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Control and selection of spatio-temporal patterns in dynamic self- assembly systems

Banff International Research Station for Mathematical Innovation and Discovery

Self-organization or dynamic self-assembly is a mechanism responsible for the formation of complex structures through multiple interactions among the microscopic components of the system. We are interested in the formation of regular stripe patterns during the transfer of surfactant monolayers from water surfaces onto moving solid substrates by means of a generalized Cahn-Hilliard equation. A combination of numerical simulations and continuation methods is employed to investigate stationary and time-periodic solutions of the model. Further, the influence of the spatio-temporal forcing on the patterning process is discussed. We show that the occurring locking effects enable a control mechanism via properties of the forcing and facilitate the production of patterns with a broader range of features. In two dimensions, the production of a variety of complex patterns can be achieved through the competition of intrinsic properties of the pattern forming system and the external forcing.

Mathematics; Fluid mechanics; Approximations and expansions; Fluid dynamics

video/mp4

Author affiliation: University of Münster

2019-10-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72088

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/