论文标题
没有亚批判性的窃笑:晶界作为非题论缺陷
Snaking without subcriticality: grain boundaries as non-topological defects
论文作者
论文摘要
诸如幅度,波长,方向等局部变化引起的模式形成系统中的非植物缺陷,例如晶界的图案形成系统,等等。我们介绍了将这种非流动性缺陷(如将空间定位的结构处理)嵌入背景模式中,而不是将其处理在层静脉模式中的构想的想法。以二维二次立方顺式Swift-Hohenberg方程为例,我们获得了完全非线性平衡,这些平衡包含晶粒边界,这些晶界构成了封闭的曲线,这些曲线包含多个Penta-Hepta缺陷,分隔了具有不同方向的Hexagons区域。这些状态来自两个稳定的六角形模式之间的局部取向不匹配,一种状态形成了局部谷物,另一种形成了其背景,并且不需要将它们连接起来的亚临界分叉。即使没有唯一的麦克斯韦点,也可以获得跨越广泛参数的多个鲁棒隔离,从而强调了在分析缺陷的模式时保留固定的重要性,这是从幅度相 - 相描述中省略的效果。
Non-topological defects such as grain boundaries abound in pattern forming systems, arising from local variations of pattern properties such as amplitude, wavelength, orientation, etc. We introduce the idea of treating such non-topological defects as spatially localised structures that are embedded in a background pattern, instead of treating them in an amplitude-phase decomposition. Using the two-dimensional quadratic-cubic Swift--Hohenberg equation as an example we obtain fully nonlinear equilibria that contain grain boundaries which are closed curves containing multiple penta-hepta defects separating regions of hexagons with different orientations. These states arise from local orientation mismatch between two stable hexagon patterns, one of which forms the localised grain and the other its background, and do not require a subcritical bifurcation connecting them. Multiple robust isolas that span a wide range of parameters are obtained even in the absence of a unique Maxwell point, underlining the importance of retaining pinning when analysing patterns with defects, an effect omitted from the amplitude-phase description.