{"id":{"repo_id":"gmu","oai_identifier":"oai:MARS:1920/6335"},"canonical_url":"https://search.dev.ndltd.org/etd/gmu/oai:MARS:1920/6335","repository":{"repo_id":"gmu","name":"George Mason University","base_url":"https://mars.gmu.edu/server/oai/request"},"display":{"title":"Long Term Dynamics of the Di-Block Copolymer Model on Higher Dimensional Domains","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","abstract_html":"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","abstract_has_math":false,"creators":["Atkins, Michael R."],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-24","date_published":"2011-05-24","updated_at":"2026-07-27T19:51:48Z","subjects":["Differential equations","Cahn-Hilliard","Non-local","Copolymer"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:1920/6335"],"render_values":[{"text":"hdl:1920/6335","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2011-05-24"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Differential equations","Cahn-Hilliard","Non-local","Copolymer"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:1920/6335"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["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"]},{"key":"dc:title","label":"Title","values":["Long Term Dynamics of the Di-Block Copolymer Model on Higher Dimensional Domains"]}]}],"canonical_facts":{"dc:date.issued":["2011-05-24"],"dc:description.other":["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":["hdl:1920/6335"],"dc:subject":["Differential equations","Cahn-Hilliard","Non-local","Copolymer"],"dc:title":["Long Term Dynamics of the Di-Block Copolymer Model on Higher Dimensional Domains"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T19:51:48Z"}