Pub Date : 2017-05-25DOI: 10.1186/s41313-017-0003-3
Andrew A. Prudil, Michael J. Welland
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Pub Date : 2017-05-25DOI: 10.1186/s41313-017-0004-2
Markus Hütter, Bob Svendsen
The purpose of the current work is the formulation of models for conservative and non-conservative dynamics in solid systems with the help of the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC: e.g., Grmela and ?ttinger, Phys. Rev. E 56(6), 6620 (1997); ?ttinger and Grmela, Phys. Rev. E 56(6), 6633 (1997)). In this context, the resulting models are inherently spatially strongly non-local (i.e., functional) and non-isothermal in character. They are applicable in particular to the modeling of phase transitions as well as mass and heat transport in multiphase, multicomponent solids. In the last part of the work, the strongly non-local model formulation is reduced to weakly non-local form with the help of generalized gradient approximation of the energy and entropy functionals. On this basis, the current model formulation is shown to be consistent with and reduce to a recent non-isothermal generalization (Gladkov et al., J. Non-Equilib. Thermodyn. 41(2), 131 (2016)) of the well-known phase-field models of Cahn and Hilliard (J. Chem. Phys. 28(2), 258 (1958)) for conservative dynamics and of Allen and Cahn (Acta Metall. 27(6), 1085 (1979)) for non-conservative dynamics. Finally, the current approach is applied to derive a non-isothermal generalization of a phase-field crystal model for binary alloys (see, e.g., Elder et al., Phys. Rev. B 75(6), 064107 (2007)).
当前工作的目的是借助非平衡可逆-不可逆耦合的一般方程(通用:例如，Grmela和?ttinger, Phys)建立固体系统中保守和非保守动力学的模型。Rev. E 56(6)， 6620 (1997);?廷格和格梅拉，物理学家。Rev. E 56(6)， 6633(1997))。在这种情况下，所得到的模型在空间上具有很强的非局部(即，功能性)和非等温特征。它们特别适用于多相、多组分固体中的相变以及质量和热传递的建模。在论文的最后部分，利用能量和熵泛函的广义梯度逼近，将强非局部模型简化为弱非局部形式。在此基础上，目前的模型公式被证明与最近的非等温概化一致并简化为(Gladkov et al.， J. non- equilibrium。热动力学，41(2)，131(2016))。物理学报，28(2)，258(1958))和非保守动力学的Allen和Cahn(金属学报，27(6)，1085(1979))。最后，目前的方法被应用于推导二元合金相场晶体模型的非等温推广(例如，见Elder等人，Phys。生物工程学报(英文版)，2009(5):481 - 481。
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