James H. Nolen
- Associate Professor of Mathematics
Research Areas and Keywords
PDE & Dynamical Systems
I study partial differential equations, which have been used to model many phenomena in the natural sciences and engineering. In many cases, the parameters for such equations are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in equations modeling random phenomena and whether one can describe the statistical properties of the solution to these equations. For example, I have worked on nonlinear partial differential equations that describe waves and moving interfaces in random media. This work involves ideas from both analysis and probability. I also study the asymptotic behavior of stochastic processes.
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. "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. "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. "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