Farey sequence in the appearance of subharmonic Shapiro steps
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2015
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The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence. In the standard regime, the appearance of half-integer and other subharmonic steps between the large harmonic steps, and their relative sizes follow the Farey construction. In the nonstandard regime, however, the half-integer steps are larger than harmonic ones, and Farey construction is only present in the appearance of higher order subharmonic steps. The examination of Lyapunov exponents has also shown that regardless of the substrate potential or deformation, there was no chaos in the system.
Izvor:
Physical Review E, 2015, 91, 5Finansiranje / projekti:
- Uticaj elementarnih ekscitacija i konformacija na fizička svojstva novih materijala baziranih na jako korelisanim niskodimenzionalnim sistemima (RS-MESTD-Basic Research (BR or ON)-171009)
- Fotonika mikro i nano strukturnih materijala (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45010)
DOI: 10.1103/PhysRevE.91.052904
ISSN: 2470-0045; 2470-0053
PubMed: 26066226
WoS: 000354252100007
Scopus: 2-s2.0-84929193292
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VinčaTY - JOUR AU - Odavic, Jovan AU - Mali, Petar AU - Tekić, Jasmina PY - 2015 UR - https://vinar.vin.bg.ac.rs/handle/123456789/531 AB - The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence. In the standard regime, the appearance of half-integer and other subharmonic steps between the large harmonic steps, and their relative sizes follow the Farey construction. In the nonstandard regime, however, the half-integer steps are larger than harmonic ones, and Farey construction is only present in the appearance of higher order subharmonic steps. The examination of Lyapunov exponents has also shown that regardless of the substrate potential or deformation, there was no chaos in the system. T2 - Physical Review E T1 - Farey sequence in the appearance of subharmonic Shapiro steps VL - 91 IS - 5 DO - 10.1103/PhysRevE.91.052904 ER -
@article{ author = "Odavic, Jovan and Mali, Petar and Tekić, Jasmina", year = "2015", abstract = "The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence. In the standard regime, the appearance of half-integer and other subharmonic steps between the large harmonic steps, and their relative sizes follow the Farey construction. In the nonstandard regime, however, the half-integer steps are larger than harmonic ones, and Farey construction is only present in the appearance of higher order subharmonic steps. The examination of Lyapunov exponents has also shown that regardless of the substrate potential or deformation, there was no chaos in the system.", journal = "Physical Review E", title = "Farey sequence in the appearance of subharmonic Shapiro steps", volume = "91", number = "5", doi = "10.1103/PhysRevE.91.052904" }
Odavic, J., Mali, P.,& Tekić, J.. (2015). Farey sequence in the appearance of subharmonic Shapiro steps. in Physical Review E, 91(5). https://doi.org/10.1103/PhysRevE.91.052904
Odavic J, Mali P, Tekić J. Farey sequence in the appearance of subharmonic Shapiro steps. in Physical Review E. 2015;91(5). doi:10.1103/PhysRevE.91.052904 .
Odavic, Jovan, Mali, Petar, Tekić, Jasmina, "Farey sequence in the appearance of subharmonic Shapiro steps" in Physical Review E, 91, no. 5 (2015), https://doi.org/10.1103/PhysRevE.91.052904 . .