Dynamical phase diagram of the dc-driven underdamped Frenkel-Kontorova chain

Paliy, Maxim; Braun, O. M.; Dauxois, Thierry; Hu, Bambi

doi:10.1103/physreve.56.4025

Cited by 39 publications

(27 citation statements)

References 21 publications

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“…To demonstrate that concretely, we choose one of the simplest tribological models, the one-dimensional Frenkel-Kontorova (FK) model [7] in its atomic stick-slip regime [8,9]. The MSM construction leads to the identification of a handful of natural variables which describe the steady-state dynamics of friction in this model.…”

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Markov state modeling of sliding friction

et al. 2016

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Markov State Modeling has recently emerged as a key technique for analyzing rare events in thermal equilibrium molecular simulations and finding metastable states. Here we export this technique to the study of friction, where strongly non-equilibrium events are induced by an external force. The approach is benchmarked on the well-studied Frenkel-Kontorova model, where we demonstrate the unprejudiced identification of the minimal basis microscopic states necessary for describing sliding, stick-slip and dissipation. The steps necessary for the application to realistic frictional systems are highlighted.PACS numbers: 68.35. Af, 46.55.+d, 02.50.Ga Despite the relevance of friction between solids from the macroscale to the nanoscale, its physical description still needs theoretical basis and understanding. Even the simplest, classical atomistic sliding problem has too many degrees of freedom, and there is so far no method for the unprejudiced identification of a few dynamical collective variables suitable for a mesoscopic description of fundamental sliding events such as stick-slip [1]. In the field of equilibrium biomolecular simulations, where computational scientists often meet similar problems, powerful tools have been developed in the last decade, aimed at identifying the relevant metastable conformations, the reactions paths, and the rates associated to transition events between them. In particular, Markov State Models [2-5] (MSMs) have emerged as a key technique, with clear theoretical foundations and great flexibility. In that approach, the dynamical trajectory in phase space of a large collection of molecular entities is projected onto a much smaller space defined by a discrete set of states that are deemed typical, and the dynamics is reduced to Markovian jumps between these states. In most cases so far MSMs were applied to systems at equilibrium, where a stationary measure is defined and the Markov description is natural. In the physics of friction we deal with strongly nonequilibrium dynamics, even in steady state sliding. Application of MSMs to nonequilibrium problems is still in its infancy, with apparently only one instance, related to periodic driving [6].Here we show how the MSM framework can be extended to the study of nanofriction dynamics. To demonstrate that concretely, we choose one of the simplest tribological models, the one-dimensional Frenkel-Kontorova (FK) model [7] in its atomic stick-slip regime [8,9]. The MSM construction leads to the identification of a handful of natural variables which describe the steady-state dynamics of friction in this model.Starting from the set of configurations obtained with a simulation of steady-state sliding, the first step of the construction is to define a metric in the high dimensional phase space of the original model, then used to identify a small number of microstates, by means of a recently proposed clustering algorithm [10]. The statistics of transitions between configurations is shown to be compatible with a description as a Markov process betwee...

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Markov state modeling of sliding friction

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“…(9). Obviously iterating the equations backward in time gives terms involving longer strings of neighboring sites and hence longer spatial correlations.…”

Section: Analytical Approachmentioning

confidence: 99%

“…[8][9][10] are quite complicated. Attempts have been made [14] to introduce simpler models which capture the essential features.…”

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“…In particular, the Frenkel-Kontorova (FK) model [3,4] and its generalizations [5][6][7] have been studied within the context of tribophysics. Braun and coworkers [8][9][10] studied the atomic current in one and two-dimensional atomic systems in the presence of a periodic potential under the influence of a dc driving force within the approach of Langevin equations. In tribophysics, the driving force emerges owing to the motion of one of the two substrates separarted by a thin atomic layer.…”

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Cellular automaton models of driven diffusive Frenkel-Kontorova-type systems

et al. 1999

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Three cellular automaton (CA) models of increasing complexity are introduced to model driven diffusive systems related to the generalized FrenkelKontorova (FK) models recently proposed by Braun et al. [Phys. Rev. E 58, 1311]. The models are defined in terms of parallel updating rules.Simulation results are presented for these models. The features are qualitatively similar to those models defined previously in terms of sequentially

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“…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].…”

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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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Dynamical phase diagram of the dc-driven underdamped Frenkel-Kontorova chain

Cited by 39 publications

References 21 publications

Markov state modeling of sliding friction

Markov state modeling of sliding friction

Cellular automaton models of driven diffusive Frenkel-Kontorova-type systems

Driven dynamics: A photodriven Frenkel-Kontorova model

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