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.