Evolution of pattern complexity in the Cahn-Hilliard theory of phase separation
- School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332 (United States)
- Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332 (United States)
- Department of Mathematical Sciences, George Mason University, 4400 University Drive, MS 3F2, Fairfax, VA 22030 (United States)
Phase separation processes in compound materials can produce intriguing and complicated patterns. Yet, characterizing the geometry of these patterns quantitatively can be quite challenging. In this paper we propose the use of computational algebraic topology to obtain such a characterization. Our method is illustrated for the complex microstructures observed during spinodal decomposition and early coarsening in both the deterministic Cahn-Hilliard theory, as well as in the stochastic Cahn-Hilliard-Cook model. While both models produce microstructures that are qualitatively similar to the ones observed experimentally, our topological characterization points to significant differences. One particular aspect of our method is its ability to quantify boundary effects in finite size systems.
- OSTI ID:
- 20637140
- Journal Information:
- Acta Materialia, Vol. 53, Issue 3; Other Information: DOI: 10.1016/j.actamat.2004.10.022; PII: S1359-6454(04)00631-7; Copyright (c) 2004 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 1359-6454
- Country of Publication:
- United States
- Language:
- English
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