James H. Nolen
- Associate Professor of Mathematics
Research Areas and Keywords
PDE & Dynamical Systems
I study partial differential equations and probability, which have been used to model many phenomena in the natural sciences and engineering. In some cases, the parameters for a partial differential equation are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in differential equations modeling random phenomena and whether one can describe the statistical properties of solutions to these equations. Asymptotic analysis has been a common theme in much of my research. Current research interests include: reaction diffusion equations, homogenization of PDEs, stochastic dynamics, interacting particle systems.
Boye, D, Silversmith, A, Nolen, J, Rumney, L, Shaye, D, Smith, B, and Brewer, K. "Red-to-green up-conversion in Er-doped SiO2 and SiO2–TiO2 sol–gel silicate glasses." Journal of Luminescence 94-95 (December 2001): 279-282. Full Text
Nolen, JH, Cohn, S, Iyer, G, and Pego, R. "Anomalous diffusion in one and two dimensional combs(Submitted).".
Nolen, JH, Lu, J, and Lu, Y. "Scaling limit of the Stein variational gradient descent: the mean field regime(Submitted).".