Name
Abstract | ||
|---|---|---|
For atomistic material models, global minimization gives the wrong qualitative behavior; a theory of equilibrium solutions needs to be defined in different terms. In this paper, a concept based on gradient flow evolutions, to describe local minimization for simple atomistic models based on the Lennard-Jones potential, is presented. As an application of this technique, it is shown that an atomistic gradient flow evolution converges to a gradient flow of a continuum energy as the spacing between the atoms tends to zero. In addition, the convergence of the resulting equilibria is investigated in the case of elastic deformation and a simple damaged state. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/050643982 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
gradient flows,lambda-convexity,atomistic models,continuum limit | Convergence (routing),Mathematical optimization,Convexity,Mathematical analysis,Atom,Continuum (design consultancy),Minification,Minimisation (psychology),Deformation (engineering),Balanced flow,Mathematics | Journal |
Volume | Issue | ISSN |
38 | 4 | 0036-1410 |
Citations | PageRank | References |
1 | 1.36 | 0 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christoph Ortner | 1 | 74 | 16.77 |