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Self-organized dynamics on a curved growth interface.

S Bottin-Rousseau¹, A Pocheau

¹IRPHE, CNRS UMR 6594, Universités Aix-Marseille I & II, 49 rue Joliot-Curie, B.P. 146, Technopole de Château-Gombert, F-13384 Marseille Cedex 13, France.

Physical Review Letters

|August 11, 2001

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Cell nucleation in directional solidification initially appears disordered but organizes over time. This long-time dynamics behavior is explained by a nonlinear advection-diffusion model, supported by a Lyapunov functional analysis.

Area of Science:

Materials Science
Physics of Complex Systems
Nonlinear Dynamics

Background:

Directional solidification is a key process in materials science for crystal growth.
Understanding interface dynamics is crucial for controlling material properties.
Artificially curved interfaces present unique challenges for nucleation and growth patterns.

Purpose of the Study:

To experimentally investigate the long-time dynamics of artificially curved growth interfaces.
To analyze the transition from disordered to ordered cell nucleation.
To validate a nonlinear advection-diffusion model for phase dynamics.

Main Methods:

Experimental setup for directional solidification with controlled interface curvature.
Observation and analysis of cell nucleation patterns over extended periods.

Related Experiment Videos

Numerical simulation using a nonlinear advection-diffusion model.

Derivation of a Lyapunov functional to analyze model stability.

Main Results:

Repetitive cell nucleations initially appear disordered.
Over long times, these nucleations spontaneously organize into a coherent pattern.
The observed dynamics are accurately reproduced by the nonlinear advection-diffusion model.
A Lyapunov functional was derived, supporting the existence of a periodic attractor.

Conclusions:

The long-time dynamics of curved growth interfaces exhibit self-organization.
Nonlinear advection-diffusion models can effectively capture complex phase dynamics.
The system possesses a stable periodic attractor, explaining the observed coherent organization.