ABSTRACT
There is a long history of developing mathematical representations capable of providing behavioral predictions of physical parameters on the atomic, molecular, microscopic, and macroscopic scales. Over the past half century, simulation programs have been developed to support the computerized solution of these mathematical representations which, in some cases, are discretized with billions of degrees of freedom (dofs) and solved on massively parallel computers with thousands of processors. Historically, scientists and engineers have applied these models (simulation programs) to solve problems on a single physical scale. However, in recent years it has become clear that to continue to make advances in the areas of nanotechnology and biotechnology, and to develop new products and treatments based on those advances, scientists and engineers must be able to solve sets of coupled models active over multiple interacting scales. For example, the development of new materials will require the design of structure and function across a hierarchy of scales, starting at the molecular scale to define nanoscale building blocks that will be used to construct mesoscale features that may be combined into micron-scale weaves that could be used in the manufacturing of complete parts (Figure 12.1). Such capabilities are clearly central to the development of nanoelectronics devices and future biomedical device design as well as many of other future products.
