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

M.A. Morales, J.F. Rojas, I. Torres and E. Rubio

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 3, 779-791

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.

Keywords: Complex Systems; Ternary mixtures; Biological pattern formation; Turing systems; Mechanochemical models; Polyelectrolytes (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:3:p:779-791

DOI: 10.1016/j.physa.2011.08.054

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