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Updated: Jan 25, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
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Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system.
D Avitabile1, M Desroches2,3, E Knobloch4
1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|December 12, 2017
Summary
This study analyzes pattern formation in a nonlinear system, identifying two types of stationary fronts. Their behavior depends on boundary conditions and system instabilities, offering insights into complex spatial structures.
Area of Science:
- Nonlinear dynamics
- Pattern formation
- Mathematical physics
Background:
- Subcritical pattern-forming systems exhibit complex behaviors.
- Nonlinear advection in bounded domains presents analytical challenges.
- Understanding stationary fronts is crucial for predicting system dynamics.
Purpose of the Study:
- To analyze a subcritical pattern-forming system with nonlinear advection in a bounded domain.
- To identify and characterize different types of stationary fronts.
- To elucidate the role of boundary conditions and instabilities in front dynamics.
Main Methods:
- Recasting the system as a slow-fast system in space.
- Applying geometric singular perturbation theory.
- Utilizing numerical continuation and Monte Carlo simulations.
- Analyzing partial differential equations.
Main Results:
- Two types of stationary fronts were identified, linked to convective and absolute instabilities.
- One front type depends on upstream boundary conditions, explaining noise-sustained structures.
- The other front type corresponds to a global mode, present even with zero upstream conditions.
- Canard trajectories' role in transitions and stability of spatial structures were clarified.
Conclusions:
- Front location in the convective regime is sensitive to upstream boundary conditions.
- Statistical properties under stochastic boundary conditions can be interpreted via the deterministic slow-fast system.
- The study provides a quantitative understanding of noise-sustained structures and spatial dynamics.
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