Using the model of fast phase transitions and previously reported equation of the Gibbs–Thomson-type, we develop an equation for the anisotropic interface motion of the Herring–Gibbs–Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship ‘velocity—Gibbs free energy’, Klein–Gordon and Born–Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained by Jeffrey J. Hoyt et al. and published in Acta Mater.47 (1999) 3181) confirms the validity of the derived hodograph equation as applicable to the slow and fast modes of interface propagation.

This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

使用快速相变模型和先前报道的 Gibbs-Thomson 型方程，我们开发了 Herring-Gibbs-Thomson 型各向异性界面运动的方程。导出的方程采用全线方程的形式，在其特定情况下，通过平均界面曲率、关系“速度-吉布斯自由能”、克莱因-戈登和博恩-因菲尔德方程与各种界面的各向异性传播有关的关系来描述运动。本模型预测与镍晶体生长的分子动力学模拟数据的比较（由 Jeffrey J. Hoyt等人获得并发表在Acta Mater. 47(1999) 3181) 证实了导出的全息图方程适用于界面传播的慢速和快速模式的有效性。

本文是主题问题“复杂系统中的传输现象（第 1 部分）”的一部分。