{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/83901"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/83901","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Modeling Collective Behavior of Dislocations in Crystalline Materials","abstract":"A part of this work deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. It is shown that the evolution equation simplifies to the Hamilton-Jacobi equations governing geometric optics and level set methods in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.","abstract_html":"A part of this work deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. It is shown that the evolution equation simplifies to the Hamilton-Jacobi equations governing geometric optics and level set methods in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.","abstract_has_math":false,"creators":["Varadhan, Satya N."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Beaudoin, Armand J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T21:12:39Z","date_published":"2015-09-25T21:12:39Z","updated_at":"2026-07-22T22:26:22Z","subjects":["Engineering, Materials Science"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3301241"],"render_values":[{"text":"(MiAaPQ)AAI3301241","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/83901","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Beaudoin, Armand J."]},{"key":"dc:creator","label":"Author","values":["Varadhan, Satya N."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T21:12:39Z","10000-01-01","2007"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Materials Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/83901","(MiAaPQ)AAI3301241"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A part of this work deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. It is shown that the evolution equation simplifies to the Hamilton-Jacobi equations governing geometric optics and level set methods in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.","Made available in DSpace on 2015-09-25T21:12:39Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3301241.pdf: 2480070 bytes, checksum: 937abb3aea1c6660f2a3a7494fd8a3cb (MD5) Previous issue date: 2007","Embargo set by: Seth Robbins for item 85182 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","89 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007."]},{"key":"dc:title","label":"Title","values":["Modeling Collective Behavior of Dislocations in Crystalline Materials"]}]}],"canonical_facts":{"dc:contributor":["Beaudoin, Armand J."],"dc:creator":["Varadhan, Satya N."],"dc:date":["2015-09-25T21:12:39Z","10000-01-01","2007"],"dc:description":["A part of this work deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. It is shown that the evolution equation simplifies to the Hamilton-Jacobi equations governing geometric optics and level set methods in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.","Made available in DSpace on 2015-09-25T21:12:39Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3301241.pdf: 2480070 bytes, checksum: 937abb3aea1c6660f2a3a7494fd8a3cb (MD5) Previous issue date: 2007","Embargo set by: Seth Robbins for item 85182 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","89 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007."],"dc:identifier":["http://hdl.handle.net/2142/83901","(MiAaPQ)AAI3301241"],"dc:language":["eng"],"dc:subject":["Engineering, Materials Science"],"dc:title":["Modeling Collective Behavior of Dislocations in Crystalline Materials"],"dc:type":["text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:22Z"}