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Exact results for curvature-driven coarsening in two dimensions
Jeferson J Arenzon1, Alan J Bray, Leticia F Cugliandolo
1Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil.
Physical Review Letters
|May 16, 2007
Summary
We studied domain boundary areas during scalar field coarsening. The number of enclosed areas follows a universal scaling law, confirming dynamical scaling in this physical system.
Area of Science:
- Physics
- Statistical Mechanics
- Materials Science
Background:
- Curvature-driven coarsening is a fundamental process in materials science.
- Understanding domain boundary statistics is key to predicting material properties.
- Nonconserved scalar fields exhibit complex dynamics during phase transitions.
Purpose of the Study:
- To analyze the statistical distribution of areas enclosed by domain boundaries (hulls).
- To investigate the dynamical scaling of these areas in a two-dimensional nonconserved scalar field.
- To determine the universality of the observed scaling behavior.
Main Methods:
- Simulating the coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state.
- Analyzing the distribution of hull areas over time.
- Deriving the scaling form for the number of hulls per unit area.
Main Results:
- The number of hulls per unit area, Nh(A,t), follows the scaling form 2c/(A+lambdat) for large times.
- This demonstrates the validity of dynamical scaling in the system, with c=1/(8π√3) as a universal constant.
- Domain area distributions exhibit similar scaling behavior, and identical forms are observed for critical initial states.
Conclusions:
- Dynamical scaling is a valid and universal characteristic of curvature-driven coarsening in this scalar field system.
- The statistical properties of domain boundaries provide insights into the large-time behavior of coarsening dynamics.
- The universality of the scaling constant suggests broader applicability across similar physical systems.
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