Gradient flows as a selection procedure for equilibria of nonconvex energies
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 Lenna...
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| Formato: | Journal article |
| Idioma: | English |
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2006
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| _version_ | 1826271598764621824 |
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| author | Ortner, C |
| author_facet | Ortner, C |
| author_sort | Ortner, C |
| collection | OXFORD |
| description | 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. © 2006 Society for Industrial and Applied Mathematics. |
| first_indexed | 2024-03-06T21:59:11Z |
| format | Journal article |
| id | oxford-uuid:4e01780e-8db7-4245-a4d3-4f92e50a1403 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:59:11Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:4e01780e-8db7-4245-a4d3-4f92e50a14032022-03-26T15:58:38ZGradient flows as a selection procedure for equilibria of nonconvex energiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4e01780e-8db7-4245-a4d3-4f92e50a1403EnglishSymplectic Elements at Oxford2006Ortner, CFor 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. © 2006 Society for Industrial and Applied Mathematics. |
| spellingShingle | Ortner, C Gradient flows as a selection procedure for equilibria of nonconvex energies |
| title | Gradient flows as a selection procedure for equilibria of nonconvex energies |
| title_full | Gradient flows as a selection procedure for equilibria of nonconvex energies |
| title_fullStr | Gradient flows as a selection procedure for equilibria of nonconvex energies |
| title_full_unstemmed | Gradient flows as a selection procedure for equilibria of nonconvex energies |
| title_short | Gradient flows as a selection procedure for equilibria of nonconvex energies |
| title_sort | gradient flows as a selection procedure for equilibria of nonconvex energies |
| work_keys_str_mv | AT ortnerc gradientflowsasaselectionprocedureforequilibriaofnonconvexenergies |