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Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization

Abstract:

For atomistic energies, global minimization gives the wrong qualitative behaviour and therefore continuum limits should be formulated in terms of local minimization. In this paper, a possible process is suggested, to describe local minimization for a simple one-dimensional problem with body and surface energy. It is shown that an atomistic gradient flow evolution converges to a continuum gradient flow as the spacing between the atomis tends to zero. In addition, the convergence of local minim...

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Publication date:
2005-07-05
URN:
uuid:cac9ea7c-d04d-4546-81c5-e23f8c4f26ab
Local pid:
oai:eprints.maths.ox.ac.uk:1142

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