Cost-Minizming Networks and Polyhedral Cones

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.

Grantor dc:publisher

University of Oregon

Year dc:date.issued

1998

Author dc:creator

• Munson, Brian Andrew

Advisor dc:contributor.advisor

• Sadofsky, Hal

• Immiscible fluid clusters
• Polyhedral surfaces
• Weighted length
• Steiner problem

Statement 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.

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/1794/33191

OAI record oai:identifier

https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F33191