{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72750"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72750","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stability analysis of the 4th order Runge Kutta method in application to colloidal particle interactions","abstract":"Colloidal particles have a wide range of industrial applications. This study is focused on the application to microstructured materials and the impact of external compressive forces on particles. Currently, in the large throughput manufacturing of microstructured materials, problems such as cracking are caused by these external forces. Numerical methods can be used to generate particle positions and obtain a better understanding of particle interactions under different conditions. The aim of this study was to obtain a better understanding of the stability limits of using the 4th order Runge Kutta method. By introducing the external forces as auxiliary functions, we were able to generate exact analytic solutions satisfying arbitrary hydrodynamic and interaction forces. This allowed rigorous comparison of the theoretical stability limits and the observed stability limits on time step. We found excellent agreement with the predicted and observed results.","abstract_html":"Colloidal particles have a wide range of industrial applications. This study is focused on the application to microstructured materials and the impact of external compressive forces on particles. Currently, in the large throughput manufacturing of microstructured materials, problems such as cracking are caused by these external forces. Numerical methods can be used to generate particle positions and obtain a better understanding of particle interactions under different conditions. The aim of this study was to obtain a better understanding of the stability limits of using the 4th order Runge Kutta method. By introducing the external forces as auxiliary functions, we were able to generate exact analytic solutions satisfying arbitrary hydrodynamic and interaction forces. This allowed rigorous comparison of the theoretical stability limits and the observed stability limits on time step. We found excellent agreement with the predicted and observed results.","abstract_has_math":false,"creators":["Velagala, Sindhuja"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Chemical Engineering","degree_department":null,"school":null,"contributors":["Higdon, Jonathan J.L."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-21T19:47:40Z","date_published":"2015-01-21T19:47:40Z","updated_at":"2026-07-22T22:26:07Z","subjects":["Colloidal Particles","Stability","4th Order Runge Kutta"],"languages":["en"],"rights":["Copyright 2014 Sindhuja Velagala"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/72750","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Higdon, Jonathan J.L."]},{"key":"dc:creator","label":"Author","values":["Velagala, Sindhuja"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-01-21T19:47:40Z","2014-12","2015-01-21"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Colloidal Particles","Stability","4th Order Runge Kutta"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Sindhuja Velagala"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72750"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Colloidal particles have a wide range of industrial applications. This study is focused on the application to microstructured materials and the impact of external compressive forces on particles. Currently, in the large throughput manufacturing of microstructured materials, problems such as cracking are caused by these external forces. Numerical methods can be used to generate particle positions and obtain a better understanding of particle interactions under different conditions. The aim of this study was to obtain a better understanding of the stability limits of using the 4th order Runge Kutta method. By introducing the external forces as auxiliary functions, we were able to generate exact analytic solutions satisfying arbitrary hydrodynamic and interaction forces. This allowed rigorous comparison of the theoretical stability limits and the observed stability limits on time step. We found excellent agreement with the predicted and observed results.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-12-01T18:38:42Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Sindhuja_Velagala.pdf: 849587 bytes, checksum: ae89bdfba6c08744178cf3742a44fef4 (MD5)","Made available in DSpace on 2015-01-21T19:47:40Z (GMT). No. of bitstreams: 1 Sindhuja_Velagala.pdf: 881621 bytes, checksum: 3a95d5478d394a2f6cdfa5ed0cdcac0d (MD5)"]},{"key":"dc:title","label":"Title","values":["Stability analysis of the 4th order Runge Kutta method in application to colloidal particle interactions"]}]}],"canonical_facts":{"dc:contributor":["Higdon, Jonathan J.L."],"dc:creator":["Velagala, Sindhuja"],"dc:date":["2015-01-21T19:47:40Z","2014-12","2015-01-21"],"dc:description":["Colloidal particles have a wide range of industrial applications. This study is focused on the application to microstructured materials and the impact of external compressive forces on particles. Currently, in the large throughput manufacturing of microstructured materials, problems such as cracking are caused by these external forces. Numerical methods can be used to generate particle positions and obtain a better understanding of particle interactions under different conditions. The aim of this study was to obtain a better understanding of the stability limits of using the 4th order Runge Kutta method. By introducing the external forces as auxiliary functions, we were able to generate exact analytic solutions satisfying arbitrary hydrodynamic and interaction forces. This allowed rigorous comparison of the theoretical stability limits and the observed stability limits on time step. We found excellent agreement with the predicted and observed results.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-12-01T18:38:42Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Sindhuja_Velagala.pdf: 849587 bytes, checksum: ae89bdfba6c08744178cf3742a44fef4 (MD5)","Made available in DSpace on 2015-01-21T19:47:40Z (GMT). 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