- Associate Professor of Mathematics

**External address:**243 Physics Bldg, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2862

**Office Hours:**

Mondays, 10:30-12:00

Wednesdays, 2:00-3:30

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# James H. Nolen

**External address: **243 Physics Bldg, Durham, NC 27708**Internal office address: **Box 90320, Durham, NC 27708-0320**Phone: **(919) 660-2862**Office Hours: **
### Research Areas and Keywords

##### Analysis

##### Biological Modeling

##### PDE & Dynamical Systems

##### Physical Modeling

##### Probability

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.

##### Education & Training

### Selected Grants

### Fellowships, Supported Research, & Other Grants

## Pages

Nolen, J, Pavliotis, GA, and Stuart, AM. "Multiscale modelling and inverse problems." January 1, 2012. Full Text

## Mathematics

## Academics

## Current Students

## Future Students

- Associate Professor of Mathematics

Mondays, 10:30-12:00

Wednesdays, 2:00-3:30

partial differential equations, probability, asymptotic analysis, homogenization

asymptotic analysis

reactive diffusion equations & applications, homogenization of partial differential equations, random media, asymptotic analysis

asymptotic analysis

homogenization of partial differential equations, stochastic dynamical systems, random media, asymptotic analysis

Ph.D., University of Texas at Austin 2006

B.S., Davidson College 2000

CAREER: Research and training in stochastic dynamics awarded by National Science Foundation (Principal Investigator). 2014 to 2019

Analysis of Fluctuations awarded by National Science Foundation (Principal Investigator). 2010 to 2015

NSF Postdoctoral Research Fellowship awarded by National Science Foundation (2006 to 2008)

Mourrat, J-C, and Nolen, J. "Scaling limit of the corrector in stochastic homogenization." *The Annals of Applied Probability* 27.2 (April 2017): 944-959.
Full Text

Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "Convergence to a single wave in the Fisher-KPP equation." *Chinese Annals of Mathematics, Series B* 38.2 (March 2017): 629-646.
Full Text

Gloria, A, and Nolen, J. "A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus." *Communications on Pure and Applied Mathematics* 69.12 (December 2016): 2304-2348.
Full Text

Nolen, J. "Normal approximation for the net flux through a random conductor." *Stochastics and Partial Differential Equations: Analysis and Computations* 4.3 (September 2016): 439-476.
Full Text

Nolen, JH, Roquejoffre, J-M, and Ryzhik, L. "Refined long time asymptotics for Fisher-KPP fronts (Submitted)." (2016).

Hamel, F, Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "The logarithmic delay of KPP fronts in a periodic medium." *Journal of the European Mathematical Society* 18.3 (2016): 465-505.
Full Text

Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "Power-Like Delay in Time Inhomogeneous Fisher-KPP Equations." *Communications in Partial Differential Equations* 40.3 (March 4, 2015): 475-505.
Full Text

Lu, J, and Nolen, J. "Reactive trajectories and the transition path process." *Probability Theory and Related Fields* 161.1-2 (February 2015): 195-244.
Full Text Open Access Copy

Huckemann, S, Mattingly, J, Miller, E, and Nolen, J. "Sticky central limit theorems at isolated hyperbolic planar singularities." *Electronic Journal of Probability* 20.0 (2015).
Full Text Open Access Copy

Bhamidi, S, Hannig, J, Lee, CY, and Nolen, J. "The importance sampling technique for understanding rare events in Erdős–Rényi random graphs." *Electronic Journal of Probability* 20.0 (2015).
Full Text

120 Science Drive

117 Physics Building

Campus Box 90320

Durham, NC 27708-0320

phone: 919.660.2800

fax: 919.660.2821

dept@math.duke.edu