James H. Nolen | Scholars@Duke

James H. Nolen
Professor of Mathematics

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.

Office Hours

Mondays 10:30am-12:00
Wednesdays 2:00pm-3:30

Current Appointments & Affiliations

Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2021

Contact Information

120 Science Drive, Durham, NC 27708
Box 90320, Durham, NC 27708-0320
nolen@math.duke.edu (919) 660-2862
http://math.duke.edu/~nolen/

Background
Education, Training, & Certifications
- Ph.D., University of Texas, Austin 2006
- B.S., Davidson College 2000
Previous Appointments & Affiliations
- Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2016 - 2021
- Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2009 - 2015
Leadership & Clinical Positions at Duke
- Director of Postdoctoral Training, August 2019
Academic Positions Outside Duke
- Postdoctoral Scholar, Mathematics Department, Stanford University. 2006 - 2008
Research
Selected Grants
- RTG: Training Tomorrow's Workforce in Analysis and Applications awarded by National Science Foundation 2021 - 2026
- Support for Southeastern Probability Conference awarded by National Science Foundation 2020 - 2024
- CAREER: Research and training in stochastic dynamics awarded by National Science Foundation 2014 - 2020
- Analysis of Fluctuations for PDEs with Random Coefficients awarded by National Science Foundation 2010 - 2015
Fellowships, Supported Research, & Other Grants
- NSF Postdoctoral Research Fellowship awarded by National Science Foundation 2006 - 2008
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Berestycki, J., Brunet, E., Nolen, J., & Penington, S. (2020). Brownian bees in the infinite swarm limit (Submitted).
    Link to Item
  - Hebbar, P., Koralov, L., & Nolen, J. (2020). Asymptotic behavior of branching diffusion processes in periodic media. Electronic Journal of Probability, 25, 1–40. https://doi.org/10.1214/20-EJP527
    Full Text Open Access Copy
  - Lim, T. S., Lu, Y., & Nolen, J. H. (2020). Quantitative propagation of chaos in a bimolecular chemical reaction-diffusion model. Siam Journal on Mathematical Analysis, 52(2), 2098–2133. https://doi.org/10.1137/19M1287687
    Full Text
  - Berestycki, J., Brunet, E., Nolen, J., & Penington, S. (2020). A free boundary problem arising from branching Brownian motion with selection (Accepted). Transactions of the American Mathematical Society. https://doi.org/10.1090/tran/8370
    Full Text Link to Item
  - Nolen, J. H., Cohn, S., Iyer, G., & Pego, R. (2020). Anomalous diffusion in comb-shaped domains and graphs. Communications in Mathematical Sciences, 18(7), 1815–1862. https://doi.org/10.4310/CMS.2020.v18.n7.a2
    Full Text Link to Item
  - Nolen, J., Roquejoffre, J.-M., & Ryzhik, L. (2019). Refined long-time asymptotics for Fisher–KPP fronts. Communications in Contemporary Mathematics, 21(07), 1850072–1850072. https://doi.org/10.1142/s0219199718500724
    Full Text
  - Henderson, N. T., Pablo, M., Ghose, D., Clark-Cotton, M. R., Zyla, T. R., Nolen, J., … Lew, D. J. (2019). Ratiometric GPCR signaling enables directional sensing in yeast. Plos Biol, 17(10), e3000484. https://doi.org/10.1371/journal.pbio.3000484
    Full Text Open Access Copy Link to Item
  - Lu, J., Lu, Y., & Nolen, J. (2019). Scaling limit of the Stein variational gradient descent: The mean field regime. Siam Journal on Mathematical Analysis, 51(2), 648–671. https://doi.org/10.1137/18M1187611
    Full Text
  - Nolen, J. H., Lu, J., & Lu, Y. (2019). Scaling limit of the Stein variational gradient descent: the mean field regime. Siam Journal on Mathematical Analysis, 51(2), 648–671.
    Link to Item
  - Nolen, J. H., Cristali, I., Ranjan, V., Steinberg, J., Beckman, E., Durrett, R., & Junge, M. (2018). Block size in Geometric(p)-biased permutations. Electronic Communications in Probability, 23, 1–10. https://doi.org/10.1214/18-ECP182
    Full Text Link to Item
  - Hamel, F., Nolen, J., Roquejoffre, J. M., & Ryzhik, L. (2016). The logarithmic delay of KPP fronts in a periodic medium. Journal of the European Mathematical Society, 18(3), 465–505. https://doi.org/10.4171/JEMS/595
    Full Text
  - Nolen, J., & Mourrat, J.-C. (2016). Scaling limit of the corrector in stochastic homogenization (Accepted). Annals of Applied Probability.
    Link to Item
