# James H. Nolen

- Associate Professor of Mathematics

**External address:**243 Physics Bldg, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2862

**Office Hours:**

Mondays, 10:30-12:00

Wednesdays, 2:00-3:30

### Research Areas and Keywords

##### Analysis

##### Biological Modeling

##### PDE & Dynamical Systems

##### Physical Modeling

##### Probability

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.

### Fellowships, Supported Research, & Other Grants

NSF Postdoctoral Research Fellowship awarded by National Science Foundation (2006 to 2008)

Nolen, J, and Xin, J. "Computing reactive front speeds in random flows by variational principle." *Physica D: Nonlinear Phenomena* 237.23 (2008): 3172-3177.
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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.
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Xin, J, and Nolen, 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 (September 2005): 1217-1234.
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Nolen, J, and Xin, J. "A variational principle based study of KPP minimal front speeds in random shears." *Nonlinearity* 18.4 (2005): 1655-1675.
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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)

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 (June 2004): 43-47.
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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)

Nolen, J, and Xin, J. "Reaction-Diffusion Front Speeds in Spatially-Temporally Periodic Shear Flows." *Multiscale Modeling & Simulation* 1.4 (January 2003): 554-570.
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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.
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