James H. Nolen | Scholars@Duke

James H. Nolen
Associate 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 2:30-4:00
Wednesdays, 10:30-12:00

Current Appointments & Affiliations

Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2016

Contact Information

243 Physics Bldg, 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 at Austin 2006
- B.S., Davidson College 2000
Duke Appointment History
- Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2009 - 2015
Academic Positions Outside Duke
- Postdoctoral Scholar, Mathematics Department, Stanford University. 2006 - 2008
Research
Selected Grants
- CAREER: Research and training in stochastic dynamics awarded by National Science Foundation 2014 - 2019
- Analysis of Fluctuations 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
  - Cristali, I, Ranjan, V, Steinberg, J, Beckman, E, Durrett, R, Junge, M, & Nolen, J. (2018). Block size in Geometric($p$)-biased permutations. Electronic Communications in Probability , 23 (0). Full Text
  - Mourrat, J-C, & Nolen, J. (2017, April). Scaling limit of the corrector in stochastic homogenization. The Annals of Applied Probability , 27 (2), 944-959. Full Text
  - Nolen, J, Roquejoffre, J-M, & Ryzhik, L. (2017, March). Convergence to a single wave in the Fisher-KPP equation. Chinese Annals of Mathematics, Series B , 38 (2), 629-646. Full Text
  - Gloria, A, & Nolen, J. (2016, December). A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus. Communications on Pure and Applied Mathematics , 69 (12), 2304-2348. Full Text
  - Nolen, J. (2016, September). Normal approximation for the net flux through a random conductor. Stochastics and Partial Differential Equations: Analysis and Computations , 4 (3), 439-476. Full Text
  - 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. Full Text
  - Nolen, J, Roquejoffre, J-M, & Ryzhik, L. (2015, March 4). Power-Like Delay in Time Inhomogeneous Fisher-KPP Equations. Communications in Partial Differential Equations , 40 (3), 475-505. Full Text
  - Lu, J, & Nolen, J. (2015, February). Reactive trajectories and the transition path process. Probability Theory and Related Fields , 161 (1-2), 195-244. Full Text Open Access Copy
  - Bhamidi, S, Hannig, J, Lee, CY, & Nolen, J. (2015). The importance sampling technique for understanding rare events in Erdős–Rényi random graphs. Electronic Journal of Probability , 20 (0). Full Text
  - Huckemann, S, Mattingly, J, Miller, E, & Nolen, J. (2015). Sticky central limit theorems at isolated hyperbolic planar singularities. Electronic Journal of Probability , 20 (0). Full Text Open Access Copy
  - Nolen, J. (2014, August). Normal approximation for a random elliptic equation. Probability Theory and Related Fields , 159 (3-4), 661-700. Full Text
  - Nolen, J. (2014). Normal approximation for a random elliptic equation. Probability Theory and Related Fields , 159 (3-4), 661-700. Full Text
  - Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, & Skwerer, S. (2013, December). Sticky central limit theorems on open books. The Annals of Applied Probability , 23 (6), 2238-2258. Full Text Open Access Copy
  - Hamel, F, Nolen, J, Roquejoffre, JM, & Ryzhik, L. (2012). A short proof of the logarithmic Bramson correction in Fisher-KPP equations(Accepted). Networks and Heterogeneous Media ,. (Academic Article) 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. Full Text
  - Mellet, A, & Nolen, J. (2012). Capillary drops on a rough surface. Interfaces and Free Boundaries , 14 (2), 167-184. Full Text
  - Nolen, J, Roquejoffre, JM, Ryzhik, L, & Zlatoš, A. (2012). Existence and Non-Existence of Fisher-KPP Transition Fronts. Archive for Rational Mechanics and Analysis , 203 (1), 217-246. Full Text
  - Cardaliaguet, P, Nolen, J, & Souganidis, PE. (2011). Homogenization and Enhancement for the G-Equation. Archive for Rational Mechanics and Analysis , 199 (2), 527-561. 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. Full Text
  - Nolen, J. (2011). An invariance principle for random traveling waves in one dimension. Siam Journal on Mathematical Analysis , 43 (1), 153-188. Full Text
