The Mathematical Institute, University of Oxford, Eprints Archive

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

Ortner, Christoph (2005) Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization. Technical Report. Unspecified. (Submitted)

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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 minimizers is investigated, in the case of both elastic deformation and fracture.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1142
Deposited By:Lotti Ekert
Deposited On:12 May 2011 08:34
Last Modified:12 May 2011 08:34

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