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Updated: Jun 14, 2026
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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
Published on: May 15, 2017
Transition between Kelvin's equilibria
Hamid Ait Abderrahamne1, Kamran Siddiqui, Georgios H Vatistas
1Department of Mechanical and Industrial Engineering, Concordia University Montreal, 1455 de Maisonneuve Boulevard West, Quebec, Canada.
Summary
This study reveals Kelvin
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Mathematical physics
Background:
- Kelvin's equilibrium states describe stable configurations of vortices.
- Understanding transitions between these states is crucial for fluid dynamics.
- Previous models did not fully capture the dynamics of pattern transitions.
Purpose of the Study:
- To investigate the transition mechanism between Kelvin's equilibrium states.
- To model the observed pattern transitions using nonlinear theory.
- To hypothesize a universal route for transitions between equilibria.
Main Methods:
- Application of nonlinear theory to analyze vortex core patterns.
- Modeling the transition using a one-dimensional circle map.
- Analysis of frequency locking and quasiperiodicity.
Main Results:
- The transition from mode N=2 to N=4 occurs in two distinct steps: quasiperiodicity and frequency locking.
- The transition process is accurately modeled by a one-dimensional circle map.
- Frequency locking ratios follow a Farey sum and staircase pattern.
Conclusions:
- The transition between Kelvin's equilibria follows a route involving quasiperiodicity and frequency locking.
- The observed staircase function represents rational frequency ratios of (N-1)/N.
- This provides a framework for understanding complex transitions in fluid systems.
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