The Experiment
The Project
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 spacetime characteristics of liquid crystal electroconvection were very popular. Following the theoretical studies on the control of chaos carried out at the Centre de Physique Théorique in Marseille [1], L. Fronzoni of the University of Pisa has shown the possibility of using these methods of control in a simple experimental situation [2]. 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 "spacetime intermittency"), have also been observed in a fluid mechanics experiment done at the Institut de Recherche sur les Phénomènes Hors Équilibre in Marseille [6]. In this case, the authors studied the instabilities of the flow of water between a rotating and a fixed disk, see also [7].
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.
References

R. Lima, M. Pettini, Suppression of Chaos by Resonant Parametric Perturbations, Phys. Rev. Lett., 1990.

L. Fronzoni, M. Giocondo, M. Pettini, Experimental evidence of suppression of chaos by resonant parametric perturbation, Phys. Rev. A 43, 64836487, 1991.

L. Fronzoni, Suppression of chaos in an experiment on liquid crystals, in The Sciences of Complexity, Madeira Symposium, 1998.

L. Fronzoni, G. Giocondo, Controlling Chaos with Parametric Perturbations, Int. J. Bif. Chaos, 1998, vol. 8, p. 1693.

L. Fronzoni, Hydrodynamics of Liquid Crystals, in Physics of Liquid Crystalline Materials, edited by I.C. Khoo and F. Simoni. Chapter XII, pp. 279299, Gordon and Breach Science Publishers, Philadelphia 1991.

L. Schouveiler, P. Le Gal, M.P. Chauve, Stability of a Spiral Rol System in a Rotating Disk Experiment, Phys. of Fluids, 1999, vol 10, 2567.

E. Floriani, T. Dudok de Wit, P. Le Gal, Nonlinear Interactions in a Rotating Disk Flow: from a Volterra Model to the GinzburgLandau Equation, to be published in Chaos, 2000.

A.E. White, P.E. Cladis, S.Torza, Study of Liquid Crystals in Flow, Mol. Cryst. Liq. Cryst., 1977, vol. 43, pp. 1331.

K. Skarp, T. Carlsson, S.T. Lagerwall, B. Stebler, Flow Properties of Nematics 8 CB: an example of Diverging and Vanishing alpha3, Mol. Cryst. Liq. Cryst., 1981, vol 66, pp 199208.

J. Wahl, F. Fisher, Elastic and Viscosity Constants of Nematic Liquid Crystals from a new Optical Method, Mol. Cryst. Liq. Cryst., 1973, vol 22, pp. 359373.

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. 7582.
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