James H. Nolen, Professor

My research is in the area of probability and partial differential equations, which have been used to model many phenomena in the natural sciences and engineering.  Asymptotic analysis has been a common theme in much of my research.  Current research interests include: stochastic dynamics, interacting particle systems, reaction-diffusion equations, applications to biological models.

Contact Info:

Office Location:	120 Science Drive, Durham, NC 27708
Email Address:
Web Page:	http://math.duke.edu/~nolen/

Teaching (Fall 2024):

• ETHICS 247S.01, HUMAN FLOURISHING, DIGITAL AGE Synopsis

  Perkins 060, M 03:05 PM-05:35 PM

  (also cross-listed as COMPSCI 247S.01)

• MATH 340.01, ADVANCED INTRO PROBABILITY Synopsis

  Gray 220, TuTh 10:05 AM-11:20 AM

  (also cross-listed as STA 231.01)

• MATH 740.01, ADVANCED INTRO PROBABILITY Synopsis

  Gray 220, TuTh 10:05 AM-11:20 AM

• MATH 545.01, STOCHASTIC CALCULUS Synopsis

  Gross Hall 330, TuTh 10:05 AM-11:20 AM

• MATH 790-90.01, MINICOURSE IN ADVANCED TOPICS Synopsis

  Physics 205, MW 01:25 PM-02:40 PM

Office Hours:

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

Education:

Ph.D.	University of Texas, Austin	2006
B.S.	Davidson College	2000

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. 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.