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dc.contributor.authorPace, Salvatore D.en_US
dc.contributor.authorReiss, Kevin A.en_US
dc.contributor.authorCampbell, David K.en_US
dc.coverage.spatialUnited Statesen_US
dc.date.accessioned2020-04-27T15:27:46Z
dc.date.available2020-04-27T15:27:46Z
dc.date.issued2019-11
dc.identifierhttps://www.ncbi.nlm.nih.gov/pubmed/31779356
dc.identifier.citationSalvatore D Pace, Kevin A Reiss, David K Campbell. 2019. "The β Fermi-Pasta-Ulam-Tsingou recurrence problem.." Chaos, Volume 29, Issue 11, pp. 113107. https://doi.org/10.1063/1.5122972
dc.identifier.issn1089-7682
dc.identifier.urihttps://hdl.handle.net/2144/40369
dc.description.abstractWe perform a thorough investigation of the first Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in the β-FPUT chain for both positive and negative β. We show numerically that the rescaled FPUT recurrence time Tr=tr/(N+1)3 depends, for large N, only on the parameter S≡Eβ(N+1). Our numerics also reveal that for small |S|, Tr is linear in S with positive slope for both positive and negative β. For large |S|, Tr is proportional to |S|-1/2 for both positive and negative β but with different multiplicative constants. We numerically study the continuum limit and find that the recurrence time closely follows the |S|-1/2 scaling and can be interpreted in terms of solitons, as in the case of the KdV equation for the α chain. The difference in the multiplicative factors between positive and negative β arises from soliton-kink interactions that exist only in the negative β case. We complement our numerical results with analytical considerations in the nearly linear regime (small |S|) and in the highly nonlinear regime (large |S|). For the former, we extend previous results using a shifted-frequency perturbation theory and find a closed form for Tr that depends only on S. In the latter regime, we show that Tr∝|S|-1/2 is predicted by the soliton theory in the continuum limit. We then investigate the existence of the FPUT recurrences and show that their disappearance surprisingly depends only on Eβ for large N, not S. Finally, we end by discussing the striking differences in the amount of energy mixing between positive and negative β and offer some remarks on the thermodynamic limit.en_US
dc.format.extentp. 113107en_US
dc.languageeng
dc.language.isoen_US
dc.relation.ispartofChaos
dc.rightsThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Salvatore D Pace, Kevin A Reiss, David K Campbell. 2019. "The β Fermi-Pasta-Ulam-Tsingou recurrence problem." Chaos, Volume 29, Issue 11: 113107, and may be found at https://doi.org/10.1063/1.5122972.en_US
dc.subjectApplied mathematicsen_US
dc.subjectNumerical and computational mathematicsen_US
dc.subjectOther physical sciencesen_US
dc.subjectFluids & plasmasen_US
dc.titleThe β Fermi-Pasta-Ulam-Tsingou recurrence problemen_US
dc.typeArticleen_US
dc.description.versionPublished versionen_US
dc.identifier.doi10.1063/1.5122972
dc.description.embargo2020-11-30
pubs.elements-sourcepubmeden_US
pubs.notesEmbargo: No embargoen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Physicsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-4502-5629 (Campbell, David K)
dc.identifier.mycv495126


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