This three-year award for US-France cooperative research in applied mathematics involves Walter A. Strauss, C. Shu and Yan Guo of Brown University and Pierre Degond of the Universite Paul Sabatier and Frederic Poupaud of the Universite de Nice. The project is aimed at the design, development, analysis and numerical simulation of hybrid quantum kinetic models and their application to the simulation of quantum semiconductor devices. In many applications, the quantum effects are important only in subregions of the device, while the phenomena in a larger domain are governed by classical transport. The objective of this project is to design models that are able to switch from a classical description to a quantum description. The US investigators bring to this collaboration expertise in classical modeling and simulation. This is complemented by French expertise in quantum models.