James H. Nolen

  • Associate Professor of Mathematics
External address: 243 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2800
Office Hours: 

Mondays, 1-2:30
Wednesdays, 10:30-12

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, 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.   I also study the asymptotic behavior of stochastic processes.

Education & Training
  • 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

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

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