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.

Includes supplementary material: sn.pub/extras

Tutorials.- Multiscale Methods for Subsurface Flow.- Multiscale Modelling of Complex Fluids: A Mathematical Initiation.- Fast Algorithms for Boundary Integral Equations.- Wavelets andWavelet Based Numerical Homogenization.- Multiscale Computations for Highly Oscillatory Problems.- Projects.- Quantum Mechanics/Classical Mechanics Modeling of Biological Systems.- Multiple Scales in Solid State Physics.- Climate Sensitivity and Variability Examined in a Global Climate Model.- Coarse-scale Modeling of Flow in Gas-injection Processes for Enhanced Oil Recovery.- Photo-Ionization Dynamics Simulation.- Time Scales in Molecular Reaction Dynamics.- Complex Band Structures of Spintronics Materials.