Homogenization of the Peierls-Nabarro model for dislocation dynamics
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Publication:444923
DOI10.1016/j.jde.2012.06.019zbMath1264.35264arXiv1007.2915OpenAlexW2964072561MaRDI QIDQ444923
Stefania Patrizi, Régis Monneau
Publication date: 24 August 2012
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1007.2915
Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Crystals in solids (74N05) Viscosity solutions to PDEs (35D40) Integro-partial differential equations (35R09)
Related Items (18)
Variational modeling of dislocations in crystals in the line-tension limit ⋮ A fractional glance to the theory of edge dislocations ⋮ Relaxation times for atom dislocations in crystals ⋮ Strongly Nonlocal Dislocation Dynamics in Crystals ⋮ Reduced ODE dynamics as formal relativistic asymptotics of a Peierls–Nabarro model ⋮ Discrete-to-continuum convergence of charged particles in 1D with annihilation ⋮ Derivation of the 1-D Groma-Balogh equations from the Peierls-Nabarro model ⋮ A gradient system with a wiggly energy and relaxed EDP-convergence ⋮ Discrete Dislocation Dynamics with Annihilation as the Limit of the Peierls–Nabarro Model in One Dimension ⋮ Properties of Screw Dislocation Dynamics: Time Estimates on Boundary and Interior Collisions ⋮ From the Peierls-Nabarro model to the equation of motion of the dislocation continuum ⋮ The Peierls-Nabarro model as a limit of a Frenkel-Kontorova model ⋮ Chaotic orbits for systems of nonlocal equations ⋮ Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ Discrete-To-Continuum Limits of Particles with an Annihilation Rule ⋮ The continuum limit of interacting dislocations on multiple slip systems ⋮ Homogenization and Orowan's law for anisotropic fractional operators of any order
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