# 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, 3:30-5:00

Wednesdays, 10:30-12:00

### 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 Novikov, A. "Homogenization of the G-equation with incompressible random drift in two dimensions." *Communications in Mathematical Sciences* 9.2 (2011): 561-582.

Nolen, J, Xin, J, and Yu, Y. "Bounds on front speeds for inviscid and viscous G-equations." *Methods and Applications of Analysis* 16.4 (December 2009). (Academic Article)

Nolen, J, and Xin, J. "KPP Fronts in 1D Random Drift." *Discrete and Continuous Dynamical Systems B* 11.2 (2009). (Academic Article)

Mellet, A, Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "Stability of generalized transition fronts." *Communications in Partial Differential Equations* 34.6 (2009): 521-552.
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Nolen, J, and Ryzhik, L. "Traveling waves in a one-dimensional heterogeneous medium." *Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis* 26.3 (2009): 1021-1047.
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Nolen, J, and Xin, J. "Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows." *Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis* 26.3 (2009): 815-839.
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Nolen, J, and Papanicolaou, G. "Fine scale uncertainty in parameter estimation for elliptic equations." *Inverse Problems* 25.11 (2009).
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Nolen, J, and Xin, J. "KPP fronts in a one-dimensional random drift." *Discrete and Continuous Dynamical Systems - Series B* 11.2 (2009): 421-442.
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Nolen, J, and Xin, J. "Variational principle and reaction-diffusion front speeds in random flows." *ICIAM07-Proceedings* (December 2008): 1040701-1040702. (Academic Article)

Nolen, J, Papanicolaou, G, and Pironneau, O. "A framework for adaptive multiscale methods for elliptic problems." *Multiscale Modeling and Simulation* 7.1 (2008): 171-196.
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