A fundamental improvement to Ericksen-Leslie kinematics

Pourmatin, Hossein; Acharya, Amit; Dayal, Kaushik

doi:10.1090/S0033-569X-2015-01375-5

Authors: Hossein Pourmatin, Amit Acharya and Kaushik Dayal
Journal: Quart. Appl. Math. 73 (2015), 435-466
MSC (2010): Primary 76A15
DOI: https://doi.org/10.1090/S0033-569X-2015-01375-5
Published electronically: March 17, 2015
MathSciNet review: 3400752
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Abstract: We demonstrate theory and computations for finite-energy line defect solutions in an improvement of Ericksen-Leslie liquid crystal theory. Planar director fields are considered in two and three space dimensions, and we demonstrate straight as well as loop disclination solutions. The possibility of static balance of forces in the presence of a disclination and in the absence of flow and body forces is discussed. The work exploits an implicit conceptual connection between the Weingarten-Volterra characterization of possible jumps in certain potential fields and the Stokes-Helmholtz resolution of vector fields. The theoretical basis of our work is compared and contrasted with the theory of Volterra disclinations in elasticity. Physical reasoning precluding a gauge-invariant structure for the model is also presented.

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