Kinks in the Frenkel-Kontorova model with long-range interparticle interactions

Braun, O. M.; Kivshar, Yu. S.; Zelenskaya, I.

doi:10.1103/physrevb.41.7118

Cited by 97 publications

(74 citation statements)

References 38 publications

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“…the number of geometrical (residual) kinks. These excitations can be defined for any background commensurate atomic structure θ 0 = p/q, where p and q are relative prime integers [13,17]. If the concentration θ slightly deviates from the background value θ 0 , the ground state of the system corresponds to large domains with background commensurate coverage θ 0 , separated by localized incommensurate zones of compression (expansion) called kinks (antikinks).…”

Section: The Modelmentioning

confidence: 99%

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

et al. 1997

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Multistep dynamical phase transition from the locked to the running state of atoms in response to a dc external force is studied by MD simulations of the generalized Frenkel-Kontorova model in the underdamped limit. We show that the hierarchy of transition recently reported [Braun et al, Phys. Rev. Lett. 78, 1295] strongly depends on the value of the friction constant. A simple phenomenological explanation for the friction dependence of the various critical forces separating intermediate regimes is given.

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Section: The Modelmentioning

confidence: 99%

“…As in the simulation we study finite systems, we have to chose an appropriate system size to insert N k kinks into the θ 0 = p/q commensurate background structure; the integers N and M must satisfy the equation [17] …”

Section: The Modelmentioning

confidence: 99%

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

et al. 1997

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“…Kinks in the Frenkel-Kontorova model with long-range interparticle interactions were studied in Ref. [28]. The properties of time periodic spatially localized solutions (breathers) on discrete chains in the presence of algebraically decaying interactions were considered in Refs.…”

Section: Introductionmentioning

confidence: 99%

Map of discrete system into continuous

Tarasov

2006

Journal of Mathematical Physics

114

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Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the continuous limit is discussed. The one-dimensional systems of coupled oscillators for this type of longrange interactions are considered. The discrete equations of motion are mapped into the continuum equation with the Riesz fractional derivative.

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“…Solitons in a one-dimensional lattice with the long-range Lennard-Jones-type interaction were considered in [38]. Kinks in the Frenkel-Kontorova model with long-range interparticle interactions were studied in [39]. The properties of time periodic spatially localized solutions (breathers) on discrete chains in the presence of algebraically decaying interactions were considered in [35] and recently in [36].…”

Section: Introductionmentioning

confidence: 99%

Coupled oscillators with power-law interaction and their fractional dynamics analogues

Korabel

Zaslavsky

Tarasov

2007

Communications in Nonlinear Science and Numerical Simulation

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The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order α, when 0 < α < 2. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both types of simulations: using the chain of oscillators and using the continuous medium equation with the fractional derivative.

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Kinks in the Frenkel-Kontorova model with long-range interparticle interactions

Cited by 97 publications

References 38 publications

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

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

Map of discrete system into continuous

Coupled oscillators with power-law interaction and their fractional dynamics analogues

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