9 citations · 19 across the 7 of their papers we have counts for
10 papers
On the linearised force balance condition in the analysis of atomistic dislocation models
Julian Braun, Thomas Hudson
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…
Higher-order Far-field Boundary Conditions for Crystalline Defects
Julian Braun, Christoph Ortner, Yangshuai Wang +1
Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field ex…
Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect
Julian Braun, Thomas Hudson, Christoph Ortner
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance…
An atomistic derivation of von-Kármán plate theory
Julian Braun, Bernd Schmidt
We derive von-Kármán plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a -limit when considerin…
Sharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect
Julian Braun, Christoph Ortner
We consider the geometry relaxation of an isolated point defect embedded in a homogeneous crystalline solid, within an atomistic description. We prove a sharp convergence rate for…
Thermodynamic Limit of the Transition Rate of a Crystalline Defect
Julian Braun, Manh Hong Duong, Christoph Ortner
We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation f…