2020
DOI: 10.1103/physreve.101.012703
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Liquid crystal distortions revealed by an octupolar tensor

Abstract: The classical theory of liquid crystal elasticity as formulated by Oseen and Frank describes the (orientable) optic axis of these soft materials by a director n. The ground state is attained when n is uniform in space; all other states, which have a non-vanishing gradient ∇n, are distorted. This paper proposes an algebraic (and geometric) way to describe the local distortion of a liquid crystal by constructing from n and ∇n a third-rank, symmetric and traceless tensor A (the octupolar tensor). The (nonlinear) … Show more

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Cited by 16 publications
(20 citation statements)
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References 47 publications
(103 reference statements)
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“…We make a final observation about pure twist: Sadoc et al conjucture that a positive Ricci curvature along one direction is a necessary condition for a pure nonzero twist state [2]. This conjecture is correct and follows immediately from the computation of K 13 +K 23 (26), which in a pure twist case is simply equal to q 2 /2, so that the Ricci curvature along the director is always positive.…”
Section: A Curvature Of Pure Distortionsmentioning
confidence: 75%
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“…We make a final observation about pure twist: Sadoc et al conjucture that a positive Ricci curvature along one direction is a necessary condition for a pure nonzero twist state [2]. This conjecture is correct and follows immediately from the computation of K 13 +K 23 (26), which in a pure twist case is simply equal to q 2 /2, so that the Ricci curvature along the director is always positive.…”
Section: A Curvature Of Pure Distortionsmentioning
confidence: 75%
“…In this approach we still need the structure functions c 1 12 and c 2 12 . Alternatively, the formula (26) gives the projection of the director onto the vector ∇s…”
Section: Geometric Reconstruction In Three Dimensionsmentioning
confidence: 99%
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“…We record both formulae in Appendix C, for the reader's convenience; the energy of the sphere in (C2) is the one that especially interests us here. Contrasting it with (45) shows that the asymptotic behavior as α → ∞ of F t (1) and F α ( π 2 , 1) is the same. Now, since the minimizing shapes for both F t and F α converge to the sphere as α → ∞, we conclude that for sufficiently large α we cannot distinguish between the two theories.…”
Section: Comparison With Previous Workmentioning
confidence: 87%
“…Recently, an equivalent modal decomposition has been put forward for f OF[20], which has also been given a graphical representation in terms of an octupolar tensor[21].…”
mentioning
confidence: 99%