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James H. Nolen, Associate Professor

James H. Nolen

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.

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 (Fall 2016):

  • MATH 555.01, ORDINARY DIFF EQUATIONS Synopsis
    Physics 235, TuTh 10:05 AM-11:20 AM
Office Hours:

Mondays 2-3:30pm, Wednesdays 2-3:30pm.
Education:

Ph.D.University of Texas at 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

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. 3-4 (2014), pp. 661-700, 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. 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, ISSN 1556-1801 [pdf], [doi]  [abs]
    4. J Nolen and L Ryzhik, 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, ISSN 0294-1449 [pdf], [doi]  [abs]
    5. A Mellet, J Nolen, JM Roquejoffre and L Ryzhik, Stability of generalized transition fronts, Communications in Partial Differential Equations, vol. 34 no. 6 (2009), pp. 521-552, ISSN 0360-5302 [pdf], [doi]  [abs]
    6. J Nolen and J Xin, 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, ISSN 0294-1449 [pdf], [doi]  [abs]
    7. P Cardaliaguet, J Nolen and PE Souganidis, Homogenization and Enhancement for the G-Equation, Archive for Rational Mechanics and Analysis, vol. 199 no. 2 (2011), pp. 527-561, ISSN 0003-9527 [4160], [doi]  [abs]
    Selected Grant Support

    • Analysis of Fluctuations, 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