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Updated: Jan 26, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Weakly subcritical stationary patterns: Eckhaus instability and homoclinic snaking.
Hsien-Ching Kao1, Edgar Knobloch
1Department of Physics, University of California, Berkeley, California 94720, USA. hckao@berkeley.edu
This study analyzes pattern formation using the cubic-quintic Ginzburg-Landau equation, revealing how instabilities lead to localized structures and defect states during phase transitions.
Area of Science:
- Nonlinear Dynamics
- Pattern Formation
- Mathematical Physics
Background:
- Stationary periodic patterns are crucial in many physical systems.
- Understanding transitions from subcritical to supercritical states is key.
- The cubic-quintic Ginzburg-Landau equation models complex pattern dynamics.
Purpose of the Study:
- To investigate pattern transitions in a 1D system.
- To analyze Eckhaus instability in periodic solutions.
- To characterize resulting localized and defect states.
Main Methods:
- Utilized the one-dimensional cubic-quintic Ginzburg-Landau equation.
- Determined conditions for Eckhaus instability.
- Computed spatially modulated states and their evolution.
Main Results:
- Identified conditions for Eckhaus instability of periodic solutions.
- Computed evolving spatially modulated states.
- Observed transitions to localized structures near Maxwell points and defect states.
Conclusions:
- Eckhaus instability drives the formation of complex spatial structures.
- Localized structures and defect states emerge during subcritical to supercritical transitions.
- Results provide insight into homoclinic snaking phenomena.
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