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Modeling ternary mixtures by mean-field theory of polyelectrolytes: Coupled Ginzburg–Landau and Swift–Hohenberg equations

Author

Listed:
  • Morales, M.A.
  • Rojas, J.F.
  • Torres, I.
  • Rubio, E.

Abstract

The purpose of this work is to model ternary mixtures using the theory of pattern formation and of polyelectrolytes, with mean-field approximations. The model has two local, non-conserved order parameters. In the free energy short-range and long-range nonlocal interactions between elements of the mixture are considered. The spatiotemporal dynamics of the system is described by coupling the time-dependent Ginzburg–Landau equation and the Swift–Hohenberg equation. These non-linear partial differential equations are solved with numerical methods to study the emergent spatially stable configurations. The model shows a large diversity of patterns, which permit an interpretation of the behavior of some biological systems and presents different growth lengths within its spatial structures.

Suggested Citation

  • Morales, M.A. & Rojas, J.F. & Torres, I. & Rubio, E., 2012. "Modeling ternary mixtures by mean-field theory of polyelectrolytes: Coupled Ginzburg–Landau and Swift–Hohenberg equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 779-791.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:779-791
    DOI: 10.1016/j.physa.2011.08.054
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