Modeling ternary mixtures by mean-field theory of polyelectrolytes: Coupled Ginzburg-Landau and Swift-Hohenberg equations |
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Authors: | M.A. Morales J.F. Rojas |
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Affiliation: | a Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 sur, Col. San manuel, C.P. 72570, Mexicob Centro Universitario de Vinculación, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y prolongación de la 24 sur, Col. San manuel, C.P. 72570, Mexicoc Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro No. 1, Tonantzintla, Puebla, Mexico |
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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. |
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Keywords: | Complex Systems Ternary mixtures Biological pattern formation Turing systems Mechanochemical models Polyelectrolytes |
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