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Analytical and numerical simulations for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo,Cu)) based on ternary alloys

Author

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  • Lu, D.
  • Osman, M.S.
  • Khater, M.M.A.
  • Attia, R.A.M.
  • Baleanu, D.

Abstract

In this paper, we investigate the physical behavior of the basic elements that related to phase decomposition in ternary alloys of (Fe–Cr–Mo) and (Fe–Cr–Cu) according to analytical and approximate simulation. We study the dynamic of the separation phase for the ternary alloys of iron. The dynamical process of this separation has been described in a mathematical model called the Cahn–Hilliard equation. The minor element behavior in the process has been described by the Cahn–Hilliard equation. It describes the process of phase separation for two components of a binary fluid in ternary alloys of (Fe–Cr–Mo) and (Fe–Cr–Cu). We implement a modified auxiliary equation method and the cubic B-spline scheme on this mathematical model to show the dynamical process of phase separation and the concentration of one of two components in a system. We try obtaining the solitary and approximate solutions of this model to show the relation between the components in this phase. We discuss our solutions in view of a Stefan, Thomas-Windle, and Navier–Stokes models. Whereas, these models describe the motion of viscous fluid substance.

Suggested Citation

  • Lu, D. & Osman, M.S. & Khater, M.M.A. & Attia, R.A.M. & Baleanu, D., 2020. "Analytical and numerical simulations for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo,Cu)) based on ternary alloys," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315055
    DOI: 10.1016/j.physa.2019.122634
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    1. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
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    3. Xu Yi & Qi-Fan Yang & Ki Youl Yang & Kerry Vahala, 2018. "Imaging soliton dynamics in optical microcavities," Nature Communications, Nature, vol. 9(1), pages 1-8, December.
    4. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 520-531.
    5. Osman, M.S. & Wazwaz, Abdul-Majid, 2018. "An efficient algorithm to construct multi-soliton rational solutions of the (2+ 1)-dimensional KdV equation with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 282-289.
    6. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
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    2. Ali, Khalid K. & Cattani, Carlo & Gómez-Aguilar, J.F. & Baleanu, Dumitru & Osman, M.S., 2020. "Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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