{"id":{"repo_id":"oregon","oai_identifier":"oai:scholarsbank.uoregon.edu:1794/33191"},"canonical_url":"https://search.dev.ndltd.org/etd/oregon/oai:scholarsbank.uoregon.edu:1794/33191","repository":{"repo_id":"oregon","name":"University of Oregon","base_url":"https://scholarsbank.uoregon.edu/server/oai/request"},"display":{"title":"Cost-Minizming Networks and Polyhedral Cones","abstract":"We model immiscible fluid clusters in space by cost-minimizing polyhedral surfaces, where “cost” is a weighted area. We also discuss planar configurations of immiscible fluid clusters modeled by costminimizing networks, where cost is a weighted length. We give necessary and sufficient conditions for local minimization of networks in the plane and cones of planes meeting along a line in space. A cone is minimizing if and only if a certain geometric upoint-placing” condition is fulfilled. We extend these results to allow a single additional fluid not present in the original configuration. It is not known whether point-placing and minimization are equivalent for cones of planes meeting at a point, but we conjecture the same point-placing condition and discuss some special examples of such minimizing configurations.","abstract_html":"We model immiscible fluid clusters in space by cost-minimizing polyhedral surfaces, where “cost” is a weighted area. We also discuss planar configurations of immiscible fluid clusters modeled by costminimizing networks, where cost is a weighted length. We give necessary and sufficient conditions for local minimization of networks in the plane and cones of planes meeting along a line in space. A cone is minimizing if and only if a certain geometric upoint-placing” condition is fulfilled. We extend these results to allow a single additional fluid not present in the original configuration. It is not known whether point-placing and minimization are equivalent for cones of planes meeting at a point, but we conjecture the same point-placing condition and discuss some special examples of such minimizing configurations.","abstract_has_math":false,"creators":["Munson, Brian Andrew"],"institution":"University of Oregon","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Sadofsky, Hal"],"committee_chairs":[],"committee_members":[],"year":1998,"date_issued":"1998","date_published":"1998","updated_at":"2026-08-21T16:47:20Z","subjects":["Immiscible fluid clusters","Polyhedral surfaces","Weighted length","Steiner problem"],"languages":["en_US"],"rights":["Creative Commons BY-NC-ND 4.0-US","UO theses and dissertations are provided for research and educational purposes and may be under copyright by the author or the author’s heirs. Please contact scholars@uoregon.edu with any questions or comments. In your email, be sure to include the URL and title of the specific items that you are inquiring about."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1794/33191","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F33191","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sadofsky, Hal"]},{"key":"dc:creator","label":"Author","values":["Munson, Brian Andrew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-07-31T18:55:42Z"]},{"key":"dc:date.issued","label":"Date","values":["1998"]},{"key":"dc:publisher","label":"Institution","values":["University of Oregon"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation or thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Immiscible fluid clusters","Polyhedral surfaces","Weighted length","Steiner problem"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons BY-NC-ND 4.0-US","UO theses and dissertations are provided for research and educational purposes and may be under copyright by the author or the author’s heirs. Please contact scholars@uoregon.edu with any questions or comments. In your email, be sure to include the URL and title of the specific items that you are inquiring about."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1794/33191"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["38 pages."]},{"key":"dc:description.abstract","label":"Abstract","values":["We model immiscible fluid clusters in space by cost-minimizing polyhedral surfaces, where “cost” is a weighted area. We also discuss planar configurations of immiscible fluid clusters modeled by costminimizing networks, where cost is a weighted length. We give necessary and sufficient conditions for local minimization of networks in the plane and cones of planes meeting along a line in space. A cone is minimizing if and only if a certain geometric upoint-placing” condition is fulfilled. We extend these results to allow a single additional fluid not present in the original configuration. It is not known whether point-placing and minimization are equivalent for cones of planes meeting at a point, but we conjecture the same point-placing condition and discuss some special examples of such minimizing configurations."]},{"key":"dc:title","label":"Title","values":["Cost-Minizming Networks and Polyhedral Cones"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sadofsky, Hal"],"dc:creator":["Munson, Brian Andrew"],"dc:date.accessioned":["2026-07-31T18:55:42Z"],"dc:date.issued":["1998"],"dc:description":["38 pages."],"dc:description.abstract":["We model immiscible fluid clusters in space by cost-minimizing polyhedral surfaces, where “cost” is a weighted area. We also discuss planar configurations of immiscible fluid clusters modeled by costminimizing networks, where cost is a weighted length. We give necessary and sufficient conditions for local minimization of networks in the plane and cones of planes meeting along a line in space. A cone is minimizing if and only if a certain geometric upoint-placing” condition is fulfilled. We extend these results to allow a single additional fluid not present in the original configuration. It is not known whether point-placing and minimization are equivalent for cones of planes meeting at a point, but we conjecture the same point-placing condition and discuss some special examples of such minimizing configurations."],"dc:identifier.uri":["https://hdl.handle.net/1794/33191"],"dc:language.iso":["en_US"],"dc:publisher":["University of Oregon"],"dc:rights":["Creative Commons BY-NC-ND 4.0-US","UO theses and dissertations are provided for research and educational purposes and may be under copyright by the author or the author’s heirs. Please contact scholars@uoregon.edu with any questions or comments. In your email, be sure to include the URL and title of the specific items that you are inquiring about."],"dc:subject":["Immiscible fluid clusters","Polyhedral surfaces","Weighted length","Steiner problem"],"dc:title":["Cost-Minizming Networks and Polyhedral Cones"],"dc:type":["Dissertation or thesis"]},"updated_at":"2026-08-21T16:47:20Z"}