EAN: 9783540888567

MULTISCALE MODELING AND SIMULATION IN SCIENCE K...

Most problems in science involve many scales in time and space. An example is turbulent ?ow
where the important large scale quantities of lift and drag of a wing depend on the behavior of
the small vortices in the boundarylayer. Another example is chemical reactions with
concentrations of the species varying over seconds and hours while the time scale of the
oscillations of the chemical bonds is of the order of femtoseconds. A third example from
structural mechanics is the stress and strain in a solid beam which is well described by
macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A
common dif?culty with the simulation of these problems and many others in physics  chemistry
and biology is that an attempt to represent all scales will lead to an enormous computational
problem with unacceptably long computation times and large memory requirements. On the other
hand  if the discretization at a coarse level ignoresthe?nescale
informationthenthesolutionwillnotbephysicallymeaningful. The in?uence of the ?ne scales must be
incorporated into the model. This volume is the result of a Summer School on Multiscale
Modeling and S- ulation in Science held at Boso ¤n  Lidingo ¤ outside Stockholm  Sweden  in
June 2007. Sixty PhD students from applied mathematics  the sciences and engineering parti-
pated in the summer school.

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