# James H. Nolen

- Associate Professor of Mathematics

**External address:**029C Physics Bldg, Durham, NC 27708

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

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

**Office Hours:**

Mondays 1:30-3:00pm

Wednesdays 1:30-3:00pm

### Research Areas and Keywords

##### Analysis

partial differential equations, probability, asymptotic analysis, homogenization

##### Biological Modeling

asymptotic analysis

##### PDE & Dynamical Systems

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

##### Physical Modeling

asymptotic analysis

##### Probability

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

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.

### Selected Grants

Support for Southeastern Probability Conference awarded by National Science Foundation (Co Investigator). 2020 to 2024

CAREER: Research and training in stochastic dynamics awarded by National Science Foundation (Principal Investigator). 2014 to 2020

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

### Fellowships, Supported Research, & Other Grants

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

Nolen, James, et al. “Refined long-time asymptotics for Fisher–KPP fronts.” *Communications in Contemporary Mathematics*, vol. 21, no. 07, World Scientific Pub Co Pte Lt, Nov. 2019, pp. 1850072–1850072. *Crossref*, doi:10.1142/s0219199718500724.
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Henderson, Nicholas T., et al. “Ratiometric GPCR signaling enables directional sensing in yeast.” *Plos Biol*, vol. 17, no. 10, Oct. 2019, p. e3000484. *Pubmed*, doi:10.1371/journal.pbio.3000484.
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Lu, J., et al. “Scaling limit of the Stein variational gradient descent: The mean field regime.” *Siam Journal on Mathematical Analysis*, vol. 51, no. 2, Jan. 2019, pp. 648–71. *Scopus*, doi:10.1137/18M1187611.
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Cristali, I., et al. “Block size in geometric(P)-biased permutations.” *Electronic Communications in Probability*, vol. 23, Jan. 2018. *Scopus*, doi:10.1214/18-ECP182.
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Mourrat, J. C., and J. Nolen. “Scaling limit of the corrector in stochastic homogenization.” *Annals of Applied Probability*, vol. 27, no. 2, Apr. 2017, pp. 944–59. *Scopus*, doi:10.1214/16-AAP1221.
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Nolen, J., et al. “Convergence to a single wave in the Fisher-KPP equation.” *Chinese Annals of Mathematics. Series B*, vol. 38, no. 2, Mar. 2017, pp. 629–46. *Scopus*, doi:10.1007/s11401-017-1087-4.
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Gloria, A., and J. Nolen. “A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus.” *Communications on Pure and Applied Mathematics*, vol. 69, no. 12, Dec. 2016, pp. 2304–48. *Scopus*, doi:10.1002/cpa.21614.
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Nolen, J. “Normal approximation for the net flux through a random conductor.” *Stochastics and Partial Differential Equations: Analysis and Computations*, vol. 4, no. 3, Jan. 2016, pp. 439–76. *Scopus*, doi:10.1007/s40072-015-0068-4.
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Hamel, F., et al. “The logarithmic delay of KPP fronts in a periodic medium.” *Journal of the European Mathematical Society*, vol. 18, no. 3, Jan. 2016, pp. 465–505. *Scopus*, doi:10.4171/JEMS/595.
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Bhamidi, S., et al. “The importance sampling technique for understanding rare events in Erdős-Rényi random graphs.” *Electronic Journal of Probability*, vol. 20, Oct. 2015. *Scopus*, doi:10.1214/EJP.v20-2696.
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## Pages

Nolen, J., et al. “Multiscale modelling and inverse problems.” *Lecture Notes in Computational Science and Engineering*, vol. 83, 2012, pp. 1–34. *Scopus*, doi:10.1007/978-3-642-22061-6_1.
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