Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization
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 surf...
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| Fformat: | Report |
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2005
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| _version_ | 1826296693955493888 |
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| author | Ortner, C |
| author_facet | Ortner, C |
| author_sort | Ortner, C |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:20:17Z |
| format | Report |
| id | oxford-uuid:cac9ea7c-d04d-4546-81c5-e23f8c4f26ab |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:20:17Z |
| publishDate | 2005 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:cac9ea7c-d04d-4546-81c5-e23f8c4f26ab2022-03-27T07:09:53ZContinuum Limit of a One-Dimensional Atomistic Energy Based on Local MinimizationReporthttp://purl.org/coar/resource_type/c_93fcuuid:cac9ea7c-d04d-4546-81c5-e23f8c4f26abMathematical Institute - ePrintsUnspecified2005Ortner, CFor 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. |
| spellingShingle | Ortner, C Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization |
| title | Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization |
| title_full | Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization |
| title_fullStr | Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization |
| title_full_unstemmed | Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization |
| title_short | Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization |
| title_sort | continuum limit of a one dimensional atomistic energy based on local minimization |
| work_keys_str_mv | AT ortnerc continuumlimitofaonedimensionalatomisticenergybasedonlocalminimization |