Nematic liquid crystals on curved surfaces: a thin film limit. (20th June 2018)

• Record Type: Journal Article
• Authors: Nitschke, Ingo; Nestler, Michael; Praetorius, Simon; Löwen, Hartmut; Voigt, Axel
• Is Part Of: Proceedings. Volume 474:Number 2214(2018)
• Publication Date: 2018-06-20
• Subjects: nematic liquid crystals -- thin film limit -- surface equation; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2017.0686
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : 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. The 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 L 2 -gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.