{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/131013"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/131013","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Analytical and numerical study of the unstable limit cycles of walking droplets","abstract":"Recent studies have shown that a vibrating fluid bath can support a bouncing droplet, generating a pilot wave which propels the droplet into horizontal motion. Walking droplets have been demonstrated not only to follow linear trajectories, but to exhibit a range of rich dynamical behavior, including tunneling, diffraction, and orbital quantization. Current theoretical models for the walking droplet system can be difficult to analyze. Here, by reducing the dimension of the bath, a simpler model has been derived and analyzed. We summarize this derivation, explore the stability of the system's dynamical states, and provide evidence of a previously unreported homoclinic bifurcation.","abstract_html":"Recent studies have shown that a vibrating fluid bath can support a bouncing droplet, generating a pilot wave which propels the droplet into horizontal motion. Walking droplets have been demonstrated not only to follow linear trajectories, but to exhibit a range of rich dynamical behavior, including tunneling, diffraction, and orbital quantization. Current theoretical models for the walking droplet system can be difficult to analyze. Here, by reducing the dimension of the bath, a simpler model has been derived and analyzed. We summarize this derivation, explore the stability of the system's dynamical states, and provide evidence of a previously unreported homoclinic bifurcation.","abstract_has_math":false,"creators":["Kurzban, Benjamin(Benjamin A.)"],"institution":"Massachusetts Institute of Technology","degree_name":"Bachelor","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mechanical Engineering","school":null,"contributors":[],"advisors":["Matthew Durey"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-22T22:21:52Z","subjects":["Mechanical Engineering."],"languages":["eng"],"rights":["MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/131013","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Matthew Durey"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Mechanical Engineering","MechE"]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided."]},{"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":["https://hdl.handle.net/1721.1/131013"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis: S.B., Massachusetts Institute of Technology, Department of Mechanical Engineering, September, May, 2020","Cataloged from the official PDF of thesis.","Includes bibliographical references (page 8)."]},{"key":"dc:description.abstract","label":"Abstract","values":["Recent studies have shown that a vibrating fluid bath can support a bouncing droplet, generating a pilot wave which propels the droplet into horizontal motion. Walking droplets have been demonstrated not only to follow linear trajectories, but to exhibit a range of rich dynamical behavior, including tunneling, diffraction, and orbital quantization. Current theoretical models for the walking droplet system can be difficult to analyze. Here, by reducing the dimension of the bath, a simpler model has been derived and analyzed. We summarize this derivation, explore the stability of the system's dynamical states, and provide evidence of a previously unreported homoclinic bifurcation."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.B."]},{"key":"dc:title","label":"Title","values":["Analytical and numerical study of the unstable limit cycles of walking droplets"]}]}],"canonical_facts":{"dc:contributor.advisor":["Matthew Durey"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mechanical Engineering","MechE"],"dc:contributor.other":["Massachusetts Institute of Technology. Department of Mechanical Engineering."],"dc:creator":["Kurzban, Benjamin(Benjamin A.)"],"dc:date.accessioned":["2021-06-17T17:21:29Z"],"dc:date.available":["2021-06-17T17:21:29Z"],"dc:date.issued":["2020"],"dc:description":["Thesis: S.B., Massachusetts Institute of Technology, Department of Mechanical Engineering, September, May, 2020","Cataloged from the official PDF of thesis.","Includes bibliographical references (page 8)."],"dc:description.abstract":["Recent studies have shown that a vibrating fluid bath can support a bouncing droplet, generating a pilot wave which propels the droplet into horizontal motion. Walking droplets have been demonstrated not only to follow linear trajectories, but to exhibit a range of rich dynamical behavior, including tunneling, diffraction, and orbital quantization. Current theoretical models for the walking droplet system can be difficult to analyze. Here, by reducing the dimension of the bath, a simpler model has been derived and analyzed. We summarize this derivation, explore the stability of the system's dynamical states, and provide evidence of a previously unreported homoclinic bifurcation."],"dc:description.degree":["S.B."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/131013"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mechanical Engineering."],"dc:title":["Analytical and numerical study of the unstable limit cycles of walking droplets"],"dc:type":["Thesis"],"thesis:degree_name":["Bachelor"]},"updated_at":"2026-07-22T22:21:52Z"}