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Patterns formation in ferrofluids and solid dissolutions using stochastic models with dissipative dynamics

Author

Listed:
  • Marco A. Morales

    (Facultad de Ingeniería Química, Benemérita Universidad Autónoma de Puebla)

  • Irving Fernández-Cervantes

    (Facultad de Ingeniería Química, Benemérita Universidad Autónoma de Puebla)

  • Ricardo Agustín-Serrano

    (Centro Universitario de Vinculación, Benemérita Universidad Autónoma de Puebla)

  • Andrés Anzo

    (Instituto de Física, Universidad Autónoma de San Luis Potosi, Manuel Nava 6 Zona Universitaria)

  • Mercedes P. Sampedro

    (Facultad de Ingeniería Química, Benemérita Universidad Autónoma de Puebla)

Abstract

A functional with interactions short-range and long-range low coarse-grained approximation is proposed. This functional satisfies models with dissipative dynamics A, B and the stochastic Swift-Hohenberg equation. Furthermore, terms associated with multiplicative noise source are added in these models. These models are solved numerically using the method known as fast Fourier transform. Results of the spatio-temporal dynamic show similarity with respect to patterns behaviour in ferrofluids phases subject to external fields (magnetic, electric and temperature), as well as with the nucleation and growth phenomena present in some solid dissolutions. As a result of the multiplicative noise effect over the dynamic, some microstructures formed by changing solid phase and composed by binary alloys of Pb-Sn, Fe-C and Cu-Ni, as well as a NiAl-Cr(Mo) eutectic composite material. The model A for active-particles with a non-potential term in form of quadratic gradient explain the formation of nanostructured particles of silver phosphate. With these models is shown that the underlying mechanisms in the patterns formation in all these systems depends of: (a) dissipative dynamics; (b) the short-range and long-range interactions and (c) the appropiate combination of quadratic and multiplicative noise terms.

Suggested Citation

  • Marco A. Morales & Irving Fernández-Cervantes & Ricardo Agustín-Serrano & Andrés Anzo & Mercedes P. Sampedro, 2016. "Patterns formation in ferrofluids and solid dissolutions using stochastic models with dissipative dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(8), pages 1-17, August.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:8:d:10.1140_epjb_e2016-70344-7
    DOI: 10.1140/epjb/e2016-70344-7
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    Cited by:

    1. Bashkirtseva, Irina & Kolinichenko, Alexander & Ryashko, Lev, 2021. "Stochastic sensitivity of Turing patterns: methods and applications to the analysis of noise-induced transitions," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. Franco, Rebeca & Morales, Marco A. & Rodríguez-Mora, J.Isrrael & Agustín-Serrano, Ricardo, 2024. "A new reaction-diffusion-advection model with long-range inhibition for vegetation-desertification pattern-formation as a unified approach," Ecological Modelling, Elsevier, vol. 492(C).

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    Keywords

    Statistical and Nonlinear Physics;

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