James Nolen, Assistant Professor of Mathematics

James Nolen
Office Location:  243 Physics
Office Phone:  919-660-2862
Email Address: send me a message
Web Page:  http://math.duke.edu/~nolen/

Education:

PhDUniversity of Texas at Austin2006
BSDavidson College2000
Specialties:

Applied Math
Analysis
Probability
Research Interests: Partial differential equations, stochastic processes, random media, applied mathematics, 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.

Areas of Interest:

partial differential equations
stochastic processes
asymptotic analysis
homogenization theory
front propagation
reaction-diffusion equations

Keywords:

partial differential equations • stochastic processes • asymptotic analysis • applied mathematics

Current Ph.D. Students  

  • Esteban Chavez  
Representative Publications

  1. J. Nolen and L. Ryzhik, Traveling waves in a one-dimensional heterogeneous medium, Annales de l'institut Henri Poincare -- Analyse Non Lineaire, vol. 26 no. 3 (2009), pp. 1021-1047 [pdf]
  2. A. Mellet, J. Nolen, J.-M. Roquejoffre, and L. Ryzhik, Stability of generalized transition fronts, Comm. PDE, vol. 34 no. 6 (2009), pp. 521-552 [pdf]
  3. J. Nolen and J. Xin, Asymptotic Spreading of KPP Reactive Fronts in Incompressible Space-Time Random Flows, Annales de l'institut Henri Poincare -- Analyse Non Lineaire, vol. 26 no. 3 (2009), pp. 815-839 [pdf]
  4. J. Nolen, G. Papanicolaou, O. Pironneau, A Framework for Adaptive Multiscale Methods for Elliptic Problems, SIAM Multiscale Modeling and Simulation, vol. 7 (2008), pp. 171-196, SIAM [pdf]
Selected Grant Support

  • AMC-SS: Analysis of Fluctuations for PDEs with Random Coefficients, National Science Foundation, DMS-1007572.