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1 LMD - Laboratoire de Météorologie Dynamique 2 Section de Mathématiques and Bernoulli Center, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland 3 Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom

Abstract : There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to show that the micropolar theory includes the director theory. In this paper we show that this is the case by using symmetry reduction techniques and introducing a new system that is equivalent to the Ericksen-Leslie equations and may include disclination dynamics. The resulting equations of motion are verified to be completely equivalent, although one of the two different reductions offers the possibility of accounting for orientational defects. After applying these two approaches to the ordered micropolar theory of Lhuiller and Rey, all the results are eventually extended to flowing complex fluids, such as nematic liquid crystals. © 2013 Springer-Verlag Berlin Heidelberg.





Author: François Gay-Balmaz - T.S. Ratiu - C. Tronci -

Source: https://hal.archives-ouvertes.fr/



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