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### James H. Nolen, Associate Professor of Mathematics

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: | 243 Physics Bldg, Durham, NC 27708 |

Office Phone: | (919) 660-2862 |

Email Address: | |

Web Page: | http://math.duke.edu/~nolen/ |

**Teaching (Fall 2018):**

- MATH 340.01,
*ADVANCED INTRO PROBABILITY*Synopsis- Physics 235, TuTh 01:25 PM-02:40 PM

**Office Hours:**- Mondays, 3:30-5:00

Wednesdays, 10:30-12:00

**Education:**Ph.D. University of Texas at 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)- Nolen, J,
*Normal approximation for a random elliptic equation*, Probability Theory and Related Fields, vol. 159 no. 3-4 (2013), pp. 1-40, ISSN 0178-8051 [pdf], [doi] [abs] - J. Lu and J. Nolen,
*Reactive trajectories and the transition path process.*, Probability Theory and Related Fields (January, 2014) [1744], [doi] - 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, ISSN 1556-1801 [pdf], [doi] [abs] - Nolen, J; Ryzhik, L,
*Traveling waves in a one-dimensional heterogeneous medium*, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 26 no. 3 (2009), pp. 1021-1047, ISSN 0294-1449 [pdf], [doi] [abs] - Mellet, A; Nolen, J; Roquejoffre, J-M; Ryzhik, L,
*Stability of generalized transition fronts*, Communications in Partial Differential Equations, vol. 34 no. 6 (2009), pp. 521-552, ISSN 0360-5302 [pdf], [doi] [abs] - Nolen, J; Xin, J,
*Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows*, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 26 no. 3 (2009), pp. 815-839, ISSN 0294-1449 [pdf], [doi] [abs] - 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, ISSN 0003-9527 [4160], [doi] [abs]

- Nolen, J,

**Selected Grant Support***Analysis of Fluctuations*, National Science Foundation, DMS-1007572.