James H. Nolen, Professor of Mathematics

James H. Nolen

Please note: James has left the "Probability: Theory and Applications" group at Duke University; some info here might not be up to date.

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.

Office Location:  120 Science Drive, Durham, NC 27708
Office Phone:  (919) 660-2862
Email Address: send me a message
Web Page:  http://math.duke.edu/~nolen/

Teaching (Spring 2024):

Teaching (Fall 2024):

Office Hours:

Mondays 10:30am-12:00
Wednesdays 2:00pm-3:30

Education:

Ph.D.University of Texas, Austin2006
B.S.Davidson College2000
Specialties:

Analysis
Probability
Applied Math
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  

    Representative Publications

    1. Nolen, J, Normal approximation for a random elliptic equation, Probability Theory and Related Fields, vol. 159 no. 3-4 (2013), pp. 1-40, Springer Nature, ISSN 0178-8051 [pdf], [doi]  [abs]
    2. J. Lu and J. Nolen, Reactive trajectories and the transition path process., Probability Theory and Related Fields (January, 2014) [1744], [doi]
    3. Nolen, J, A central limit theorem for pulled fronts in a random medium, Networks and Heterogeneous Media, vol. 6 no. 2 (2011), pp. 167-194, American Institute of Mathematical Sciences (AIMS), ISSN 1556-1801 [pdf], [doi]  [abs]
    4. Nolen, J; Ryzhik, L, Traveling waves in a one-dimensional heterogeneous medium, Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, vol. 26 no. 3 (2009), pp. 1021-1047, Elsevier BV, ISSN 0294-1449 [pdf], [doi]  [abs]
    5. Mellet, A; Nolen, J; Roquejoffre, JM; Ryzhik, L, Stability of generalized transition fronts, Communications in Partial Differential Equations, vol. 34 no. 6 (2009), pp. 521-552, Informa UK Limited, ISSN 0360-5302 [pdf], [doi]  [abs]
    6. Nolen, J; 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, vol. 26 no. 3 (2009), pp. 815-839, Elsevier BV, ISSN 0294-1449 [pdf], [doi]  [abs]
    7. Cardaliaguet, P; Nolen, J; Souganidis, PE, Homogenization and Enhancement for the G-Equation, Archive for Rational Mechanics and Analysis, vol. 199 no. 2 (2011), pp. 527-561, Springer Nature, ISSN 0003-9527 [4160], [doi]  [abs]
    Selected Grant Support

    • Analysis of Fluctuations for PDEs with Random Coefficients, National Science Foundation, DMS-1007572.      
    • CAREER: Research and training in stochastic dynamics, National Science Foundation, DMS-1351653.