Long Term Dynamics of the Di-Block Copolymer Model on Higher Dimensional Domains

In this thesis, we examine the di-block copolymer model as proposed by Ohta and Kawasaki. We derive a nonlinear evolution equation from the Ohta-Kawasaki functional. We then nd an approximation to this equation via Galerkin's method. A semi-implicit scheme is then applied to the Galerkin system. This solver is then implemented in C with a python user interface. This implementation is then used to investigate the long term dynamics of the model in 2D and 3D. Speci cally, we arrive at a solution to the 3D case which partially reproduces the results of Teramoto and Nishiura which describe the existence of a Double Gyroid equilibrium state. In the 2D case, we nd a long term solution for many di erent parameter con gurations. In fact, our results in the 2D case call in to question the e cacy of a nonstandard numerical method introduced by Choksi et al. i

Author

• Atkins, Michael R.

• Differential equations
• Cahn-Hilliard
• Non-local
• Copolymer

Identifier

hdl:1920/6335

OAI identifier oai:identifier

oai:MARS:1920/6335