Potential field theory and its applications to classical mechanical problems

Advances in many scientific fields are expected to come from work in nanotechnology. Engineering at nano-scales presents novel problems that classical mechanics cannot solve. Many engineers are uncomfortable designing at this level because classical or continuum mechanics does not apply and quantum mechanics is said to apply in a tangible way. There are unique opportunities to contribute to the design, controls, and analysis of systems that are particularly suited to mechanical engineering. Within the derivations of classical mechanics are assumptions that limit its use to bulk engineering. These assumptions are examined to determine what principles can be extended to smaller scales. To allow engineers to do their job at these scales, it is necessary to understand strength and how changing scales affects the strength of material this leads directly to sets of variables necessary for engineering at any scale. Potential field theory is an old method that is experiencing a resurgence of interest. Potential fields are used to study quantum mechanics at the atomic scale, crack and dislocation mobility at the micro-scale, and even bulk analysis. It encompasses many problems that can be formulated using partial differential equations. These series solutions are well suited for computerized numerical approximation. Because of recent advances in computational abilities, potential field theory deserves a fresh look as a candidate for multiscale modeling and as the math that binds each level together