'Dancing' two-dimensional patterns in nematics above the flexoelectric instability threshold
Abstract
Various types of electrohydrodynamic instabilities in liquid crystals (LCs) are a recurring theme in LC research. The nonlinear stage of the flexoelectric instability in nematics remains the least studied aspect of this phenomenon. This work highlights a key advancement in nonlinear physics, providing a compelling example of nonlinear dynamical system behavior. By solving the system of nonlinear equations for a nematic in an alternating external field, we derive from first principles the unique "dancing" behavior of truly two-dimensional patterns above the flexoelectric instability threshold. Our analysis is restricted to liquid crystals with negative dielectric permittivity and electrical conductivity anisotropies. The resulting solution represents a stable limit cycle near above the Hopf bifurcation, valid within the parameters range where the solutions characteristic exponent is complex. The generalized two-dimensional Ginzburg-Landau-like phenomenological theory of the phenomenon is developed.
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BibTeX
@misc{pikina2026dancing,
title = {{'Dancing' two-dimensional patterns in nematics above the flexoelectric instability threshold}},
author = {E. S. Pikina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31849},
eprint = {2610.31849},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31849},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - 'Dancing' two-dimensional patterns in nematics above the flexoelectric instability threshold
AU - E. S. Pikina
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31849
UR - https://arxiv.org/abs/2610.31849
AB - Various types of electrohydrodynamic instabilities in liquid crystals (LCs) are a recurring theme in LC research. The nonlinear stage of the flexoelectric instability in nematics remains the least studied aspect of this phenomenon. This work highlights a key advancement in nonlinear physics, providing a compelling example of nonlinear dynamical system behavior. By solving the system of nonlinear equations for a nematic in an alternating external field, we derive from first principles the unique "dancing" behavior of truly two-dimensional patterns above the flexoelectric instability threshold. Our analysis is restricted to liquid crystals with negative dielectric permittivity and electrical conductivity anisotropies. The resulting solution represents a stable limit cycle near above the Hopf bifurcation, valid within the parameters range where the solutions characteristic exponent is complex. The generalized two-dimensional Ginzburg-Landau-like phenomenological theory of the phenomenon is developed.
ER -