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Robust Numerical Resolution of Nakamura Crystallization Kinetics

Received: 1 December 2016     Accepted: 16 December 2016     Published: 23 October 2017
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Abstract

The numerical prediction of crystallization transformation is of great interest in several applications. One such application is the polymer-forming process. In this short communication, the integration of the widely used Nakamura kinetics is discussed. A robust time integration method is proposed. In order to overcome its singularities, the Nakamura function is thresholded. A convergence analysis provides guidelines for the threshold values and time discretization.

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 4)
DOI 10.11648/j.ijtam.20170304.13
Page(s) 143-147
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Crystallization Kinetics, Nakamura, Time Integration, Robust, Phase Change

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  • APA Style

    Arthur Levy. (2017). Robust Numerical Resolution of Nakamura Crystallization Kinetics. International Journal of Theoretical and Applied Mathematics, 3(4), 143-147. https://doi.org/10.11648/j.ijtam.20170304.13

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    ACS Style

    Arthur Levy. Robust Numerical Resolution of Nakamura Crystallization Kinetics. Int. J. Theor. Appl. Math. 2017, 3(4), 143-147. doi: 10.11648/j.ijtam.20170304.13

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    AMA Style

    Arthur Levy. Robust Numerical Resolution of Nakamura Crystallization Kinetics. Int J Theor Appl Math. 2017;3(4):143-147. doi: 10.11648/j.ijtam.20170304.13

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  • @article{10.11648/j.ijtam.20170304.13,
      author = {Arthur Levy},
      title = {Robust Numerical Resolution of Nakamura Crystallization Kinetics},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {3},
      number = {4},
      pages = {143-147},
      doi = {10.11648/j.ijtam.20170304.13},
      url = {https://doi.org/10.11648/j.ijtam.20170304.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170304.13},
      abstract = {The numerical prediction of crystallization transformation is of great interest in several applications. One such application is the polymer-forming process. In this short communication, the integration of the widely used Nakamura kinetics is discussed. A robust time integration method is proposed. In order to overcome its singularities, the Nakamura function is thresholded. A convergence analysis provides guidelines for the threshold values and time discretization.},
     year = {2017}
    }
    

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    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
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    UR  - https://doi.org/10.11648/j.ijtam.20170304.13
    AB  - The numerical prediction of crystallization transformation is of great interest in several applications. One such application is the polymer-forming process. In this short communication, the integration of the widely used Nakamura kinetics is discussed. A robust time integration method is proposed. In order to overcome its singularities, the Nakamura function is thresholded. A convergence analysis provides guidelines for the threshold values and time discretization.
    VL  - 3
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Author Information
  • Laboratoire de Thermique et Energie de Nantes, Université de Nantes, Nantes, France

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