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Phenomenological model of nonequilibrium solidification


  • Martyushev, L.M.
  • Soboleva, A.S.


The maximum entropy production principle is used as a foundation for the nonequilibrium solidification theory. Based on this principle, a new simple model of dendrite solidification is proposed. The model predicts the explicit dependency of a dendrite’s rate and tip size on supercooling. The obtained results are devoid of the contradictions of the previous models and show quantitative agreement with the recent experimental data for the SCN dendrite.

Suggested Citation

  • Martyushev, L.M. & Soboleva, A.S., 2013. "Phenomenological model of nonequilibrium solidification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5757-5763.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:22:p:5757-5763 DOI: 10.1016/j.physa.2013.07.037

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    References listed on IDEAS

    1. Telesca, Luciano & Czechowski, Zbigniew, 2012. "Discriminating geoelectrical signals measured in seismic and aseismic areas by using Ito models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 809-818.
    2. Stanton, Richard, 1997. " A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    3. Czechowski, Zbigniew & Telesca, Luciano, 2011. "The construction of an Ito model for geoelectrical signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2511-2519.
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