A Variational Approach to Crystalline Triple-Junction Motion
A Variational Approach to Crystalline Triple-Junction Motion
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晶体三结运动的变分方法
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
Jean E. Taylor
中科院分区：
文献类型：
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作者：
Jean E. Taylor
对于法向速度 v=M(C+κΦ) 的运动，给出了具有三结点的曲线的变分描述，其中 κΦ 代表晶体曲率，由曲线和每个界面的晶体（多边形武尔夫形状）表面自由能函数 Φ 确定，C 在每个界面上是常数，M 是每个界面的兼容法线相关迁移率函数。该变分公式基于这样的思想：对于表面自由能和体积自由能之和，运动应该是 L2 内积中的梯度流。如果表面自由能函数 Φ 完全为零，则运动为 Taylor (1995) 给出的运动。如果表面自由能函数为正且结晶，则运动是由 Taylor (1993) 给出的。最后，如果表面自由能函数写为 Φ=εΦ0，则 ε↓0 的极限运动通常不同于 ε=0 的运动 [因此与 Taylor (1993) 给出的不同；极限运动大概是由 Reitich 和 Mete Soner (1996) 给出的。
A variational description is given for curves with triple junctions for the motion with normal velocity v=M(C+κΦ), where κΦ stands for the crystalline curvature as determined by the curves and by the crystalline (polygonal Wulff shape) surface free energy functions Φ for each interface, C is constant on each interface, and M is a compatible normal-dependent mobility function for each interface. This variational formulation is based on the idea that the motion should be gradient flow, in the L2 inner product, for the sum of the surface free energy and the bulk free energy. If the surface free energy functions Φ are identically zero, the motion is that given by Taylor (1995). If the surface free energy functions are positive and crystalline, then the motion is that given by Taylor (1993). Finally, if the surface free energy functions are written as Φ=εΦ0, then the limiting motion as ε↓0 is in general different from the motion for ε=0 [and hence different from that given by Taylor (1993); the limiting motion is presumably that given by Reitich and Mete Soner (1996)].