dorsal/arxiv
View SchemaPhysical Meaning and Experimental Check of a Variational Principle for Macro-to-Micro Transition
| Authors | Mayeul Arminjon, Didier Imbault |
|---|---|
| Categories | |
| ArXiv ID | physics/0611226 |
| URL | https://arxiv.org/abs/physics/0611226 |
| Journal | Micro- and Macrostructural Aspects of Thermoplasticity, Allemagne (1999) 197-206 |
Abstract
It is argued that, for strongly non-linear behaviors, a fully deterministic position can hardly be maintained in the micro-macro transitions. This is due to the lack of information on the relevant boundary conditions, and to the tendency of non-linear dynamical systems to have a "horizon of predictibility". In the variational micro-macro model proposed by us, the data of the microscopic behavior plus the overall stimulus has to be supplemented by a "heterogeneity parameter". In this model, the macro-to-micro transition depends on the validity of a "principle of minimal heterogeneity" (PMH). It is shown that the PMH has a close relation to the maximum entropy principle.
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"abstract": "It is argued that, for strongly non-linear behaviors, a fully deterministic\nposition can hardly be maintained in the micro-macro transitions. This is due\nto the lack of information on the relevant boundary conditions, and to the\ntendency of non-linear dynamical systems to have a \"horizon of predictibility\".\nIn the variational micro-macro model proposed by us, the data of the\nmicroscopic behavior plus the overall stimulus has to be supplemented by a\n\"heterogeneity parameter\". In this model, the macro-to-micro transition depends\non the validity of a \"principle of minimal heterogeneity\" (PMH). It is shown\nthat the PMH has a close relation to the maximum entropy principle.",
"arxiv_id": "physics/0611226",
"authors": [
"Mayeul Arminjon",
"Didier Imbault"
],
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"physics.class-ph"
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"journal_ref": "Micro- and Macrostructural Aspects of Thermoplasticity, Allemagne\n (1999) 197-206",
"title": "Physical Meaning and Experimental Check of a Variational Principle for Macro-to-Micro Transition",
"url": "https://arxiv.org/abs/physics/0611226"
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