各向异性非齐次系统中稳定分支模式的共存性
Coexistence of Stable Branched Patterns in Anisotropic Inhomogeneous Systems
摘要：
一类新的图案形成系统的识别和研究：各向异性系统，是空间不均匀的方向垂直于首选的。通过研究这个新的类和模型方程的通用振幅方程，我们表明，分支条纹图案出现，这对于一个给定的参数集是稳定的带内不同的波数和不同数量的分支点（缺陷）。此外，分支模式和未分支的（无缺陷条纹）共存于一个有限的参数范围内。我们提出了两个系统，这种通用的情况下，可以发现实验，弹性基板上的表面摩擦和电对流的液晶，并将它们与振幅方程的结果。
英文摘要：
A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class and a model equation, we show that branched stripe patterns emerge, which for a given parameter set are stable within a band of different wavenumbers and different numbers of branching points (defects). Moreover, the branched patterns and unbranched ones (defect-free stripes) coexist over a finite parameter range. We propose two systems where this generic scenario can be found experimentally, surface wrinkling on elastic substrates and electroconvection in nematic liquid crystals, and relate them to the findings from the amplitude equation.
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