Long Term Dynamics of the Di-Block Copolymer Model on Higher Dimensional Domains
| dc.contributor.advisor | Wanner, Thomas | |
| dc.contributor.author | Atkins, Michael R. | |
| dc.creator | Atkins, Michael R. | |
| dc.date | 2011-05-06 | |
| dc.date.accessioned | 2011-05-24T17:57:41Z | |
| dc.date.available | NO_RESTRICTION | |
| dc.date.available | 2011-05-24T17:57:41Z | |
| dc.date.issued | 2011-05-24 | |
| dc.description.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 | |
| dc.identifier.uri | https://hdl.handle.net/1920/6335 | |
| dc.language.iso | en_US | |
| dc.subject | Differential equations | |
| dc.subject | Cahn-Hilliard | |
| dc.subject | Non-local | |
| dc.subject | Copolymer | |
| dc.title | Long Term Dynamics of the Di-Block Copolymer Model on Higher Dimensional Domains | |
| dc.type | Thesis | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | George Mason University | |
| thesis.degree.level | Master's | |
| thesis.degree.name | Master's in Mathematics |