Nematic liquid crystals on curved surfaces: a thin film limit
2018 ◽
Vol 474
(2214)
◽
pp. 20170686
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Keyword(s):
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.
1999 ◽
Vol 232
(1)
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pp. 20-33
Keyword(s):
2012 ◽
Vol 17
(1)
◽
pp. 35-44
2000 ◽
Vol 413
◽
pp. 355-378
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1961 ◽
2018 ◽
Vol 28
(7)
◽
pp. 1596-1612
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Keyword(s):
2007 ◽
Vol 10
(7)
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pp. 657-676
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2011 ◽
Vol 31
(3)
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pp. 753-756
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2010 ◽
Vol 12
(2)
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pp. 125-131