  - Nolen, J., Roquejoffre, J.-M., & Ryzhik, L. (2016). Convergence to a single wave in the Fisher-KPP equation (Submitted).
    Link to Item
  - Bhamidi, S., Hannig, J., Lee, C. Y., & Nolen, J. (2015). The importance sampling technique for understanding rare events in Erdős-Rényi random graphs. Electronic Journal of Probability, 20. https://doi.org/10.1214/EJP.v20-2696
    Full Text
  - Nolen, J., Roquejoffre, J. M., & Ryzhik, L. (2015). Power-Like Delay in Time Inhomogeneous Fisher-KPP Equations. Communications in Partial Differential Equations, 40(3), 475–505. https://doi.org/10.1080/03605302.2014.972744
    Full Text
  - Lu, J., & Nolen, J. (2015). Reactive trajectories and the transition path process. Probability Theory and Related Fields, 161(1–2), 195–244. https://doi.org/10.1007/s00440-014-0547-y
    Full Text Open Access Copy
  - Gloria, A., & Nolen, J. (2015). A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus. Communications on Pure and Applied Mathematics. https://doi.org/10.1002/cpa.21614
    Full Text Link to Item
  - Nolen, J. (2015). Normal approximation for the net flux through a random conductor. Stochastic Partial Differential Equations: Analysis and Computations. https://doi.org/10.1007/s40072-015-0068-4
    Full Text
  - Huckemann, S., Mattingly, J. C., Miller, E., & Nolen, J. (2014). Sticky central limit theorems at isolated hyperbolic planar singularities. Arxiv Preprint Arxiv:1410.6879.
    Open Access Copy
  - Hotz, T., Huckemann, S., Le, H., Marron, J. S., Mattingly, J. C., Miller, E., … Skwerer, S. (2013). Sticky central limit theorems on open books. The Annals of Applied Probability, 23, 2238–2258. https://doi.org/10.1214/12-AAP899
    Full Text Open Access Copy
  - Nolen, J. (2013). Normal approximation for a random elliptic equation. Probability Theory and Related Fields, 1–40. https://doi.org/10.1007/s00440-013-0517-9
    Full Text
  - Hamel, F., Nolen, J., Roquejoffre, J. M., & Ryzhik, L. (2012). A short proof of the logarithmic Bramson correction in Fisher-KPP equations (Accepted). Networks and Heterogeneous Media.
    Link to Item
  - Matic, I., & Nolen, J. (2012). A Sublinear Variance Bound for Solutions of a Random Hamilton-Jacobi Equation. Journal of Statistical Physics, 149(2), 342–361. https://doi.org/10.1007/s10955-012-0590-y
    Full Text
  - Mellet, A., & Nolen, J. (2012). Capillary drops on a rough surface. Interfaces and Free Boundaries, 14(2), 167–184. https://doi.org/10.4171/IFB/278
    Full Text
  - Nolen, J., Roquejoffre, J. M., Ryzhik, L., & Zlatoš, A. (2012). Existence and Non-Existence of Fisher-KPP Transition Fronts. Archive for Rational Mechanics and Analysis, 203(1), 217–246. https://doi.org/10.1007/s00205-011-0449-4
    Full Text
  - Cardaliaguet, P., Nolen, J., & Souganidis, P. E. (2011). Homogenization and Enhancement for the G-Equation. Archive for Rational Mechanics and Analysis, 199(2), 527–561. https://doi.org/10.1007/s00205-010-0332-8
    Full Text
  - Nolen, J. (2011). An invariance principle for random traveling waves in one dimension. Siam Journal on Mathematical Analysis, 43(1), 153–188. https://doi.org/10.1137/090746513
    Full Text
  - Nolen, J. (2011). A central limit theorem for pulled fronts in a random medium. Networks and Heterogeneous Media, 6(2), 167–194. https://doi.org/10.3934/nhm.2011.6.167
    Full Text
  - Nolen, J., & Novikov, A. (2011). Homogenization of the G-equation with incompressible random drift in two dimensions. Communications in Mathematical Sciences, 9(2), 561–582. https://doi.org/10.4310/CMS.2011.v9.n2.a11
    Full Text
  - Nolen, J., Xin, J., & Yu, Y. (2009). Bounds on front speeds for inviscid and viscous G-equations. Methods and Applications of Analysis, 16(4).
    Link to Item
  - Nolen, J., & Papanicolaou, G. (2009). Fine scale uncertainty in parameter estimation for elliptic equations. Inverse Problems, 25(11). https://doi.org/10.1088/0266-5611/25/11/115021
    Full Text
  - Mellet, A., Nolen, J., Roquejoffre, J. M., & Ryzhik, L. (2009). Stability of generalized transition fronts. Communications in Partial Differential Equations, 34(6), 521–552. https://doi.org/10.1080/03605300902768677
    Full Text
  - Nolen, J., & Xin, J. (2009). KPP Fronts in 1D Random Drift. Discrete and Continuous Dynamical Systems B, 11(2).
    Link to Item
