{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/14382"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/14382","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Constructing realistic Szekeres models from initial and final data","abstract":"The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Within this family, the quasispherical case is the best understood, and is interpreted as being an arrangement on non-concentric mass shells, each a density dipole. Here we present a model construction procedure for the quasispherical case using given data at initial and final times. Of the six arbitrary metric functions, the three which are common to both Szekeres and Lemaitre-Tolman models are determined by the model construction procedure of Krasinski & Hellaby. For the remaining three functions, which are unique to Szekeres models, we derive exact analytic expressions in terms of more physically intuitive quantities - density profiles and dipole orientation angles. Using MATLAB, we implement the model construction procedure and simulate the time evolution.","abstract_html":"The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Within this family, the quasispherical case is the best understood, and is interpreted as being an arrangement on non-concentric mass shells, each a density dipole. Here we present a model construction procedure for the quasispherical case using given data at initial and final times. Of the six arbitrary metric functions, the three which are common to both Szekeres and Lemaitre-Tolman models are determined by the model construction procedure of Krasinski & Hellaby. For the remaining three functions, which are unique to Szekeres models, we derive exact analytic expressions in terms of more physically intuitive quantities - density profiles and dipole orientation angles. Using MATLAB, we implement the model construction procedure and simulate the time evolution.","abstract_has_math":false,"creators":["Walters, Anthony Paul"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Hellaby, Charles"],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-22T22:22:46Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/14382","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hellaby, Charles"]},{"key":"dc:creator","label":"Author","values":["Walters, Anthony Paul"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-10-28T05:29:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-10-28T05:29:57Z"]},{"key":"dc:date.issued","label":"Date","values":["2012"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/14382"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Within this family, the quasispherical case is the best understood, and is interpreted as being an arrangement on non-concentric mass shells, each a density dipole. Here we present a model construction procedure for the quasispherical case using given data at initial and final times. Of the six arbitrary metric functions, the three which are common to both Szekeres and Lemaitre-Tolman models are determined by the model construction procedure of Krasinski & Hellaby. For the remaining three functions, which are unique to Szekeres models, we derive exact analytic expressions in terms of more physically intuitive quantities - density profiles and dipole orientation angles. Using MATLAB, we implement the model construction procedure and simulate the time evolution."]},{"key":"dc:title","label":"Title","values":["Constructing realistic Szekeres models from initial and final data"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hellaby, Charles"],"dc:creator":["Walters, Anthony Paul"],"dc:date.accessioned":["2015-10-28T05:29:57Z"],"dc:date.available":["2015-10-28T05:29:57Z"],"dc:date.issued":["2012"],"dc:description.abstract":["The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Within this family, the quasispherical case is the best understood, and is interpreted as being an arrangement on non-concentric mass shells, each a density dipole. Here we present a model construction procedure for the quasispherical case using given data at initial and final times. Of the six arbitrary metric functions, the three which are common to both Szekeres and Lemaitre-Tolman models are determined by the model construction procedure of Krasinski & Hellaby. For the remaining three functions, which are unique to Szekeres models, we derive exact analytic expressions in terms of more physically intuitive quantities - density profiles and dipole orientation angles. Using MATLAB, we implement the model construction procedure and simulate the time evolution."],"dc:identifier.uri":["http://hdl.handle.net/11427/14382"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Constructing realistic Szekeres models from initial and final data"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:46Z"}