A model for a driven Frenkel–Kontorova chain

Quapp, Wolfgang; Bofill, Josep María

doi:10.1140/epjb/e2019-90703-0

Cited by 9 publications

(61 citation statements)

References 90 publications

(134 reference statements)

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“…The iMin can be a compressed structure, or, contrary, a stretched structure, compare again the case N =23 in Ref. [26]. In the cases N =17 and N =20, other lower iMin exist.…”

Section: Examples Of Fk Chains For Commensurate Misfit 2/3 41 Low DIsupporting

confidence: 59%

“…Then the full chain is moved by approximate a s along the NT. The existence of such a path does not mean that it is the MEP over the lowest possible SPs through the mountains, as was already obtained in the case N =23, discussed elsewhere [26], but it should be an LEP with SP 1 energy near the other MEP. The iMin can be a compressed structure, or, contrary, a stretched structure, compare again the case N =23 in Ref.…”

Section: Examples Of Fk Chains For Commensurate Misfit 2/3 41 Low DImentioning

confidence: 76%

“…They are flat SPs near a shoulder, in the promontory region. The obtained NT can be accepted if we sort these two SPs as shoulders [26]. A connection of two SPs of index one is forbidden for regular NTs by the NT theory.…”

Section: Chains With Critical Lengthmentioning

confidence: 99%

“…Beginning with Section 4 we enrol a gallery of examples for different misfit parameters, and different small chains with 6 to 101 particles. For M F =2/3, the cases N =2 to N =5, and N =23 particles are discussed elsewhere [25,26]. Here we first continue this case M F =2/3 in Section 4.…”

Section: Introductionmentioning

confidence: 98%

“…One can find recent applications of the Newton trajectory (NT) theory to the FK model in Refs. [25,26]. In many applications, one particularly interesting aspect of the FK model is its driven form.…”

Section: Introductionmentioning

confidence: 99%

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Sliding paths for series of Frenkel-Kontorova models – a contribution to the concept of 1D-superlubricity

Quapp

Bofill

2019

Eur. Phys. J. B

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Newton trajectories are used to calculate low energy pathways for a series of Frenkel-Kontorova models with 6 and up to 69 particles thus up to a medium chain, and an expedition to 101 particles. The model is a finite chain with free-end boundary conditions. It has two competing potentials and an additional, external force. We optimize stationary structures and calculate the low energy paths between global minimums for a movement of the chain over its on-site potential, if an external tilting by a pushand/or pull direction is applied. We propose to understand a low energy path for a possibility of a superlubricity of the chain. We compare different misfit parameters. The result is that the minimums differ only little, however, the critical length of the chain, Ncr, depends on the misfit parameter. Ncr describes the end of a 'good' calculability of the Newton trajectory which follows the low energy pathway of the chain through the potential energy surface, for a movement of the chain along the axis. We discuss reasons for the boundary of an Ncr. However, we assume that the low energy paths exist beyond their calculability by NTs.

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“…The iMin can be a compressed structure, or, contrary, a stretched structure, compare again the case N =23 in Ref. [26]. In the cases N =17 and N =20, other lower iMin exist.…”

Section: Examples Of Fk Chains For Commensurate Misfit 2/3 41 Low DIsupporting

confidence: 59%

Section: Examples Of Fk Chains For Commensurate Misfit 2/3 41 Low DImentioning

confidence: 76%

Section: Chains With Critical Lengthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sliding paths for series of Frenkel-Kontorova models – a contribution to the concept of 1D-superlubricity

Quapp

Bofill

2019

Eur. Phys. J. B

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Barnes Update Applied in the Gauss–Newton Method: An Improved Algorithm to Locate Bond Breaking Points

Bofill

Valero

Ribas‐Ariño

et al. 2021

J. Chem. Theory Comput.

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A mechanochemical reaction is a reaction induced by mechanical energy. A general accepted model for this type of reaction consists of a first-order perturbation on the associated potential energy surface (PES) of the unperturbed molecular system due to mechanical stress or pulling force. Within this theoretical framework, the so-called optimal barrier breakdown points or optimal bond breaking points (BBPs) are critical points of the unperturbed PES where the Hessian matrix has a zero eigenvector that coincides with the gradient vector. Optimal BBPs are “catastrophe points” that are particularly important because their associated gradient indicates how to optimally harness tensile forces to induce reactions by transforming a chemical reaction into a barrierless process. Building on a previous method based on a nonlinear least-squares minimization to locate BBPs (Bofill et al., J. Chem. Phys. 2017, 147, 152710-10), we propose a new algorithm to locate BBPs of any molecular system based on the Gauss–Newton method combined with the Barnes update for a nonsymmetric Jacobian matrix, which is shown to be more appropriate than the Broyden update. The efficiency of the new method is demonstrated for a multidimensional model PES and two medium size molecular systems of interest in enzymatic catalysis and mechanochemistry.

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The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model

2020

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We propose a Frenkel-Kontorova model for a 1D chain of electrons forming a Wigner solid over 4 He. It is a highly idealized picture, but with the model at hand we can study the movement of the chain. We find out that the energetically most preferable movement is the successive sliding of a kink or an antikink through the chain. Then the force for a movement does not depend on the length of the chain. The force uniformly applied to all electrons must be larger than a force exciting only a kink or an antikink. We calculate two cases, one with stiff 'springs' between the electrons and one with weak 'springs'. The side potential of the 'dimples' is additionally damped at the periphery. We study the cases with 33, 66, and 101 particles.

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A model for a driven Frenkel–Kontorova chain

Cited by 9 publications

References 90 publications

Sliding paths for series of Frenkel-Kontorova models – a contribution to the concept of 1D-superlubricity

Sliding paths for series of Frenkel-Kontorova models – a contribution to the concept of 1D-superlubricity

Barnes Update Applied in the Gauss–Newton Method: An Improved Algorithm to Locate Bond Breaking Points

The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model

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