WIAS Preprint No. 725, (2002)

Micro-macro transitions by interpolation, smoothing, averaging and scaling of particle trajectories


  • Dreyer, Wolfgang
  • Guckel, Ralf

2010 Mathematics Subject Classification

  • 35D05


  • Micro-macro transitions, Multiscale problems, Young measures




We consider a Newtonian system of many diatomicmolecules each of which consisting of two atoms of equal mass whichare separated by a fixed distance. The barycenters are allowed to movealong some fixed straight line. Moreover each molecule has an additionalrotational degree of freedom. The atoms of neighbouring moleculesinteract to each other by a generic pair potential. By means of thisexample we propose a new method for deriving macroscopic models from microscopic ones. The method is based on the definition of macroscopicobservables and the derivation of corresponding balance laws by interpolation smoothing/averaging and subsequent scaling of particle trajectories.

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