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.
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