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.
Nolen, J, and Xin, J. "Computing reactive front speeds in random flows by variational principle." Physica D: Nonlinear Phenomena 237.23 (2008): 3172-3177. Full Text
Nolen, J, and Xin, J. "Variational Principle of KPP Front Speeds in Temporally Random Shear Flows with Applications." Communications in Mathematical Physics 269 (2007): 493-532. (Academic Article)
Nolen, J, and Xin, J. "A variational principle for KPP front speeds in temporally random shear flows." Communications in Mathematical Physics 269.2 (2007): 493-532. Full Text
Nolen, J, and Xin, J. "Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle." Discrete and Continuous Dynamical Systems 13.5 (2005): 1217-1234.
Nolen, J, Rudd, M, and Xin, J. "Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds." Dynamics of PDE 2 (2005): 1-24. (Academic Article)
Nolen, J, and Xin, J. "A variational principle based study of KPP minimal front speeds in random shears." Nonlinearity 18.4 (2005): 1655-1675. Full Text
Nolen, J, and Xin, J. "Min-Max Variational Principles and Fronts Speeds in Random Shear Flows." Methods and Applications of Analysis 11.4 (2004): 635-644. (Academic Article)
Boye, DM, Valdes, TS, Nolen, JH, Silversmith, AJ, Brewer, KS, Anderman, RE, and Meltzer, RS. "Transient and persistent spectral hole burning in Eu3+-doped sol-gel produced SiO2 glass." Journal of Luminescence 108.1-4 (2004): 43-47. Full Text
Nolen, J, and Xin, J. "Reaction-Diffusion Front Speeds in Spatially-Temporally Periodic Shear Flows." Multiscale Modeling & Simulation 1.4 (January 2003): 554-570. Full Text
Boye, DM, Silversmith, AJ, Nolen, J, Rumney, L, Shaye, D, Smith, BC, and Brewer, KS. "Red-to-green up-conversion in Er-doped SiO2 and SiO2-TiO2 sol-gel silicate glasses." Journal of Luminescence 94-95 (2001): 279-282. Full Text