Physical analysis of phase transformation of materials consisting from several (both substitutional and interstitial) components, coming from the Onsager extremal thermodynamic principle, leads, from the mathematical point of view, to a system of partial differential equations of evolution type, including certain integral term, with substantial differences in particular phases ($\alpha$, $\gamma$) and in moving interface of finite thickness ($\beta$), in whose center the ideal liquid material behaviour can be detected. The numerical simulation of this process in MATLAB is able to explain some phenomena (e.g. the interface velocity as a function of temperature) better than known simplified models assuming the sharp interface and additional boundary and transfer conditions.

EUDML-ID : urn:eudml:doc:271311
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@article{702875,
     title = {Modelling of multicomponent diffusive phase transformation in solids},
     booktitle = {Programs and Algorithms of Numerical Mathematics},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2008},
     pages = {207-219},
     zbl = {1202.82032},
     url = {http://dml.mathdoc.fr/item/702875}
}

Vala, Jiří. Modelling of multicomponent diffusive phase transformation in solids, dans Programs and Algorithms of Numerical Mathematics, GDML_Books,  (2008), pp. 207-219. http://gdmltest.u-ga.fr/item/702875/