{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/8223"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/8223","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Mathematical modeling of shock induced martensitic phase transitions","abstract":"Recently Bruno and Vaynblat introduced a new mathematical model to describe shock induced martensitic phase transitions. This model is much simpler than prior ones -- requiring, essentially, no quantities that cannot be measured directly. Nevertheless, its predictions are in very good agreement with the experimental results. In the calculations that Bruno and Vaynblat did to match their model against experiments, they simplified the dynamics - replacing rarefaction waves by \"rarefaction discontinuities\". In this thesis we implement the Bruno-Vaynblat model without any such simplifications. In the process of doing this, a new numerical method for nonlinear hyperbolic conservation laws with phase transitions is developed. Furthermore, in order to improve the quantitative agreement with experiments, several extensions of the Bruno-Vaynblat model are introduced and studied. These include the addition of dissipative effects, and the introduction of a modification to the equation of state (for the Austenite phase) near the critical transition pressure.","abstract_html":"Recently Bruno and Vaynblat introduced a new mathematical model to describe shock induced martensitic phase transitions. This model is much simpler than prior ones -- requiring, essentially, no quantities that cannot be measured directly. Nevertheless, its predictions are in very good agreement with the experimental results. In the calculations that Bruno and Vaynblat did to match their model against experiments, they simplified the dynamics - replacing rarefaction waves by "rarefaction discontinuities". In this thesis we implement the Bruno-Vaynblat model without any such simplifications. In the process of doing this, a new numerical method for nonlinear hyperbolic conservation laws with phase transitions is developed. Furthermore, in order to improve the quantitative agreement with experiments, several extensions of the Bruno-Vaynblat model are introduced and studied. These include the addition of dissipative effects, and the introduction of a modification to the equation of state (for the Austenite phase) near the critical transition pressure.","abstract_has_math":false,"creators":["Weatherwax, John Lloyd, 1973-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Rodolfo Ruben Rosales."],"committee_chairs":[],"committee_members":[],"year":2001,"date_issued":"2001","date_published":"2001","updated_at":"2026-07-22T22:22:31Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/8223","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Rodolfo Ruben Rosales."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/8223"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.","Includes bibliographical references (p. 123-129)."]},{"key":"dc:description.abstract","label":"Abstract","values":["Recently Bruno and Vaynblat introduced a new mathematical model to describe shock induced martensitic phase transitions. This model is much simpler than prior ones -- requiring, essentially, no quantities that cannot be measured directly. Nevertheless, its predictions are in very good agreement with the experimental results. In the calculations that Bruno and Vaynblat did to match their model against experiments, they simplified the dynamics - replacing rarefaction waves by \"rarefaction discontinuities\". In this thesis we implement the Bruno-Vaynblat model without any such simplifications. In the process of doing this, a new numerical method for nonlinear hyperbolic conservation laws with phase transitions is developed. Furthermore, in order to improve the quantitative agreement with experiments, several extensions of the Bruno-Vaynblat model are introduced and studied. These include the addition of dissipative effects, and the introduction of a modification to the equation of state (for the Austenite phase) near the critical transition pressure."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Mathematical modeling of shock induced martensitic phase transitions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rodolfo Ruben Rosales."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Weatherwax, John Lloyd, 1973-"],"dc:date.accessioned":["2005-08-23T18:25:25Z"],"dc:date.available":["2005-08-23T18:25:25Z"],"dc:date.issued":["2001"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.","Includes bibliographical references (p. 123-129)."],"dc:description.abstract":["Recently Bruno and Vaynblat introduced a new mathematical model to describe shock induced martensitic phase transitions. This model is much simpler than prior ones -- requiring, essentially, no quantities that cannot be measured directly. Nevertheless, its predictions are in very good agreement with the experimental results. In the calculations that Bruno and Vaynblat did to match their model against experiments, they simplified the dynamics - replacing rarefaction waves by \"rarefaction discontinuities\". In this thesis we implement the Bruno-Vaynblat model without any such simplifications. In the process of doing this, a new numerical method for nonlinear hyperbolic conservation laws with phase transitions is developed. Furthermore, in order to improve the quantitative agreement with experiments, several extensions of the Bruno-Vaynblat model are introduced and studied. These include the addition of dissipative effects, and the introduction of a modification to the equation of state (for the Austenite phase) near the critical transition pressure."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1721.1/8223"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Mathematical modeling of shock induced martensitic phase transitions"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:22:31Z"}