Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A fundamental improvement to Ericksen-Leslie kinematics

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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Additional Information

Hossein Pourmatin
Affiliation: Civil and Environmental Engineering, Carnegie Mellon University
Email: mpourmat@andrew.cmu.edu

Amit Acharya
Affiliation: Civil and Environmental Engineering, Carnegie Mellon University
Email: acharyaamit@cmu.edu

Kaushik Dayal
Affiliation: Civil and Environmental Engineering, Carnegie Mellon University
Email: kaushik@cmu.edu

DOI: https://doi.org/10.1090/S0033-569X-2015-01375-5
Received by editor(s): May 25, 2013
Published electronically: March 17, 2015
Article copyright: © Copyright 2015 Brown University

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