Multiscale modeling and computation

Multiscale modeling and computation is a rapidly evolving area of research that will have a fundamental impact on computational science and applied mathematics and will influence the way we view the relation between mathematics and science. Even though multiscale problems have long been studied in mathematics, the current excitement is driven mainly by the use of mathematical models in the applied sciences: in particular, material science, chemistry, fluid dynamics, and biology. Problems in these areas are often multiphysics in nature; namely, the processes at different scales are governed by physical laws of different character: for example, quantum mechanics at one scale and classical mechanics at another. Emerging from this intense activity is a need for new mathematics and new ways of interacting with mathematics. Fields such as mathematical physics and stochastic processes, which have so far remained in the background as far as modeling and computation is concerned, will move to the frontier. New questions will arise, new priorities will be set as a result of the rapid evolution in the computational fields. There are several reasons for the timing of the current interest. Modeling at the level of a single scale, such as molecular dynamics or continuu