Intrinsic Geometry and Director Reconstruction for Three-Dimensional Liquid Crystals
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In this paper, the intrinsic geometry of elastic distortions in three-dimensional nematic liquid crystals is described and necessary and sufficient conditions for a set of functions to represent these distortions by describing how they couple to the curvature tensor.Abstract:
We give a description of the intrinsic geometry of elastic distortions in three-dimensional nematic liquid crystals and establish necessary and sufficient conditions for a set of functions to represent these distortions by describing how they couple to the curvature tensor. We demonstrate that, in contrast to the situation in two dimensions, the first-order gradients of the director alone are not sufficient for full reconstruction of the director field from its intrinsic geometry: it is necessary to provide additional information about the second-order director gradients. We describe several different methods by which the director field may be reconstructed from its intrinsic geometry. Finally, we discuss the coupling between individual distortions and curvature from the perspective of Lie algebras and groups and describe homogeneous spaces on which pure modes of distortion can be realised.read more
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Journal ArticleDOI
Orientation-Dependent Handedness and Chiral Design
Efi Efrati,William T. M. Irvine +1 more
TL;DR: The authors showed that quantifying handedness as direction-dependent properties actually makes fundamental physical sense and can guide both our understanding of known handedness phenomena and design of materials with novel handed-response properties.
Journal ArticleDOI
Three-dimensional active defect loops
TL;DR: A correlation between local curvature and the local orientational profile of the defect loop is demonstrated, indicating dynamic coupling between geometry and topology.
Journal ArticleDOI
Geometric frustration and compatibility conditions for two-dimensional director fields
Idan Niv,Efi Efrati +1 more
TL;DR: In this article, the necessary and sufficient conditions for two scalar functions, s and b, to describe the splay and bend of a director field in the plane were established for geometries with non-vanishing constant Gaussian curvature.
Journal ArticleDOI
The Geometry of the Cholesteric Phase
Daniel A. Beller,Thomas Machon,Simon Čopar,Daniel M. Sussman,Gareth P. Alexander,Randall D. Kamien,Ricardo A. Mosna +6 more
TL;DR: In this article, a cholesteric pitch axis for an arbitrary nematic director field is constructed as an eigenvalue problem, which leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director and the mutually perpendicular direction.
Journal ArticleDOI
Geometry of the cholesteric phase
Daniel A. Beller,Thomas Machon,Simon Čopar,Simon Čopar,Simon Čopar,Daniel M. Sussman,Gareth P. Alexander,Randall D. Kamien,Ricardo A. Mosna,Ricardo A. Mosna +9 more
TL;DR: In this article, a cholesteric pitch axis for an arbitrary nematic director field is constructed as an eigenvalue problem, which leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director and the mutually perpendicular direction.
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