NSF East Asia and Pacific Summer Institute for FY 2012 in China

Villavert John, Fountain CO

Investigators

Abstract

This action funds John Villavert of the University of Colorado at Boulder to conduct a research project, entitled "Mathematical examination of properties of solutions to important models in science and engineering," during the summer of 2012 at Shanghai Jiao Tong University in Shanghai, China. The host scientist is Lihe Wang. The Intellectual Merit of the research project is the development of novel mathematical tools that enable a deeper understanding of properties of solutions to physical models - models which are central to many branches of science and engineering. Some examples of such properties include whether the model of differential equations has solutions. If so, how many solutions are there, and do these solutions exhibit the correct physical behavior the model is attempting to capture? Further, the tools developed here may prove valuable in studying more general classes of mathematical models. Moreover, this research has far-reaching impacts not limited only to fundamental theory. For instance, the successful examination of one of the proposed models, important in fluid flow, would allow scientists to numerically compute its solutions - solutions which historically appeared to be nearly impossible to obtain and required vast computational resources. Tools developed in this research can help solve similar difficulties in long-standing open problems from other disciplines. Broader Impacts of an EAPSI fellowship include providing the Fellow a first-hand research experience outside the U.S.; an introduction to the science, science policy, and scientific infrastructure of the respective location; and an orientation to the society, culture and language. These activities meet the NSF goal to educate for international collaborations early in the career of its scientists, engineers, and educators, thus ensuring a globally aware U.S. scientific workforce.