James H. Nolen

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.

Education & Training
  • Ph.D., University of Texas, Austin 2006

  • B.S., Davidson College 2000

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. Full Text

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. Full Text

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. Full Text

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. Full Text

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. Full Text

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. Full Text

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. Full Text

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. Full Text

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. Full Text

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. Full Text

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. Full Text