IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v553y2020ics0378437120300820.html
   My bibliography  Save this article

Nonlinear normal modes in the β-Fermi-Pasta–Ulam-Tsingou chain

Author

Listed:
  • Fuller, Nathaniel J.
  • Sen, Surajit

Abstract

Nonlinear normal mode solutions of the β-FPUT chain with fixed boundaries are presented in terms of the Jacobi sn function. Exact solutions for the two particle chain are found for arbitrary linear and nonlinear coupling strengths. Solutions for the N-body chain are found for the case of purely nonlinear couplings. Three distinct solution types are presented: a linear analogue, a chaotic amplitude mapping, and a localized nonlinear mode. The relaxation of perturbed modes are also explored using l1-regularized least squares regression to estimate the free energy functional near the nonlinear normal mode solution. The perturbed modes are observed to decay sigmoidally towards a quasi-equilibrium state and a logarithmic relationship between the perturbation strength and mode lifetime is found.

Suggested Citation

  • Fuller, Nathaniel J. & Sen, Surajit, 2020. "Nonlinear normal modes in the β-Fermi-Pasta–Ulam-Tsingou chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    • Handle: RePEc:eee:phsmap:v:553:y:2020:i:c:s0378437120300820
    DOI: 10.1016/j.physa.2020.124283
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120300820
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.124283?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sen, Surajit & Krishna Mohan, T.R. & M.M. Pfannes, Jan, 2004. "The quasi-equilibrium phase in nonlinear 1D systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 336-343.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fuller, Nathaniel J. & Sen, Surajit, 2021. "Quasi-stable localized excitations in the β-Fermi Pasta Ulam Tsingou system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Avalos, Edgar & Datta, Amitava & Rosato, Anthony D. & Blackmore, Denis & Sen, Surajit, 2020. "Dynamics in a confined mass–spring chain with 1∕r repulsive potential: Strongly nonlinear regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:553:y:2020:i:c:s0378437120300820. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.