Mode locking in discrete soliton dynamics under ac forces

Martínez, Pedro J.; Falo, Fernando; Mazo, J. J.; Floría, L. M.; Sánchez, Ángel

doi:10.1103/physrevb.56.87

Cited by 14 publications

(31 citation statements)

References 14 publications

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“…This mechanism for unlocking transitions was already observed in the purely dissipative dynamics of ac driven modulated structures of the FK model [24]. Intermittencies of type I are also known to be responsible for the depinning transition of discrete solitons (discommensurations) of the underdamped FK model [21].…”

Section: Unlocking Transitionsupporting

confidence: 56%

“…3) the resonant state destabilizes inside the plateau and the new attracting solution (with locking velocity v b ) is more complex: either periodic with a larger period, or even chaotic, as revealed by the computed (largest) Lyapunov exponent. These types of complex behaviors inside a locking plateau are known to happen for a single driven-damped anharmonic oscillator [20], as well as for moving discommensurations [21]. In this regard, the result for discommensurations can be reducible to the single-particle case using collective variable approaches.…”

Section: Mbmentioning

confidence: 99%

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Mode-locking of mobile discrete breathers

et al. 2005

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We study numerically synchronization phenomena of mobile discrete breathers in dissipative nonlinear lattices periodically forced. When varying the driving intensity, the breather velocity generically locks at rational multiples of the driving frequency. In most cases, the locking plateau coincides with the linear stability domain of the resonant mobile breather and the desynchronization occurs by regular appearance of type I intermittencies. However, some plateaux also show chaotic mobile breathers with locked velocity in the locking region. The addition of a small subharmonic driving tames the locked chaotic solution and enhances the stability of resonant mobile breathers.

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Section: Unlocking Transitionsupporting

confidence: 56%

Section: Mbmentioning

confidence: 99%

Mode-locking of mobile discrete breathers

et al. 2005

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“…In contrast with that, a recent work [15] reported other results of simulations of a FK lattice that consisted of 20 particles with a = 1, the ac-drive's period T ≡ 2π/ω took the values 50 or 25, while the dissipative constant was α = 0.1. Note that the corresponding friction-braking time ∼ 1/α is essentially smaller than the period T , hence this regime was, as a matter of fact, overdamped.…”

Section: Introductionmentioning

confidence: 75%

“…Note that the corresponding friction-braking time ∼ 1/α is essentially smaller than the period T , hence this regime was, as a matter of fact, overdamped. The most essential effect observed in [15] was depinning of a kink trapped in the lattice under the action of a rather strong ac drive. In most cases, the overdamped motion of the depinned kink was a diffusive drift; however, at some values of the driving force, a nonzero mean velocity predicted by Eq.…”

Section: Introductionmentioning

confidence: 99%

The alternating-current-driven motion of dislocations in a weakly damped Frenkel - Kontorova lattice

Филатрелла

Malomed

1999

J. Phys.: Condens. Matter

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By means of numerical simulations, we demonstrate that ac field can support stably moving collective nonlinear excitations in the form of dislocations (topological solitons, or kinks) in the Frenkel-Kontorova (FK) lattice with weak friction, which was qualitatively predicted by Bonilla and Malomed [Phys. Rev. B 43, 11539 (1991)]. Direct generation of the moving dislocations turns out to be virtually impossible; however, they can be generated initially in the lattice subject to an auxiliary spatial modulation of the on-site potential strength. Gradually relaxing the modulation, we are able to get the stable moving dislocations in the uniform FK lattice with the periodic boundary conditions, provided that the driving frequency is close to the gap frequency of the linear excitations in the uniform lattice. The excitations that can be generated this way have a large and noninteger index of commensurability with the lattice (so suggesting that the actual value of the commensurability index is irrational). The simulations reveal two dif-1 ferent types of the moving dislocations: broad ones, that extend, roughly, to half the full length of the periodic lattice (in that sense, they cannot be called solitons), and localized soliton-like dislocations, that can be found in an excited state, demonstrating strong persistent internal vibrations. The minimum (threshold) amplitude of the driving force necessary to support the traveling excitation is found as a function of the friction coefficient. Its extrapolation suggests that the threshold does not vanish at the zero friction, which may be explained by radiation losses. The moving dislocation can be observed experimentally in an array of coupled small Josephson junctions in the form of an inverse Josephson effect, i.e., a dc-voltage response to the uniformly applied ac bias current.

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“…It is of interest to note that a Josephson junction array is just an technically and physically excellent demonstration, of many typical nonlinear features of the driven FK-type systems biased by, for instance, dc forces [9] and ac forces [10].…”

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confidence: 99%

Driven dynamics: A photodriven Frenkel-Kontorova model

Zhu

2001

Phys. Rev. E

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In this study, we examine the dynamics of a one-dimensional Frenkel-Kontorova chain consisting of nanosize clusters (the "particles") and photochromic molecules (the "bonds"), and being subjected to a periodic substrate potential. Whether the whole chain should be running or be locked depends on both the frequency and the wavelength of the light (keeping the other parameters fixed), as observed through numerical simulation. In the locked state, the particles are bound at the bottom of the external potential and vibrate backwards and forwards at a constant amplitude. In the running state, the initially fed energy is transformed into directed motion as a whole. It is of interest to note that the driving energy is introduced to the system by the irradiation of light, and the driven mechanism is based on the dynamical competition between the inherent lengths of the moving object (the chain) and the supporting carrier (the isotropic surface). However, the most important is that the light-induced conformational changes of the chromophore lead to the time-and-space dependence of the rest lengths of the bonds.PACS numbers: 66.90.+r, 63.20.Ry The driven dynamics of a system of interacting particles in atomic or mesoscopic scale has been attracting much attention. It is very important in technology, very rich in physics, and widely applicable in many fields, such as mass transport, conductivity, tribology, etc. As far as we know, one of the most typical examples conducted on the driven dynamics has been the driven Frenkel-Kontorova-type systems biased by dc, and ac external forces, respectively.The Frenkel-Kontorova (FK) model [1] may describe, for example, a closely packed row of atoms in crystals, a layer of atoms adsorbed on crystal surface, a chain of ions in a "channel" of quasi-one-dimensional conductors, hydrogen atoms in hydrogen-bonded systems, and so on. In general, such a system can be treated with two parts in the driven dynamical model: the moving object and the supporting carrier. First, the moving object is considered an atomic subsystem, in which the interparticle interaction is taken as a harmonic interaction between the nearest neighbors. Second, the action of the supporting carrier to the moving object is modeled as an external potential, a damping constant, and a thermal bath. When, for instance, an external dc driving force f is applied to such a system, its response can be very nonlinear and complex. The overdamped case (η ≫ ω 0 , where η is the external damping and ω 0 is the vibrational frequency at the bottom of the periodic potential), has been studied in a number of papers [2,3,4]. When the driving force f changes, the multistep and the hysteretic transition of the system from the locked state to the sliding state in the underdamped case (η ≪ ω 0 ) has also been delineated in detail [5,6]. At the same time, various intermediate regimes can be described by resonance phenomena [7] and by the moving quasiparticle excitation, kinks [8].A theoretical demonstration of driven dynamical behavior, as...

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Mode locking in discrete soliton dynamics under ac forces

Cited by 14 publications

References 14 publications

Mode-locking of mobile discrete breathers

Mode-locking of mobile discrete breathers

The alternating-current-driven motion of dislocations in a weakly damped Frenkel - Kontorova lattice

Driven dynamics: A photodriven Frenkel-Kontorova model

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