Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis

Tekić, Jasmina; Botha, A. E.; Mali, Petar; Shukrinov, Yu. M.

doi:10.1103/physreve.99.022206

Cited by 21 publications

(49 citation statements)

References 52 publications

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“…We believe that application of KC could help in the solution of this and similar problems. We have been focused here only on Shapiro steps in the presence of thermal effects, but KC could be used for studies of other effects among which certainly interesting is the chaos [9,38]. Application of Kolmogorov complexity on the studies of chaotic behavior in systems which exhibit Shapiro steps are part of our future studies and will be published separately.…”

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confidence: 99%

Complexity of Shapiro steps

et al. 2020

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We demonstrate on the example of the dc+ac driven overdamped Frenkel-Kontorova model that an easily calculable measure of complexity can be used for the examination of Shapiro steps in presence of thermal noise. In real systems, thermal noise causes melting or even disappearance of Shapiro steps, which makes their analysis in the standard way from the response function difficult. Unlike in the conventional approach, here, by calculating the Kolmogorov complexity of certain areas in the response function we were able to detect Shapiro steps, measure their size with desired precision and examine their temperature dependence. The aim of this work is to provide scientists, particularly experimentalists, an unconventional but a practical and easy tool for examination of Shapiro steps in real systems.

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confidence: 99%

Complexity of Shapiro steps

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“…Overall, we treat here the PES for N particles of the chain and search for global valleys through the 'mountains' of the N -dimensional PES for a sliding of the chain. Beside the use of a Langevin equation [2], an important part of the theory is the use of Newton trajectories (NT) for the description of the 'running' stationary points of the PES under an external force. The NTs are curves in the configuration space of the chain.…”

Section: Supplementary Informationmentioning

confidence: 99%

“…In Sect. 4, the case of the spring potential with N =8 chain length [2,15] and k/v = 1/4 soft springs is discussed. Using the tool of NTs we explore the many 'floors' of the PES of the 8-chain.…”

Section: Supplementary Informationmentioning

confidence: 99%

“…We emphasize that we do not use the so-called 'periodic boundary conditions' [2]. The spring potential (1) belongs to the standard FK model.…”

Section: The Fk Modelmentioning

confidence: 99%

“…Shapiro steps are reported in many experiments, see part I of this series for references [1]. We concentrate here on such steps in calculations of a Langevin equation with the FK model [2], which many workers saw for a good model of real Shapiro steps. Shapiro steps emerge for a combination of direct and alternating external forces where the frequency of the oscillation of the FK-chain is locked, and its sliding velocity is constant, though the direct force is increased.…”

Section: Introductionmentioning

confidence: 99%

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Description of Shapiro steps on the potential energy surface of a Frenkel–Kontorova model, Part II: free boundaries of the chain

Quapp

Bofill

2021

Eur. Phys. J. B

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We explain Shapiro steps in a Frenkel–Kontorova (FK) model for a 1D chain of particles with free boundaries. The action of an external alternating force for the oscillating structure of the chain is important here. The different ’floors’ of the potential energy surface (PES) of this model play an important role. They are regions of kinks, double kinks, and so on. We will find out that the preferable movements are the sliding of kinks or antikinks through the chain. The more kinks / antikinks are included the higher is the ’floor’ through the PES. We find the Shapiro steps moving and oscillating anywhere between the floors. They start with a single jump over the highest SP in the global valley through the PES, like in part I of this series. They finish with complicated oscillations in the PES, for excitations directly over the critical depinning force. We use an FK model with free boundary conditions. In contrast to other results in the past, for this model, we obtain Shapiro steps in an unexpected, inverse sequence. We demonstrate Shapiro steps for a case with soft ’springs’ between an 8-particle FK chain. Graphic abstract

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Hysteresis in the underdamped three-layer model

Jia

Tekić

2020

Sci Rep

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The hysteretic phenomena were investigated in the three-layer model consisting of a chain of harmonically interacting atoms confined between two rigid periodical substrate potentials, where the top substrate was driven by a external force. The pinning to running and the running-to pinning transitions were examined as the driving force was varied and the influence of the equilibrium spacing and strength of the interaction of the particles in the middle layer on the static and kinetic friction force analyzed in detail. The parameter space in which the friction forces could reach their maxima or minima was determined. These results could be interesting for the selection of lubricant materials and minimization of energy loss in tribology.

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Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis

Cited by 21 publications

References 52 publications

Complexity of Shapiro steps

Complexity of Shapiro steps

Description of Shapiro steps on the potential energy surface of a Frenkel–Kontorova model, Part II: free boundaries of the chain

Hysteresis in the underdamped three-layer model

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