TY  - JOUR
AU  - Tekić, Jasmina
AU  - Botha, Andre E.
AU  - Mali, Petar
AU  - Shukrinov, Yury M.
PY  - 2019
UR  - https://link.aps.org/doi/10.1103/PhysRevE.99.022206
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8058
AB  - The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction. © 2019 American Physical Society.
T2  - Physical Review E
T1  - Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis
VL  - 99
IS  - 2
SP  - 022206
DO  - 10.1103/PhysRevE.99.022206
ER  - 

@article{
author = "Tekić, Jasmina and Botha, Andre E. and Mali, Petar and Shukrinov, Yury M.",
year = "2019",
abstract = "The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction. © 2019 American Physical Society.",
journal = "Physical Review E",
title = "Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis",
volume = "99",
number = "2",
pages = "022206",
doi = "10.1103/PhysRevE.99.022206"
}

Tekić, J., Botha, A. E., Mali, P.,& Shukrinov, Y. M.. (2019). Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis. in Physical Review E, 99(2), 022206.
https://doi.org/10.1103/PhysRevE.99.022206

Tekić J, Botha AE, Mali P, Shukrinov YM. Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis. in Physical Review E. 2019;99(2):022206.
doi:10.1103/PhysRevE.99.022206 .

Tekić, Jasmina, Botha, Andre E., Mali, Petar, Shukrinov, Yury M., "Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis" in Physical Review E, 99, no. 2 (2019):022206,
https://doi.org/10.1103/PhysRevE.99.022206 . .