## Tensorial extension of the Leslie-Ericksen theory and applications

By: Alain Veron

From: FCT and CENIMAT/I3N da UNL

At: Complexo Interdisciplinar, Anfiteatro

[2008-12-17]

The nematic liquid crystals are well described by the Leslie-Ericksen theory in which the local order is characterised by a unit vector (director) defining the mean orientation of the molecules. Within the scope of this theory the defects observed in real systems are interpreted as discontinuities in the director field at a point or along a line (topological defects). However this approach fails when one wants to consider the dynamics of the defects (mathematically the theory is not defined at the discontinuities since the gradients are not defined and it is hard to get the time evolution of the position of one defect). One way to overcome this difficulty consists in employing additional degrees of freedom allowing regularising the theory at the discontinuities, which is justified by the tensorial nature of the full orientational order parameter. It is why we propose a tensorial extension of Leslie-Ericksen theory by partially re-introducing the tensorial character of the order parameter while staying as close as possible to the Leslie-Ericksen theory. The new model keeps the mathematical structure of Leslie-Ericksen theory and consequently the Leslie viscosities and the Frank elastic constants are still clearly defined while just one additional parameter is necessary. The main objective is not to describe precisely the structure of the defect core but rather to get a tool allowing investigating the effect of a distribution of defects on the texture. We will briefly indicate how the tensorial model is derived and some numerical simulations will be shown and discussed. In particular we will present one simulation for a spinning tube subjected to a magnetic field.