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

Köpf MH, Thiele U

Forschungsartikel (Zeitschrift) | Peer reviewed

Zusammenfassung

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.

Details zur Publikation

FachzeitschriftNonlinearity
Jahrgang / Bandnr. / Volume27
Seitenbereich2711-2734
StatusVeröffentlicht
Veröffentlichungsjahr2014
Sprache, in der die Publikation verfasst istEnglisch
DOI10.1088/0951-7715/27/11/2711

Autor*innen der Universität Münster

Thiele, Uwe
Professur für Theoretische Physik (Prof. Thiele)
Center for Nonlinear Science (CeNoS)
Center for Multiscale Theory and Computation (CMTC)