Vorschau

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Abstract

In this thesis, we derive a macroscopic limit for a sharp interface version of a modelproposed by Komura, Shimokawa and Andelman (2006) to investigate pattern formationdue to competition of chemical and mechanical forces. The problem is reformulated as anon-local isoperimetric problem, for which we identify sub- and supercritical parameterregimes in terms of the relative strength of the competing local and non-local interactions.Using the Autocorrelation Function, we find an asymptotic expansion of the energyin terms of the length scale parameter up to first order and derive the Γ–limit in thesubcritical regime, and the Γ–limit of the rescaled energy in the critical regime. Concerningthe analysis of the Autocorrelation Function, we show that regularity near the origin isinherited from the regularity of the corresponding set and present formulas for higherderivatives at the origin.