【摘 要】
：
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 dis
【机 构】
：
Ecole Normale Superieure de Paris, France
【出 处】
：
The XXIX International Colloquium on Group-Theoretical Metho
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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 comprises the director theory.In this talk we will show that this is the case by using Lie group symmetry reduction techniques and introducing a new system that is equivalent to the Ericksen-Leslie equations and includes disclination dynamics.More precisely,we will show how these systems can be seen as Euler-Poincare equations on a semidirect product involving the diffeomorphism group and the gauge group of the theory,and how this geometric approach can be used to prove that the micropolar theory of liquid crystal comprises the well-known Ericksen-Leslie theory,by applying two symmetry reduction processes.The resulting equations of motion are verified to be completely equivalent,although one of the two 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.
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