Micro-macro transitions by interpolation, smoothing, averaging and scaling of particle trajectories
- Dreyer, Wolfgang
- Guckel, Ralf
2010 Mathematics Subject Classification
- 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.