{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/73044"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/73044","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Classical hydrodynamics of Calogero-Sutherland models","abstract":"The Calogero Sutherland model is system of particle moving on a line and interacting with long-range forces. In this thesis we consider the classical case where the particles may or may not possess a spin degree of freedom. We demonstrate the intimate connection between the Calogero-Sutherland system and the Benjamin Ono equation. We then directly obtain a classical hydrodynamical limit of both the spineless and spinful Calogero system. The continuum limit of the spinless system is known to exhibit solition solutions. We show numerically that the spinful system also exhibits localized solutions with the soliton property. This is a strong evidence that the continuum spin-Calogero model is exactly integrable.","abstract_html":"The Calogero Sutherland model is system of particle moving on a line and interacting with long-range forces. In this thesis we consider the classical case where the particles may or may not possess a spin degree of freedom. We demonstrate the intimate connection between the Calogero-Sutherland system and the Benjamin Ono equation. We then directly obtain a classical hydrodynamical limit of both the spineless and spinful Calogero system. The continuum limit of the spinless system is known to exhibit solition solutions. We show numerically that the spinful system also exhibits localized solutions with the soliton property. This is a strong evidence that the continuum spin-Calogero model is exactly integrable.","abstract_has_math":false,"creators":["Xing, Lei"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Stone, Michael","Stack, John","Cooper, S. 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In this thesis we consider the classical case where the particles may or may not possess a spin degree of freedom. We demonstrate the intimate connection between the Calogero-Sutherland system and the Benjamin Ono equation. We then directly obtain a classical hydrodynamical limit of both the spineless and spinful Calogero system. The continuum limit of the spinless system is known to exhibit solition solutions. We show numerically that the spinful system also exhibits localized solutions with the soliton property. 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We then directly obtain a classical hydrodynamical limit of both the spineless and spinful Calogero system. The continuum limit of the spinless system is known to exhibit solition solutions. We show numerically that the spinful system also exhibits localized solutions with the soliton property. This is a strong evidence that the continuum spin-Calogero model is exactly integrable.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-07-21T22:07:40Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 thesis_Lei_Xing.pdf: 1820398 bytes, checksum: bc21ce5c13ad47d9e5c6786d0694a567 (MD5) dissertation_Lei_Xing.pdf: 1820723 bytes, checksum: 5114afb422a47701f09721e20066ee10 (MD5)","Made available in DSpace on 2015-01-21T19:58:50Z (GMT). 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