Special Session 69: Mathematical Models and Analysis of (Partial) Differential Equations in the Applied Sciences

Stochastic homogenization of a droplet model in liquid-liquid phase transitions
Konstantinos Zemas
University of Bonn
Germany
Co-Author(s):    Adriana Garroni, Caterina Zeppieri
Abstract:
We rigorously derive, by means of $\Gamma$-convergence, a sharp-interface model for the coexistence of different liquid phases in a domain with a random distribution of droplets, in which a certain phase is prescribed. Starting from a diffuse-interface model of Modica-Mortola type, we show that under very broad assumptions on the droplet geometry (modelled probabilistically via a stationary marked point process), and at a critical scaling, a stochastic bulk term of capacitary type attributed to each other phase appears in the limit. This is joint work with Adriana Garroni (Sapienza University of Rome) and Caterina Zeppieri (Uni-Muenster)