Noise effects in the ac-driven Frenkel-Kontorova model

Abstract

The noise effects on dynamical-mode-locking phenomena in the ac-driven dissipative Frenkel-Kontorova model are studied by molecular-dynamics simulations. It was found that the noise strongly influences the properties of the Shapiro steps and the way they respond to the changing of system parameters. The increase of temperature produces the melting of the Shapiro steps, while the critical depinning force is significantly reduced. The oscillatory form of the amplitude dependence is strongly affected where the Bessel-like form changes as the temperature increases. In the frequency dependence of the Shapiro steps, due to the decrease of the dc threshold value, noise may transfer the system to the high-amplitude regime where oscillations of the step width with frequency or period of the ac force appear. These phenomena will additionally destabilize the steps in real systems and significantly limit the region of parameters where dynamical-mode-locking phenomena could be observed.

Dynamic mode locking in a driven colloidal system: experiments and theory

“…at z = F 1.7 AC μms −1 ), these bumps disappear, and the depinning transition is defined as a single monotonic increase. This effect has been noted previously for the Frenkel Kontorova model, for a chain of interacting particles [39,45,70]. Figure 9(b) shows the frequency dependent effective critical driving velocity for > F F AC C in more detail.…”

“…Model systems composed of colloidal particles in periodic potentials have been studied for a number of years [28,29], from simple double well potentials [30][31][32][33] to directed motion [34][35][36][37][38][39], particle sorting [40], and kink generation [41] in two-dimensional (2D) optical lattices. Colloidal systems are easy to manipulate, and have accessible length and time scales, making them attractive models for the study of synchronisation at the microscale.…”

Complexity of Shapiro steps

“…However, in experiments these systems are exposed to various environmental effects among which certainly the most significant is the noise. Noise greatly affects mode locking by melting and changing properties of Shapiro steps such as their amplitude [16,17] and frequency dependence [17,18]. It is, therefore, very difficult or even impossible to detect, measure or control them, and often, different methods have to be developed in order to address this problem.…”

“…In particular, we will consider the dc+ac driven overdamped Frenkel-Kontorova (FK) model with deformable substrate potential in the presence of noise. The standard FK model represents a chain of harmonically interacting identical particles subjected to sinusoidal substrate potential [26,27]. It can describes various commensurate and incommensurate structures, which exhibit very rich dynamics under external forces.…”

Friction phenomena in the overdamped three-layer model

“…Their properties and some interesting phenomena have been studied recently in the dc+ac driven Frenkel-Kontorova (FK) model [3][4][5][6]. Those works have been stimulated by theoretical and experimental studies of the Shapiro steps in physical systems such as charge-density or spin-density wave conductors [7][8][9][10][11][12][13], vortex lattices [14], Josephson-junction arrays biased by external currents [15][16][17][18][19][20], and superconducting nanowires.…”