Phase Separation Patterns from Directional Quenching
Phase Separation Patterns from Directional Quenching
复制标题
定向淬火的相分离模式
DOI：
10.1007/s00332-017-9361-x
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发表时间：
2016
影响因子：
3
通讯作者：
A. Scheel
中科院分区：
文献类型：
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作者：
Rafael Monteiro;A. Scheel
我们研究了定向淬火对平面上的简单双稳态系统（如Allen-Cahn方程和Cahn-Hilliard方程）中形成图案的影响。我们将定向淬火建模为外部触发的系统参数变化，通过触发线将系统从单稳态变为双稳态。然后，我们对双稳区形成的模式感兴趣，特别是当触发器以小速度推进并增加双稳区时。我们得到了单界面和条纹图案的存在性和不存在性结果。对于零速度，我们找到平行或垂直于触发线的条纹，并排除具有倾斜方向的条纹。单接口总是垂直于触发线。对于小的正速度，条纹图案可以垂直排列。对于所有非负速度，在Allen-Cahn中不包括其他方向。Cahn-Hilliard排除了正触发速度的单接口，而Allen-Cahn则垂直对齐。
We study the effect of directional quenching on patterns formed in simple bistable systems such as the Allen–Cahn and the Cahn–Hilliard equation on the plane. We model directional quenching as an externally triggered change in system parameters, changing the system from monostable to bistable across a trigger line. We are then interested in patterns forming in the bistable region, in particular as the trigger progresses with small speed and increases this bistable region. We find existence and nonexistence results of single interfaces and striped patterns. For zero speed, we find stripes parallel or perpendicular to the trigger line and exclude stripes with an oblique orientation. Single interfaces are always perpendicular to the trigger line. For small positive speed, striped patterns can align perpendicularly. Other orientations are excluded in Allen–Cahn for all nonnegative speeds. Single interfaces for positive trigger speeds are excluded for Cahn–Hilliard and align perpendicularly in Allen–Cahn.