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Abstract: A common problem of atomistic materials modelling is to determine properties of crystalline defects, such as structure, energetics, mobility, from which

meso-scopic material properties or coarse-grained models can be derived (e.g.,

Kinetic Monte-Carlo, Discrete Dislocation Dynamics, Griffith-type fracture

laws). In this talk I will focus on one the most basic tasks, computing the

equilibrium configuration of a crystalline defect, but will also also comment on

free energy and transition rate computations.

A wide range of numerical strategies, including the classical supercell method

(periodic boundary conditions) or flexibe boundary conditions (discrete BEM),

but also more recent developments such as atomistic/continuum and QM/MM hybrid schemes, can be interpreted as Galerkin discretisations with variational crimes, for an infinite-dimensional nonlinear variational problem. This point of view is effective in studying the structure of exact solutions, identify approximation parameters, derive rigorous error bounds, optimise and construct novel schemes with superior error/cost ratio.

Time permitting I will also discuss how this framework can be used to analyse

model errors in interatomic potentials and how this can feed back into the

developing of new interatomic potentials by machine learning techniques.