A Level Set Approach Reflecting Sheet Structure with Single Auxiliary Function for Evolving Spirals on Crystal Surfaces
A Level Set Approach Reflecting Sheet Structure with Single Auxiliary Function for Evolving Spirals on Crystal Surfaces
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DOI：
10.1007/s10915-014-9877-2
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发表时间：
2012-12
影响因子：
2.5
通讯作者：
T. Ohtsuka;Y. Tsai;Y. Giga
中科院分区：
文献类型：
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作者：
T. Ohtsuka;Y. Tsai;Y. Giga
我们引入了一种新的水平集方法来模拟晶体表面的螺旋线的运动由Eikonal-Curvature流方程。我们的配方允许碰撞的几个螺旋和不同的强度（不同模量的伯格斯矢量）的螺旋位错中心。我们用一个辅助函数减去一个预先确定的多值片结构函数的水平集来表示一组螺旋线，它反映了螺旋线（螺位错中心）的强度。本文方法中所用的水平集方程与等曲率流方程相同。片结构函数的多值性质仅在准备非平凡的初始辅助函数时被调用，并且在最后步骤中在提取诸如螺旋台阶的高度的信息时被调用。我们的模拟使我们不仅能够再现所有的猜测螺旋在一个经典的文件伯顿等人。（Philos Trans R Soc Lond Ser A Math Phys Sci 243，299-358，1951），但也发现了几个新现象。
We introduce a new level set method to simulate motion of spirals in a crystal surface governed by an eikonal–curvature flow equation. Our formulation allows collision of several spirals and different strength (different modulus of Burgers vectors) of screw dislocation centers. We represent a set of spirals by a level set of a single auxiliary functionminus a pre-determined multi-valued sheet structure function, which reflects the strength of spirals (screw dislocation centers). The level set equation used in our method foris the same as that of the eikonal–curvature flow equation. The multi-valued nature of the sheet structure function is only invoked when preparing the initial auxiliary function, which is nontrivial, and in the final step when extracting information such as the height of the spiral steps. Our simulation enables us not only to reproduce all speculations on spirals in a classical paper by Burton et al.(Philos Trans R Soc Lond Ser A Math Phys Sci 243, 299–358, 1951) but also to find several new phenomena.