An advanced numerical method to describe order dynamics in nematics

An Advanced Numerical Method to Describe OrderDynamics in NematicsA. Amoddeoa, G. Lombardob, R. Barberiba Mechanics and Materials Department, University “Mediterranea” of Reggio Calabria,Via Graziella 1, Feo di Vito, 89122 Reggio Calabria, Italyb CNR-INFM LiCryL – Liquid Crystal Lab., Physics Department, University of Calabria,Via P. Bucci, Cubo 32/c, 87036 Arcavacata di Rende (CS), ItalyAbstract. Nematic liquid crystals are aggregates of calamitic molecules and most related experimental phenomena arewell described by their mean molecular orientation, i.e. by the director and by the scalar order parameter[1], considering aperfect uniaxial symmetry. However, there exist situations in which experimental results cannot be fully described by thisclassic elastic approach. When the nematic distortion is very strong and it occurs over a length scale comparable with thenematic coherence length, the molecular order may be significantly altered, as in the case of the core of a defect [2].Moreover the standard simplified elastic theory fails also for recent experimental results on phase transitions induced bynano-confinement [3] and for the electric field induced order reconstruction [4,5]. Such systems, where spatial andtemporal changes of the nematic order are relevant and biaxial transient nematic configurations arise, require a fullLandau-de Gennes Q-tensor description [4,6,7]. In this work, we will present the implementation of a Q-tensor numericalmodel, based on a one-dimensional finite element method with a r-type moving mesh technique capable to describe thedynamical electric biaxial transition between two uniaxial different topological states inside a p-cell. The use of themoving grid technique ensures no waste of computational effort in area of low spatial order variability: in fact, thetechnique concentrates the grid points in regions of largeÑQmaintaining constant the total number of the nodes in thedomain.REFERENCES1. C.W. Oseen, Trans. Faraday Soc. 29, 883 (1933).2. N. Schopohl and T.J. Sluckin, Phys. Rev. Lett. 59, 2582 (1987).3. G. Carbone, G. Lombardo, R. Barberi, I. Musevic, U. Tkalec, Phys. Rev. Lett.103, 167801 (2009).4. R. Barberi, F. Ciuchi, G. Durand, M. Iovane, D. Sikharulidze, A. Sonnet and E. Virga, Eur. Phys. J. E 13, 61 (2004).5. R. Barberi, F. Ciuchi, G. Lombardo, R. Bartolino, and G. E. Durand, Phys. Rev. Lett. 93,137801 (2004).6. P. de Gennes, Phys. Lett. 30A, 454 (1969).7. G. Lombardo, H. Ayeb, R. Barberi, Phys. Rev. E 77, 05178 (2008).