Young Researchers Workshop: Stochastic and deterministic methods in kinetic theory

On the modeling of a ternary inhibitory system

Chong Wang

George Washington University
[SLIDES]

Skin pigmentation, animal coats and block copolymers, which can be considered as multi-constituent inhibitory systems, are all around us. Theoretical analysis and numerical simulation of a ternary inhibitory system will be provided here. An inhibitory system is studied as a nonlocal geometric variational problem. The free energy of the system is the sum of two terms: the total size of the interfaces separating the constituents, and a longer ranging interaction energy that inhibits micro-domains from unlimited growth. We establish that in different parameter ranges there are corresponding assemblies of certain patterns that exist as the stationary sets of the free energy functional. Numerically, a phase field model is proposed here to study the dynamics. To reduce the computational complexity, a reduced FFT-based fast algorithm is also discussed here.