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Defects in positional and orientational order on surfaces and their potential influence on shape

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GFSW01 - Form and deformation in solid and fluid mechanics

Co-authors: Sebastian Reuther (TU Dresden), Sebastian Aland (HTW Dresden), Ingo Nitschke (TU Dresden), Simon Praetorius (TU Dresden), Michael Nestler (TU Dresden)

We consider continuum models for positional and orientational order on curved surfaces. They include surface phase field crystal models in the first case [4,6] and surface Navier-Stokes [2,3,5], surface Frank-Oseen [1] and surface Landau-deGenne models for the second case. We demonstrate the emergence of topological defects in these models and show the strong interplay between topology, geometry, dynamics and defect type and position. We comment on the derivation of these models and their numerical solution. To couple these surface models with an evolution equation for the shape of the surface is work in progress and leads to defect mediated morphologies [6].

[1] M. Nestler, I. Nitschke, S. Praetorius, A. Voigt: Orientational order on surfaces – the coupling of topology, geometry and dynamics. Journal of Nonlinear Science DOI :10.1007/s00332-017-9405-2 [2] I. Nitschke, S. Reuther, A. Voigt: Discrete exterior calculus (DEC) for the surface Navier-Stokes equation. In Transport Processes at Fluidic Interfaces. Birkhäuser, Eds. D. Bothe, A.Reusken, (2017), 177 – 197 [3] S. Reuther, A. Voigt: The interplay of curvature and vortices in flow on curved surfaces. Multiscale Model. Simul., 13 (2), (2015), 632-643 [4] V. Schmid, A. Voigt: Crystalline order and topological charges on capillary bridges. Soft Matter, 10 (26), (2014), 4694-4699 [5] I. Nitschke, A. Voigt, J. Wensch: A finite element approach to incomressible two-phase flow on manifolds. J. Fluid Mech., 708 (2012), 418-438 [6] S. Aland, A. Rätz, M. Röger, A. Voigt: Buckling instability of viral capsides – a continuum approach. Multiscale Model. Simul., 10 (2012), 82-110

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