# 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 for PDEs with Random Coefficients 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)

Lim, T. S., et al. “Quantitative propagation of chaos in a bimolecular chemical reaction-diffusion model.” *Siam Journal on Mathematical Analysis*, vol. 52, no. 2, Jan. 2020, pp. 2098–133. *Scopus*, doi:10.1137/19M1287687.
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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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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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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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## 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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