Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
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Langmuir-Blodgett 传递模型的分叉结构的出现
DOI：
10.1088/0951-7715/27/11/2711
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发表时间：
2014
期刊：
影响因子：
1.7
通讯作者：
U. Thiele
中科院分区：
文献类型：
--
作者：
M. H. Köpf;U. Thiele
我们探讨的分叉结构的修改后的Cahn-Hilliard方程，描述了一个系统，可能会发生一阶相变，并保持永久的平衡，由横向驱动。这形成了一个简单的模型，例如，用于通过Langmuir-Blodgett转移沉积不同相的表面活性剂分子的条纹图案。采用连续化技术，以无量纲转移速度为主要控制参数，对分岔结构进行了数值研究。研究发现，稳定前沿态的蛇形结构与大量时间周期解的分支交织在一起，这些分支来自于Hopf分岔或倍周期分岔，并以全局分岔（狙击分岔和同宿分岔）结束。总体而言，分叉图具有竖琴般的外观。这是补充的两个参数的研究，在无量纲的传输速度和域的大小（作为一种措施的距离的相变阈值），阐明通过局部和全局余维2分叉的整个竖琴状结构出现。
We explore the bifurcation structure of a modified Cahn–Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir–Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.
影响因子：
4.6
作者：
M. Pailha;A. Hazel;P. Glendinning;A. Juel
通讯作者：
M. Pailha;A. Hazel;P. Glendinning;A. Juel
影响因子：
1.2
作者：
D. Tseluiko;J. Baxter;U. Thiele
通讯作者：
D. Tseluiko;J. Baxter;U. Thiele