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, 3:30-5:00
Wednesdays, 10:30-12:00

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 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, 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. 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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