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, 1-2:30
Wednesdays, 10:30-12

Research Areas and Keywords

Analysis
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
Probability
homogenization of partial differential equations, stochastic dynamical systems, random media, asymptotic analysis

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.

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

  • B.S., Davidson College 2000

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 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. 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. "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. Full Text

Nolen, J, and Papanicolaou, G. "Fine scale uncertainty in parameter estimation for elliptic equations." Inverse Problems 25.11 (2009). 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

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