James H. Nolen

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 2:30-4:00
Wednesdays, 10:30-12:00

Research Areas and Keywords

partial differential equations, probability, asymptotic analysis, homogenization
Biological Modeling
asymptotic analysis
PDE & Dynamical Systems
reactive diffusion equations & applications, homogenization of partial differential equations, random media, asymptotic analysis
Physical Modeling
asymptotic analysis
homogenization of partial differential equations, stochastic dynamical systems, random media, asymptotic analysis

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.

Education & Training
  • Ph.D., University of Texas at Austin 2006

  • B.S., Davidson College 2000

Fellowships, Supported Research, & Other Grants

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

Nolen, J. "A central limit theorem for pulled fronts in a random medium." Networks and Heterogeneous Media 6.2 (2011): 167-194. Full Text

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 Papanicolaou, G. "Fine scale uncertainty in parameter estimation for elliptic equations." Inverse Problems 25.11 (November 26, 2009). Full Text

Nolen, J, and Xin, J. "Asymptotic spreading of KPP reactive fronts in incompressible space–time random flows." Annales De L'Institut Henri Poincare (C) Non Linear Analysis 26.3 (May 2009): 815-839. Full Text

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, JM, and Ryzhik, L. "Stability of generalized transition fronts." Communications in Partial Differential Equations 34.6 (2009): 521-552. Full Text

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. Full Text

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. Full Text

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. Full Text