Long Term Dynamics of the Di-Block Copolymer Model on Higher Dimensional Domains
Date
2011-05-24
Authors
Atkins, Michael R.
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Abstract
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
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Keywords
Differential equations, Cahn-Hilliard, Non-local, Copolymer