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Influence of the relative stiffness of second-neighbor interactions on chaotic discrete breathers in a square lattice

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  • Shepelev, Igor A.
  • Soboleva, Elvira G.
  • Kudreyko, Aleksey A.
  • Dmitriev, Sergey V.

Abstract

It is known that the modulational instability of a delocalized nonlinear vibrational mode (DNVM) with frequency outside the phonon band can lead to spontaneous energy localization in a nonlinear lattice on chaotic discrete breathers (CDBs). Considering a β-FPUT square lattice with nearest and next-nearest interactions, the appearance of CDBs is analyzed for different stiffnesses of the first- and second-nearest interactions, k1 and k2, keeping the density of the lattice unchanged. There are two DNVMs in the square lattice with frequencies above the phonon spectrum and both are studied. The appearance of CDBs in the lattice is monitored by calculating the time evolution of the energy localization parameter L and the maximum energy of the particles emax. For solid state physics and materials science, the important range of stiffness parameters is k2k1/4. This means that they can form in crystals if the stiffness of the second-neighbor bonds is smaller than that of the first-neighbor bonds, but not too small. Depending on the relation between the anharmonicity parameters of the first- and second-neighbor bonds CDBs can have different polarization.

Suggested Citation

  • Shepelev, Igor A. & Soboleva, Elvira G. & Kudreyko, Aleksey A. & Dmitriev, Sergey V., 2024. "Influence of the relative stiffness of second-neighbor interactions on chaotic discrete breathers in a square lattice," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004375
    DOI: 10.1016/j.chaos.2024.114885
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    References listed on IDEAS

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    1. Dina U. Abdullina & Maria N. Semenova & Aleksander S. Semenov & Elena A. Korznikova & Sergey V. Dmitriev, 2019. "Stability of delocalized nonlinear vibrational modes in graphene lattice," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(11), pages 1-5, November.
    2. Elena A. Korznikova & Alina Y. Morkina & Mohit Singh & Anton M. Krivtsov & Vitaly A. Kuzkin & Vakhid A. Gani & Yuri V. Bebikhov & Sergey V. Dmitriev, 2020. "Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chain," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(7), pages 1-9, July.
    3. O. V. Bachurina & A. A. Kudreyko, 2021. "Two-component localized vibrational modes in fcc metals," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-9, November.
    4. Kolesnikov, I.D. & Shcherbinin, S.A. & Bebikhov, Yu.V. & Korznikova, E.A. & Shepelev, I.A. & Kudreyko, A.A. & Dmitriev, S.V., 2024. "Chaotic discrete breathers in bcc lattice," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Elena A. Korznikova & Dmitry V. Bachurin & Sergey Yu. Fomin & Alexander P. Chetverikov & Sergey V. Dmitriev, 2017. "Instability of vibrational modes in hexagonal lattice," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(2), pages 1-8, February.
    6. Elham Barani & Ivan P. Lobzenko & Elena A. Korznikova & Elvira G. Soboleva & Sergey V. Dmitriev & Kun Zhou & Aliakbar Moradi Marjaneh, 2017. "Transverse discrete breathers in unstrained graphene," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(3), pages 1-5, March.
    7. Fraile, Alberto & Koukaras, Emmanuel N. & Papagelis, Konstantinos & Lazarides, Nikos & Tsironis, G.P., 2016. "Long-lived discrete breathers in free-standing graphene," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 262-267.
    8. Ramil T. Murzaev & Rita I. Babicheva & Kun Zhou & Elena A. Korznikova & Sergey Yu. Fomin & Vladimir I. Dubinko & Sergey V. Dmitriev, 2016. "Discrete breathers in alpha-uranium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(7), pages 1-6, July.
    9. O. V. Bachurina & R. T. Murzaev & A. A. Kudreyko & S. V. Dmitriev & D. V. Bachurin, 2022. "Atomistic study of two-dimensional discrete breathers in hcp titanium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(7), pages 1-10, July.
    10. Yi Peng & Wei Li & Feng Wang & Tim Still & Arjun G. Yodh & Yilong Han, 2017. "Diffusive and martensitic nucleation kinetics in solid-solid transitions of colloidal crystals," Nature Communications, Nature, vol. 8(1), pages 1-12, August.
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