  - Nolen, J., & Xin, J. (2009). KPP fronts in a one-dimensional random drift. Discrete and Continuous Dynamical Systems Series B, 11(2), 421–442. https://doi.org/10.3934/dcdsb.2009.11.421
    Full Text
  - Nolen, J., & Ryzhik, L. (2009). Traveling waves in a one-dimensional heterogeneous medium. Annales De L’Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, 26(3), 1021–1047. https://doi.org/10.1016/j.anihpc.2009.02.003
    Full Text
  - Nolen, J., & Xin, J. (2009). Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows. Annales De L’Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, 26(3), 815–839. https://doi.org/10.1016/j.anihpc.2008.02.005
    Full Text
  - Nolen, J., & Xin, J. (2008). Variational principle and reaction-diffusion front speeds in random flows. Iciam07 Proceedings, 1040701–1040702.
  - Nolen, J., & Xin, J. (2008). Computing reactive front speeds in random flows by variational principle. Physica D: Nonlinear Phenomena, 237(23), 3172–3177. https://doi.org/10.1016/j.physd.2008.04.024
    Full Text
  - Nolen, J., Papanicolaou, G., & Pironneau, O. (2008). A framework for adaptive multiscale methods for elliptic problems. Multiscale Modeling and Simulation, 7(1), 171–196. https://doi.org/10.1137/070693230
    Full Text
  - Nolen, J., & Xin, J. (2007). Variational Principle of KPP Front Speeds in Temporally Random Shear Flows with Applications. Communications in Mathematical Physics, 269, 493–532.
    Link to Item
  - Nolen, J., & Xin, J. (2005). A variational principle based study of KPP minimal front speeds in random shears. Nonlinearity, 18(4), 1655–1675. https://doi.org/10.1088/0951-7715/18/4/013
    Full Text
  - Nolen, J., & Xin, J. (2005). Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle. Discrete and Continuous Dynamical Systems, 13(5), 1217–1234. https://doi.org/10.3934/dcds.2005.13.1217
    Full Text
  - Nolen, J., Rudd, M., & Xin, J. (2005). Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds. Dynamics of Pde, 2, 1–24.
    Link to Item
  - Boye, D. M., Valdes, T. S., Nolen, J. H., Silversmith, A. J., Brewer, K. S., Anderman, R. E., & Meltzer, R. S. (2004). Transient and persistent spectral hole burning in Eu³⁺-doped sol-gel produced SiO2 glass. Journal of Luminescence, 108(1–4), 43–47. https://doi.org/10.1016/j.jlumin.2004.01.008
    Full Text
  - Nolen, J., & Xin, J. (2004). Min-Max Variational Principles and Fronts Speeds in Random Shear Flows. Methods and Applications of Analysis, 11(4), 635–644.
    Link to Item
  - Nolen, J., & Xin, J. (2003). Reaction-diffusion front speeds in spatially-temporally periodic shear flows. Multiscale Modeling and Simulation, 1(4), 554–570. https://doi.org/10.1137/S1540345902420234
    Full Text
  - Boye, D. M., Silversmith, A. J., Nolen, J., Rumney, L., Shaye, D., Smith, B. C., & Brewer, K. S. (2001). Red-to-green up-conversion in Er-doped SiO2 and SiO2-TiO2 sol-gel silicate glasses. Journal of Luminescence, 94–95, 279–282. https://doi.org/10.1016/S0022-2313(01)00301-5
    Full Text
  - Lu, Y., Lu, J., & Nolen, J. (n.d.). Accelerating Langevin Sampling with Birth-death (Unpublished).
    Link to Item
  - Tough, O., & Nolen, J. (n.d.). The Fleming-Viot Process with McKean-Vlasov Dynamics (Submitted).
    Link to Item
- Conference Papers
  - Nolen, J., Pavliotis, G. A., & Stuart, A. M. (2012). Multiscale modelling and inverse problems. In Lecture Notes in Computational Science and Engineering (Vol. 83, pp. 1–34). https://doi.org/10.1007/978-3-642-22061-6_1
    Full Text
Teaching & Mentoring
Recent Courses
Scholarly, Clinical, & Service Activities
Service to the Profession
- Participant. Faculty Curriculum on Anti-Racism. Duke Office of Faculty Advancement. January 11, 2021 - January 14, 2021 2021
Service to Duke
- Director of Postdoctoral Training. Duke Mathematics Department. August 2019 2019

Some information on this profile has been compiled automatically from Duke databases and external sources. (Our About page explains how this works.) If you see a problem with the information, please write to Scholars@Duke and let us know. We will reply promptly.

Education, Training, & Certifications

Previous Appointments & Affiliations

Leadership & Clinical Positions at Duke

Academic Positions Outside Duke

Selected Grants

Fellowships, Supported Research, & Other Grants

Selected Publications

Academic Articles

Conference Papers

Recent Courses

Service to the Profession

Service to Duke