Hamiltonian structure of passive defect dynamics in two-dimensional nematic liquid crystals in unbounded domains
File(s)
Published version
Author(s)
Miyoshi, Hiroyuki
Crowdy, Darren
Type
Journal Article
Abstract
Hamiltonian structures for the passive dynamics
of topological defects in nematic liquid crystals in
two-dimensional systems are presented. Following
the work by Miyoshi et al. (Miyoshi et al.,
2024, Proc. R. Soc. A 480, 20240405), which
demonstrated that the regularized Frank free energy
associated with topological defects is equivalent to
the Kirchhoff–Routh path function, the harmonic
conjugate of the regularized Frank energy is
investigated to elucidate the defect dynamics. Since
defect motion is driven by the gradient of the
Frank energy, the application of the Cauchy-Riemann
equations shows that the harmonic conjugate of the
regularized Frank energy serves as a Hamiltonian
governing the defect dynamics. This Hamiltonian is
expressed as a weighted sum of arguments between
defect positions. Several conserved quantities, as
well as the conditions for self-similar defect
dynamics, are identified based on this Hamiltonian.
The Hamiltonian structure is also applicable for
estimating defect motion and defect–defect collisions
within a limited field of view of the alignment angles.
of topological defects in nematic liquid crystals in
two-dimensional systems are presented. Following
the work by Miyoshi et al. (Miyoshi et al.,
2024, Proc. R. Soc. A 480, 20240405), which
demonstrated that the regularized Frank free energy
associated with topological defects is equivalent to
the Kirchhoff–Routh path function, the harmonic
conjugate of the regularized Frank energy is
investigated to elucidate the defect dynamics. Since
defect motion is driven by the gradient of the
Frank energy, the application of the Cauchy-Riemann
equations shows that the harmonic conjugate of the
regularized Frank energy serves as a Hamiltonian
governing the defect dynamics. This Hamiltonian is
expressed as a weighted sum of arguments between
defect positions. Several conserved quantities, as
well as the conditions for self-similar defect
dynamics, are identified based on this Hamiltonian.
The Hamiltonian structure is also applicable for
estimating defect motion and defect–defect collisions
within a limited field of view of the alignment angles.
Date Issued
2026-09-01
Date Acceptance
2026-07-08
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2026, 482 (2346)
ISSN
1364-5021
Publisher
The Royal Society
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
482
Issue
2346
Copyright Statement
© 2026 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
License URL
Publication Status
Published
Article Number
20260331
Date Publish Online
2026-09-16