Calculus of Variations and Geometric Measure Theory

S. Alama - L. Bronsard - I. Topaloglu

Sharp interface limit of an energy modelling nanoparticle-polymer blends

created by topaloglu1 on 03 Aug 2019



Inserted: 3 aug 2019

Year: 2015

ArXiv: 1508.01206 PDF


We identify the $\Gamma$-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the phase transition thickness of the polymer phases approach zero. The limiting energy consists of two terms: the perimeter of the interface separating the phases and a penalization term related to the density distribution of the infinitely many small nanoparticles. We prove that local minimizers of the limiting energy admit regular phase boundaries and derive necessary conditions of local minimality via the first variation. Finally we discuss possible critical and minimizing patterns in two dimensions and how these patterns vary from global minimizers of the purely local isoperimetric problem.