Online publication: September 16, 1998
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