Systems at the nanoscale are distinguished by both their material structures and their physics. The nanoscale is the intermediate length scale between systems of a few atoms and continuum systems. Nanoscale systems involve a number of atoms that is large enough so that a direct description of every atom is quite complex, but small enough that a continuum description is not valid. Second, the nanoscale is the scale at which quantum physics and classical physics intersect. Because of these characteristics, nanosystems are very complex and their descriptions are data-intensive. In addition, many degrees of freedom of nanosystems are difficult to observe and manipulate experimentally.
For these reasons, mathematical and computational methods are expected to play a major role in nanoscience and nanoengineering. Mathematics and computation can provide effective theory and simulations for analysis and interpretation of experimental results, model-based prediction of nanoscale phenomena, and design and control of nanoscale systems. Computational methods, such as density functional theory (DFT) and kinetic Monte Carlo (KMC), have already had major success in nanoscience, and there are still many opportunities for further involvement of mathematics and computation in nanoscience. Exploiting these opportunities will require collaboration between mathematical scientists and nanosystems researchers. Research at the nanoscale is naturally multi-disciplinary. Material sciences, life sciences and system sciences are all intimately involved in many of the current thrusts in nanoscale science. Mathematics also plays an important role in the interaction of these different disciplines, since they all use data, simulation and visualization.
The new National Nanotechnology Initiative has highlighted the importance of nanoscale science and technology. This initiative is directed at accelerating the pace of research on the nanoscale in order to support its applications to electronics, medicine, and other fields. This initiative has spawned major new programs, such as the Nanoscale Science and Engineering Initiative at NSF and programs on spintronics, quantum computing and bio-computing at DARPA.
(UCLA, Mathematics and Materials Science)
James Heath (UCLA)
Mitchell Luskin (University of Minnesota, Twin Cities)
Antonio Redondo (Los Alamos National Laboratory, Theoretical Division)
Peter Shor (AT&T, Research)