Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics
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Contributors
Abstract
We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient flow equation of a weak surface Frank–Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré–Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.
Details
Original language | English |
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Pages (from-to) | 147-191 |
Journal | Journal of nonlinear science |
Volume | 28 |
Early online date | 24 Jul 2017 |
Publication status | Published - Feb 2018 |
Peer-reviewed | Yes |
External IDs
WOS | 000419582200006 |
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Scopus | 85025578679 |
Keywords
Research priority areas of TU Dresden
DFG Classification of Subject Areas according to Review Boards
Keywords
- polar liquid crystals, curved surfaces, nematic shell, free energy