  - Nolen, J. (2011). A central limit theorem for pulled fronts in a random medium. Networks and Heterogeneous Media , 6 (2), 167-194. Full Text
  - Nolen, J, Xin, J, & Yu, Y. (2009, December). Bounds on front speeds for inviscid and viscous G-equations. Methods and Applications of Analysis , 16 (4). (Academic Article) Link to Item
  - Nolen, J, & Papanicolaou, G. (2009, November 1). Fine scale uncertainty in parameter estimation for elliptic equations. Inverse Problems , 25 (11), 115021-115021. Full Text
  - Nolen, J, & Xin, J. (2009, May). Asymptotic spreading of KPP reactive fronts in incompressible space–time random flows. Annales De L'Institut Henri Poincare (C) Non Linear Analysis , 26 (3), 815-839. Full Text
  - Mellet, A, Nolen, J, Roquejoffre, JM, & Ryzhik, L. (2009). Stability of generalized transition fronts. Communications in Partial Differential Equations , 34 (6), 521-552. 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. Full Text
  - Nolen, J, & Xin, J. (2009). KPP Fronts in 1D Random Drift. Discrete and Continuous Dynamical Systems B , 11 (2). (Academic Article) 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. Full Text
  - Nolen, J, & Xin, J. (2008, December). Variational principle and reaction-diffusion front speeds in random flows. Iciam07 Proceedings ,, 1040701-1040702. (Academic Article)
  - Nolen, J, & Xin, J. (2008). Computing reactive front speeds in random flows by variational principle. Physica D: Nonlinear Phenomena , 237 (23), 3172-3177. 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. 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. (Academic Article) Link to Item
  - Nolen, J, & Xin, J. (2006, November 17). A Variational Principle for KPP Front Speeds in Temporally Random Shear Flows. Communications in Mathematical Physics , 269 (2), 493-532. Full Text
  - Xin, J, & Nolen, J. (2005, September). 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. Full Text
  - Nolen, J, & Xin, J. (2005, July 1). A variational principle based study of KPP minimal front speeds in random shears. Nonlinearity , 18 (4), 1655-1675. 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. (Academic Article) Link to Item
  - Boye, DM, Valdes, TS, Nolen, JH, Silversmith, AJ, Brewer, KS, Anderman, RE, & Meltzer, RS. (2004, June). Transient and persistent spectral hole burning in Eu3+-doped sol–gel produced SiO2 glass. Journal of Luminescence , 108 (1-4), 43-47. 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. (Academic Article) Link to Item
  - Nolen, J, & Xin, J. (2003, January). Reaction-Diffusion Front Speeds in Spatially-Temporally Periodic Shear Flows. Multiscale Modeling & Simulation , 1 (4), 554-570. Full Text
  - Boye, DM, Silversmith, AJ, Nolen, J, Rumney, L, Shaye, D, Smith, BC, & Brewer, KS. (2001, December). Red-to-green up-conversion in Er-doped SiO2 and SiO2–TiO2 sol–gel silicate glasses. Journal of Luminescence , 94-95 , 279-282. Full Text
  - Nolen, J, Roquejoffre, J-M, & Ryzhik, L. Refined long-time asymptotics for Fisher–KPP fronts(Published online). Communications in Contemporary Mathematics ,, 1850072-1850072. Full Text
  - Nolen, JH, Cohn, S, Iyer, G, & Pego, R. Anomalous diffusion in one and two dimensional combs(Submitted). . Link to Item
  - Nolen, JH, Lu, J, & Lu, Y. Scaling limit of the Stein variational gradient descent: the mean field regime(Accepted). Siam Journal on Mathematical Analysis ,. Link to Item
- Conference Papers
  - Nolen, J, Pavliotis, GA, & Stuart, AM. (2012). Multiscale Modelling and Inverse Problems. Springer Berlin Heidelberg. Full Text
Teaching & Mentoring
Recent Courses
- MATH 641: Probability 2019
- MATH 790-90: Minicourse in Advanced Topics 2019
- MATH 340: Advanced Introduction to Probability 2018
- MATH 356: Elementary Differential Equations 2018
- MATH 740: Advanced Introduction to Probability 2018
- BIOLOGY 490: Topics in Biology 2017
- MATH 490: Topics in Mathematics 2017

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Education, Training, & Certifications

Duke Appointment History

Academic Positions Outside Duke

Selected Grants

Fellowships, Supported Research, & Other Grants

Selected Publications

Academic Articles

Conference Papers

Recent Courses