A first approach to engineering problems in nanosized systems requires a thorough understanding of how physical properties change as size decreases from the macroscale. One important class of properties that can be severely affected by such a downward size shift are transport properties - classical mass, momentum and energy transport. Using atomistic simulation techniques, primarily molecular dynamics, and statistical expressions for diffusion, viscosity, and thermal conductivity formulated in terms of atomistic properties, three case studies of transport in important, nanosized systems are investigated, including confined water systems, silicon-germanium nanos- tructures, and carbon nanostructures. In the first study of confined water systems, diffusion and viscosity are of primary interest, as recent experimental studies have shown notably increased rates of diffusion through nano-confined carbon nanotube structures. In this work, a full treatment of the transport properties is provided in both water clusters and water thin films, both having characteristic size scales under 11 nm. The diffusion, viscosity, and thermal conductivity in the nanosized systems are all shown to be significantly different from bulk water systems, with diffusion and thermal transport increasing and viscosity decreasing. For silicon-germanium nanostructures, the thermal transport properties are exclusively considered, with the problem of interest concerning the control of thermal transport through a strict control on the nanostructure. Quantum dot superlattices are shown to be effective structures for controlling the thermal transport properties, the available range of thermal conductivity using these structures being 0.1-160 W/mK. The final study concerns graphene nanostructures, which in terms of thermal transport have some of the highest thermal conductivities of any available materials. Control of thermal transport properties is again of primary importance, with various physical aspects - defects, shape, and size - being probed in graphene, graphene nano ribbons, carbon nanotubes, and fullerenes to determine their influence on transport; overall, these structures yield a large range of thermal transport, 10-2500 W/mK.
