Shear Flow of Liquid Crystals
Patrice Le Gal (1), Leo Fronzoni (2), Ricardo Lima (3), Elena Floriani (3), Anne Cros (1), Patrick McGuire (4)
- Institut de Recherche sur les Phénomènes Hors Équilibre, 12 avenue Général Leclerc, 13003 Marseille, France
- Dipartimento di Fisica dell'Università di Pisa, 56100 Pisa, Italy
- Centre de Physique Théorique, CNRS Luminy Case 907, 13288 Marseille Cedex 9, France
- Zentrum für interdisziplinäre Forschung der Universität Bielefeld, Wellenberg 1, 33615 Bielefeld, Germany
Some years ago, studies relating to the space-time characteristics of liquid crystal electro-convection were very popular. Following the theoretical studies on the control of chaos carried out at the Centre de Physique Théorique in Marseille , L. Fronzoni of the University of Pisa has shown the possibility of using these methods of control in a simple experimental situation . More recently, Fronzoni has extended his method to the case of a liquid crystal convective layer [3, 4, 5].
In particular, the spatial extension of the turbulent regions within the laminar flow is determined by a careful control of the parameters of the experiment. These situations, where we can see a coexsistence of turbulent and laminar domains (nowadays denoted by "space-time intermittency"), have also been observed in a fluid mechanics experiment done at the Institut de Recherche sur les Phénomènes Hors Équilibre in Marseille . In this case, the authors studied the instabilities of the flow of water between a rotating and a fixed disk, see also .
The purpose of this project is of bringing together some of the participants for the annual program The Sciences of Complexity: From Mathematics to Technology to a Sustainable World taking place at the Zentrum für interdisziplinäre Forschung (ZiF). In this context, we plan to build a liquid crystal shear flow experiment, taking place above a rotating disk. A bibliographical study shows that some amazing patterns have been visualized in [8, 9, 10, 11], suggesting that many interesting phenomena still have to be explored in the context of the ZiF project: coherent structures dynamics, synchronization, and control of chaos. Thus, the participants involved in this part of the project have met at ZiF during the whole month of February 2001.
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L. Fronzoni, Suppression of chaos in an experiment on liquid crystals, in The Sciences of Complexity, Madeira Symposium, 1998.
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E. Floriani, T. Dudok de Wit, P. Le Gal, Nonlinear Interactions in a Rotating Disk Flow: from a Volterra Model to the Ginzburg-Landau Equation, to be published in Chaos, 2000.
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K. Skarp, T. Carsson, Influence of an Electric Field on the Flow Alligment Angle in Shear Flow of Nematic Liquid Crystals, Mol. Cryst. Liq. Cryst., 1978, vol. 49 (Letters), pp. 75-82.
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