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

Michael H Köpf, Uwe Thiele

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

© 2014 IOP Publishing Ltd & London Mathematical Society. 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.
Original languageEnglish (US)
Pages (from-to)2711-2734
Number of pages24
JournalNonlinearity
Volume27
Issue number11
DOIs
StatePublished - Oct 7 2014
Externally publishedYes

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