As subsequent chapters in this report will describe, theory, modeling, and simulation (TM&S) play a significant role in almost every branch of nanotechnology. TM&S consists of three distinct components. A theory can be defined as a set of scientific principles that explains phenomena-a succinct description of a class of problems.
Modeling is the analytical/numerical applications of theory to solve specific problems.Simulation aims to faithfully render the physical problem in the greatest possible detail, so that the critical features emerge organically-not as a consequence of the ingenuity, insights, high level abstractions, and simplifications that characterize modeling. Each of the three TM&S components plays an important role, but the opportunities of the next decade will require a stronger emphasis on the modeling component. Multiscale modeling, in particular, will be essential in addressing the next decade's challenges in technology exploration and nanomanufacturing. Finally, it should be understood that each subdiscipline of nanotechnology has its own TM&S community; these communities share many commonalities in underlying theoretical foundations, numerical and computational methods, and modeling approaches. This chapter focuses on issues, challenges, and opportunities common to TM&S across the broad spectrum of nanotechnology.