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Simon Praetorius: „Stability and Dynamics of Liquid Crystalline Phases in the Phase-Field-Crystal Model”
TU Dresden

The Phase-Field-Crystal model for liquid crystals is solved numerically in two spatial dimensions, using a finite element discretization in space and a semi-implicit discretization in time. The model is formulated in two variables, the reduced translational density and the symmetric and traceless nematic order tensor, that encapsulates the nematic order parameter and the nematic director. This formulation has the advantage, to allow for minimization of the free energy without constraints. For different system parameters an initial configuration is relaxed up to equilibrium and compared qualitatively with the equilibrium solutions of [1]. All phases could be reproduced with our dynamic model. Also some dynamic evolutions of the order parameter fields are considered, i.e. phase transitions between plastic triangular crystals with non-vanishing nematic order parameter and columnar/smectic A phase.


  1. Cristian Vasile Achim, Raphael Wittkowski and Hartmut Löwen, Stability of liquid crystalline phases in the phase-field-crystal model, Phys. Rev. E 83, 061712, 2011