Anharmonic localized surface vibrations in a scalar model

Bonart, D.; Mayer, Andreas; Schröder, U.

doi:10.1103/physrevb.51.13739

Cited by 32 publications

(17 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, keeping in mind, that equations (42) are approximative solutions of the original discrete equations of motion (12) only, this is not a real restriction. The decoupling condition, which we will consider in the following, is valid in the continuum approximation only, doesn't imply that the description of the discrete model is restricted by any means.…”

Section: Solitary Waves and Their Interactionsmentioning

confidence: 95%

“…The first one is similar to the method used in [12]. It is rather heuristic but faster than the second approach which is based on the multiple-scale analysis (see Appendix).…”

Section: System and Equations Of Motionmentioning

confidence: 99%

“…Inserting equation (19) into the equations of motion and keeping terms (12) up to the second order of u (1) (n, t) we obtain the following set of coupled equations…”

Section: System and Equations Of Motionmentioning

confidence: 99%

“…Pouget et al [11] studied nonlinear a e-mail: franz.mertens@theo.phy.uni-bayreuth.de properties of two-dimensional anharmonic lattices on periodical substrates and investigated energy localization and gap local pulses. Bonart and coauthors [12] studied anharmonic excitations which are localized at the surface of two-and three-dimensional lattices.…”

Section: Introductionmentioning

confidence: 99%

“…Gaididei et al [13] showed that the propagation of axi-symmetric nonlinear acoustic pulses is governed by a radial Boussinesq equation which is a cylindrical analogue of the one-dimensional Boussinesq equation. Bonart et al [12] considered intrinsic localized anharmonic modes at an edge of a 3-dimensional crystal taking into account realistic interatomic interaction potentials and proved their stability over times much longer the vibrational period. Eilbeck [14] found in a two-dimensional hexagonal lattice model localized propagating breathers.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Envelope solitary waves on two-dimensional lattices with in-plane displacements

1998

View full text Add to dashboard Cite

We investigate envelope solitary waves on square lattices with two degrees of freedom and nonlinear nearest and next-nearest neighbor interactions. We consider solitary waves which are localized in the direction of their motion and periodically modulated along the perpendicular direction. In the quasimonochromatic approximation and low-amplitude limit a system of two coupled nonlinear Schrödinger equations (CNLS) is obtained for the envelopes of the longitudinal and transversal displacements. For the case of bright envelope solitary waves the solvability condition is discussed, also with respect to the modulation. The stability of two special solution classes (type-I and type-II) of the CNLS equations is tested by molecular dynamics simulations. The shape of type-I solitary waves does not change during propagation, whereas the width of type-II excitations oscillates in time.

show abstract

Section: Solitary Waves and Their Interactionsmentioning

confidence: 95%

“…The first one is similar to the method used in [12]. It is rather heuristic but faster than the second approach which is based on the multiple-scale analysis (see Appendix).…”

Section: System and Equations Of Motionmentioning

confidence: 99%

“…Inserting equation (19) into the equations of motion and keeping terms (12) up to the second order of u (1) (n, t) we obtain the following set of coupled equations…”

Section: System and Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Envelope solitary waves on two-dimensional lattices with in-plane displacements

1998

View full text Add to dashboard Cite

show abstract

Block architecture influence on the structure and mechanical performance of drawn polyurethane elastomers

Fernández-d’Arlas

Corcuera

Runt

et al. 2014

Polymer International

View full text Add to dashboard Cite

Some natural biopolymers such as spider silk exhibit superb mechanical properties, characterised by their great toughness. Synthetic polyurethane (PU) copolymers also endow great toughness but lack silk's stiffness and strength. The aim of this work was to elucidate the role of segment block architectural features that influence PU stiffness and strength after cold drawing. For this purpose PUs with varied soft segment character, crystalline versus rubbery, as well as with different hard segment chemistries, 4,4 -diphenylmethane diisocyanate/1,4-butanediol versus 1,6-hexamethylene diisocyanate/1,4-butanediol, were synthesised by a two-step polymerisation method. We found that the architecture of both block segments has a dramatic influence on drawn PU mechanical performance, in which PUs with crystallisable soft segments and crystalline hard segments are shown to have a greater impact on developing stiffer and stronger materials.

show abstract