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James Nolen, Assistant Professor

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

Teaching (Spring 2015):

  • MATH 453.01, INTRO PARTIAL DIFF EQUA Synopsis
    Physics 259, TuTh 10:05 AM-11:20 AM
  • MATH 545.01, STOCHASTIC CALCULUS Synopsis
    Physics 259, TuTh 08:30 AM-09:45 AM
Office Hours:

Tuesdays 4:20-5:20. Wednesdays 10:00-12:00.
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

Current Ph.D. Students   (Former Students)

    Representative Publications   (More Publications)

    1. J. Nolen, Normal approximation for a random elliptic equation, Probability Theory and Related Fields, vol. 159 no. 3 (2014), pp. 661-700 [pdf], [doi]
    2. J. Lu and J. Nolen, Reactive trajectories and the transition path process., Probability Theory and Related Fields (January, 2014) [1744], [doi]
    3. J. Nolen, A central limit theorem for pulled fronts in a random medium, Networks and Heterogeneous Media, vol. 6 no. 2 (2011), pp. 167-194 [pdf], [doi]
    4. 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]
    5. 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]
    6. 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]
    7. P. Cardaliaguet, J. Nolen, P.E. Souganidis, Homogenization and enhancement for the G-equation, Archive for Rational Mechanics and Analysis, vol. 199 no. 2 (2011), pp. 527-561 [4160]
    Selected Grant Support

    • AMC-SS: 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.      

     

    dept@math.duke.edu
    ph: 919.660.2800
    fax: 919.660.2821

    Mathematics Department
    Duke University, Box 90320
    Durham, NC 27708-0320