Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 20 min ago
PreprintCC BY 4.0arXiv

On the linearised force balance condition in the analysis of atomistic dislocation models

  • Julian Braun
  • Thomas Hudson
Open at sourcePDFDOICite

Abstract

A technical condition arising in the analysis of atomistic models for dislocations is studied. Key estimates for the far-field strain behaviour proved in Ehrlacher, Ortner, Shapeev (2016) rely on a summation-by-parts argument for linearised forces, under conditions of sufficient decay and of vanishing net force in an infinite system. In particular, the latter condition is required for an application of this theory to the standard far-field dislocation predictor, but the vanishing of the associated force sum has not been fully justified. Here, the missing verification of this condition is provided and its role in determining the far-field decay of the corrector is clarified. It is moreover shown that for more general physically compatible predictors, the linearised force sum need not vanish, leading to slower decay and potentially divergent finite-domain approximations.

Related

  1. On linearised and elliptic versions of the Kashiwara–Vergne Lie algebra
    Hidekazu Furusho, Nao Komiyama, Elise Raphael +1
    Journal of Lie TheoryPeer-reviewedLicence not statedFull text12 citedAlgebra & number theoryOpenAlex
  2. The uniform-in-time electrostatic limit of the linearised Vlasov-Maxwell system: the Poisson equilibrium
    Marnie Smith
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  3. Oversimplified dislocation dynamics from semilinear homogenization. Heat and damped wave equations
    A Ghorbel, R Monneau
    HALPreprintPublisher termsFull textGeneral mathematicsHAL
  4. Semidiscrete Modeling of Dislocation-Disclination Systems: Finite Element Formulation
    Pierluigi Cesana, Edoardo Fabbrini, Andrés A. León Baldelli +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsNumerical analysis & scientific computingarXiv
  5. Residual stress gradient in a thin film within the dislocation pile-up theory
    A. V. Druzhinin, C. Cancellieri
    arXivPreprintCC BY 4.0Full textMathematical physicsCondensed matterarXiv

Cite

BibTeXRIS
BibTeX
@misc{braun2026linearised,
  title = {{On the linearised force balance condition in the analysis of atomistic dislocation models}},
  author = {Julian Braun and Thomas Hudson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39642},
  eprint = {2609.39642},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39642},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the linearised force balance condition in the analysis of atomistic dislocation models
AU  - Julian Braun
AU  - Thomas Hudson
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39642
UR  - https://arxiv.org/abs/2609.39642
AB  - A technical condition arising in the analysis of atomistic models for dislocations is studied. Key estimates for the far-field strain behaviour proved in Ehrlacher, Ortner, Shapeev (2016) rely on a summation-by-parts argument for linearised forces, under conditions of sufficient decay and of vanishing net force in an infinite system. In particular, the latter condition is required for an application of this theory to the standard far-field dislocation predictor, but the vanishing of the associated force sum has not been fully justified. Here, the missing verification of this condition is provided and its role in determining the far-field decay of the corrector is clarified. It is moreover shown that for more general physically compatible predictors, the linearised force sum need not vanish, leading to slower decay and potentially divergent finite-domain approximations.
ER  -