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Steady states and coarsening in one-dimensional driven Allen-Cahn system
1School of Physics, IISER Thiruvananthapuram, Vithura, Kerala 695551, India.
Physical Review. E
|August 17, 2022
Summary
This study examines phase ordering dynamics in a driven Allen-Cahn system. We analyze domain size scaling and coarsening modes using derived equations of motion and numerical simulations.
Area of Science:
- Physics
- Materials Science
- Chemical Engineering
Background:
- The Allen-Cahn equation models phase transitions and ordering phenomena.
- Driven nonconserved systems exhibit complex dynamics influenced by external forces.
- Understanding coarsening dynamics is crucial for materials design and process optimization.
Purpose of the Study:
- To investigate steady states and coarsening dynamics in a one-dimensional driven nonconserved system.
- To derive and analyze equations of motion for phase boundaries in the driven Allen-Cahn system.
- To explore kink interactions and domain size scaling, and to analyze coarsening modes.
Main Methods:
- Derivation of equations of motion for phase boundaries using a nearest-neighbor interaction approach.
- Analysis of kink binary and ternary interactions to understand domain growth.
- Numerical techniques for bifurcation analysis of stationary solutions and linear stability analysis of periodic solutions.
Main Results:
- The study derives equations of motion for phase boundaries in the driven Allen-Cahn system.
- Analysis reveals insights into kink interactions and their effect on domain size scaling with time.
- Bifurcation analysis identifies various stationary solutions, and stability analysis characterizes different coarsening modes.
Conclusions:
- The driven Allen-Cahn equation provides a model for complex phase ordering dynamics.
- Phase boundary motion and kink interactions significantly influence domain coarsening.
- The identified coarsening modes offer a deeper understanding of pattern formation in driven systems.
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