Emergence of the bifurcation structure of a Langmuir-Blodgett transfer model

Michael H. Köpf; Uwe Thiele

doi:10.1088/0951-7715/27/11/2711

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arXiv · 1405.2117

Emergence of the bifurcation structure of a Langmuir-Blodgett transfer model

Michael H. Köpf·Uwe Thiele

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Abstract

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 employing the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady fronts 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) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.

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Michael H. Köpf, Uwe Thiele. 2014-05-08. Emergence of the bifurcation structure of a Langmuir-Blodgett transfer model. https://doi.org/10.1088/0951-7715%2F27%2F11%2F2711

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