Topological solitons and dislocations in two- and three-dimensional anisotropic crystals

Christiansen, Peter Leth; Savin, A. V.; Zolotaryuk, A. V.

doi:10.1103/physrevb.57.13564

Cited by 10 publications

(5 citation statements)

References 26 publications

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“…The interaction with these other atoms can be modelled by an effective periodic on-site potential. Importantly, it has been shown that the effective periodic potential can be justified via a self-consistent microscopic model where only interparticle interactions are taken into account [28].…”

Section: Simple Models: From Non-interacting To Interacting Atomsmentioning

confidence: 99%

Driven dynamics of simplified tribological models

Vanossi¹,

Braun²

2007

J. Phys.: Condens. Matter

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Over the last decade, remarkable developments in nanotechnology, notably the use of atomic and friction force microscopes (AFM/FFM), the surface-force apparatus (SFA) and the quartz-crystal microbalance (QCM), have provided the possibility to build experimental devices able to perform analysis on well-characterized materials at the nano-and microscale. Simultaneously, tremendous advances in computing hardware and methodology (molecular dynamics techniques and ab initio calculations) have dramatically increased the ability of theoreticians to simulate tribological processes, supplying very detailed information on the atomic scale for realistic sliding systems. This acceleration in experiments and computations, leading often to very detailed yet complex data, has deeply stimulated the search, rediscovery and implementation of simpler mathematical models such as the generalized Frenkel-Kontorova and Tomlinson models, capable of describing and interpreting, in a more immediate way, the essential physics involved in nonlinear sliding phenomena.

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Section: Simple Models: From Non-interacting To Interacting Atomsmentioning

confidence: 99%

Driven dynamics of simplified tribological models

Vanossi¹,

Braun²

2007

J. Phys.: Condens. Matter

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“…The problem of dynamics of interacting chains may be considered as a generalization of the Frenkel-Kontorova model about a chain in an external spatially periodic potential field [10]. In quasi-1D systems this periodic potential is created by adjacent chains and is not static, which makes the problem very difficult [11]. It was suggested in [1] that some insight can be achieved by modelling the chains interaction using the Langevin approach.…”

Section: Dissipative Chainsmentioning

confidence: 99%

Quasi‐one‐dimensional systems: fluctuations, transport and interplay

Plyukhin¹

2008

Phys. Status Solidi (c)

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In a one dimensional lattice thermal fluctuations destroy the long‐range order making particles of the lattice move on a scale much larger than the lattice spacing. We discuss the assumption that this motion may be responsible for the transport of localized electrons in a system of weakly coupled chains. The model with diffusing localization sites gives a temperature‐independent mobility with a crossover to an activated dependence at high temperature. This prediction is consistent with and might account for experimental results on discotic liquid crystals and certain biopolymers. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…The present 2D model was first introduced in Ref. 4. One can take into account also transversal displacements of particles.…”

Section: The 2d Strongly Anisotropic Crystal: Free and On Substratementioning

confidence: 99%

“…In the case of weak background potential ͑weakly discrete system͒ it seems to be especially appropriate for polymer crystals: quasi-1D topological solitonlike excitations predicted by its continuum limit, the sine-Gordon ͑sG͒ equation, can propagate in a chain of a twodimensional ͑2D͒ system of coupled chains 4,5 and even in a helix chain in a three-dimensional ͑3D͒ model of polymer crystal ͑see, for example, Ref. 6͒.…”

Section: Introductionmentioning

confidence: 99%

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

Savin¹,

Zubova

Manevitch

2005

Phys. Rev. B

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We investigate a two-dimensional ͑2D͒ strongly anisotropic crystal ͑2D SAC͒ on substrate: 2D system of coupled linear chains of particles with strong intrachain and weak interchain interactions, each chain being subjected to the sine background potential. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well known Frenkel-Kontorova ͑FK͒ model. Depending on strengh of the substrate, the 2D SAC models a variety of physical systems: polymer crystals with identical chains having light side groups, an array of inductively coupled long Josephson junctions, anisotropic crystals having light and heavy sublattices. Continuum limit of the FK model, the sine-Gordon ͑sG͒ equation, allows two types of soliton solutions: topological solitons and breathers. It is known that the quasi-one-dimensional topological solitons can propagate also in a chain of 2D system of coupled chains and even in a helix chain in a three-dimensional model of polymer crystal. In contrast to this, numerical simulation shows that the long-living breathers inherent to the FK model do not exist in the 2D SAC with weak background potential. The effect changes scenario of kink-antikink collision with small relative velocity: at weak background potential the collision always results only in intensive phonon radiation while kink-antikink recombination in the FK model results in long-living low-frequency sG breather creation. We found the survival condition for breathers in the 2D SAC on substrate depending on breather frequency and strength of the background potential. The survival condition bears no relation to resonances between breather frequency and frequencies of phonon band-contrary to the case of the FK model.

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Topological solitons and dislocations in two- and three-dimensional anisotropic crystals

Cited by 10 publications

References 26 publications

Driven dynamics of simplified tribological models

Driven dynamics of simplified tribological models

Quasi‐one‐dimensional systems: fluctuations, transport and interplay

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

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