Physical Meaning and Experimental Check of a Variational Principle for Macro-to-Micro Transition

Details Physical Meaning and Experimental Check of a Variational Principle for Macro-to-Micro Transition Physical Meaning and Experimental Check of a Variational Principle for Macro-to-Micro Transition

2006-11-23

arxiv.org/abs/physics/0611226v1

Micro- and Macrostructural Aspects of Thermoplasticity, Allemagne (1999) 197-206

Physics

Classical Physics

Scientific paper

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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