Nematic liquid crystals on curved surfaces: a thin film limit

Ingo Nitschke, Michael Nestler, Simon Praetorius, Hartmut Löwen, Axel Voigt
2018 Proceedings of the Royal Society A  
We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an L2-gradient flow. The resulting tensor-valued surface partial
more » ... surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.
doi:10.1098/rspa.2017.0686 pmid:29977124 fatcat:n7bq6gz3avc7tp3lzzurw3mlda