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Liquid crystal distortions revealed by an octupolar tensor.
Physical Review E ( IF 2.2 ) Pub Date : 2020-01-01 , DOI: 10.1103/physreve.101.012703 Andrea Pedrini 1 , Epifanio G Virga 1
Physical Review E ( IF 2.2 ) Pub Date : 2020-01-01 , DOI: 10.1103/physreve.101.012703 Andrea Pedrini 1 , Epifanio G Virga 1
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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 nonvanishing 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) eigenvectors of A associated with the local maxima of its cubic form Φ on the unit sphere (its octupolar potential) designate the directions of distortion concentration. The octupolar potential is illustrated geometrically and its symmetries are charted in the space of distortion characteristics, so as to educate the eye to capture the dominating elastic modes. Special distortions are studied, which have everywhere either the same octupolar potential or one with the same shape but differently inflated.
中文翻译：
八极张量揭示液晶变形。
由Oseen和Frank提出的经典液晶弹性理论通过指向矢n描述了这些软材料的（定向）光轴。当n在空间上均匀时，获得基态。梯度gradientn消失的所有其他状态都将失真。本文提出了一种代数（和几何）方法，通过从n和∇na构造三阶，对称且无迹的张量A（八极张量）来描述液晶的局部畸变。与其在单位球面上的立方形式Φ的局部极大值（其八极电势）相关的A（非线性）特征向量指定畸变集中的方向。八极电势以几何方式表示，其对称性在畸变特征空间内绘制，从而教育眼睛捕捉主要的弹性模态。研究了特殊的畸变，这种畸变到处都具有相同的八极电势或具有相同形状但膨胀程度不同的畸变。
更新日期：2020-01-17
中文翻译：
八极张量揭示液晶变形。
由Oseen和Frank提出的经典液晶弹性理论通过指向矢n描述了这些软材料的（定向）光轴。当n在空间上均匀时，获得基态。梯度gradientn消失的所有其他状态都将失真。本文提出了一种代数（和几何）方法，通过从n和∇na构造三阶，对称且无迹的张量A（八极张量）来描述液晶的局部畸变。与其在单位球面上的立方形式Φ的局部极大值（其八极电势）相关的A（非线性）特征向量指定畸变集中的方向。八极电势以几何方式表示，其对称性在畸变特征空间内绘制，从而教育眼睛捕捉主要的弹性模态。研究了特殊的畸变，这种畸变到处都具有相同的八极电势或具有相同形状但膨胀程度不同的畸变。
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