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 2:304:00
Wednesdays, 10:3012:00
Wednesdays, 10:3012:00
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 277080320
 nolen@math.duke.edu (919) 6602862
 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, January 1). Block size in geometric(P)biased permutations. Electronic Communications in Probability , 23 . Full Text
 Mourrat, JC, & Nolen, J. (2017, April 1). Scaling limit of the corrector in stochastic homogenization. Annals of Applied Probability , 27 (2), 944959. Full Text
 Nolen, J, Roquejoffre, JM, & Ryzhik, L. (2017, March 1). Convergence to a single wave in the FisherKPP equation. Chinese Annals of Mathematics. Series B , 38 (2), 629646. Full Text
 Gloria, A, & Nolen, J. (2016, December 1). A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus. Communications on Pure and Applied Mathematics , 69 (12), 23042348. 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), 439476. Full Text
 Hamel, F, Nolen, J, Roquejoffre, JM, & Ryzhik, L. (2016, January 1). The logarithmic delay of KPP fronts in a periodic medium. Journal of the European Mathematical Society , 18 (3), 465505. Full Text
 Bhamidi, S, Hannig, J, Lee, CY, & Nolen, J. (2015, October 19). The importance sampling technique for understanding rare events in ErdősRényi random graphs. Electronic Journal of Probability , 20 . Full Text
 Nolen, J, Roquejoffre, JM, & Ryzhik, L. (2015, March 4). PowerLike Delay in Time Inhomogeneous FisherKPP Equations. Communications in Partial Differential Equations , 40 (3), 475505. Full Text
 Lu, J, & Nolen, J. (2015, February). Reactive trajectories and the transition path process. Probability Theory and Related Fields , 161 (12), 195244. Full Text Open Access Copy
 Huckemann, S, Mattingly, JC, Miller, E, & Nolen, J. (2015, January 1). Sticky central limit theorems at isolated hyperbolic planar singularities. Electronic Journal of Probability , 20 . Full Text Open Access Copy
 Nolen, J. (2014). Normal approximation for a random elliptic equation. Probability Theory and Related Fields , 159 (34), 661700. 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), 22382258. Full Text Open Access Copy
 Nolen, J. (2013). Normal approximation for a random elliptic equation. Probability Theory and Related Fields ,, 140. Full Text
 Hamel, F, Nolen, J, Roquejoffre, JM, & Ryzhik, L. (2012). A short proof of the logarithmic Bramson correction in FisherKPP 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 HamiltonJacobi Equation. Journal of Statistical Physics , 149 (2), 342361. Full Text
 Mellet, A, & Nolen, J. (2012). Capillary drops on a rough surface. Interfaces and Free Boundaries , 14 (2), 167184. Full Text
 Nolen, J, Roquejoffre, JM, Ryzhik, L, & Zlatoš, A. (2012). Existence and NonExistence of FisherKPP Transition Fronts. Archive for Rational Mechanics and Analysis , 203 (1), 217246. Full Text
 Cardaliaguet, P, Nolen, J, & Souganidis, PE. (2011). Homogenization and Enhancement for the GEquation. Archive for Rational Mechanics and Analysis , 199 (2), 527561. Full Text
 Nolen, J, & Novikov, A. (2011, January 1). Homogenization of the Gequation with incompressible random drift in two dimensions. Communications in Mathematical Sciences , 9 (2), 561582. Full Text
 Nolen, J. (2011). An invariance principle for random traveling waves in one dimension. Siam Journal on Mathematical Analysis , 43 (1), 153188. Full Text
 Nolen, J. (2011). A central limit theorem for pulled fronts in a random medium. Networks and Heterogeneous Media , 6 (2), 167194. Full Text
 Nolen, J, Xin, J, & Yu, Y. (2009, December). Bounds on front speeds for inviscid and viscous Gequations. Methods and Applications of Analysis , 16 (4). (Academic Article) Link to Item
 Nolen, J, & Papanicolaou, G. (2009, November 26). Fine scale uncertainty in parameter estimation for elliptic equations. Inverse Problems , 25 (11). 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), 815839. Full Text
 Mellet, A, Nolen, J, Roquejoffre, JM, & Ryzhik, L. (2009). Stability of generalized transition fronts. Communications in Partial Differential Equations , 34 (6), 521552. Full Text
 Nolen, J, & Ryzhik, L. (2009). Traveling waves in a onedimensional heterogeneous medium. Annales De L'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis , 26 (3), 10211047. 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 onedimensional random drift. Discrete and Continuous Dynamical Systems Series B , 11 (2), 421442. Full Text
 Nolen, J, & Xin, J. (2008, December). Variational principle and reactiondiffusion front speeds in random flows. Iciam07 Proceedings ,, 10407011040702. (Academic Article)
 Nolen, J, & Xin, J. (2008). Computing reactive front speeds in random flows by variational principle. Physica D: Nonlinear Phenomena , 237 (23), 31723177. Full Text
 Nolen, J, Papanicolaou, G, & Pironneau, O. (2008). A framework for adaptive multiscale methods for elliptic problems. Multiscale Modeling and Simulation , 7 (1), 171196. 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 , 493532. (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), 493532. Full Text
 Nolen, J, & Xin, J. (2005, December 1). Existence of KPP type fronts in spacetime periodic shear flows and a study of minimal speeds based on variational principle. Discrete and Continuous Dynamical Systems , 13 (5), 12171234.
 Nolen, J, & Xin, J. (2005, July 1). A variational principle based study of KPP minimal front speeds in random shears. Nonlinearity , 18 (4), 16551675. Full Text
 Nolen, J, Rudd, M, & Xin, J. (2005). Existence of KPP fronts in spatiallytemporally periodic advection and variational principle for propagation speeds. Dynamics of Pde , 2 , 124. (Academic Article) Link to Item
 Boye, DM, Valdes, TS, Nolen, JH, Silversmith, AJ, Brewer, KS, Anderman, RE, & Meltzer, RS. (2004, June 1). Transient and persistent spectral hole burning in Eu3+doped solgel produced SiO2 glass. Journal of Luminescence , 108 (14), 4347. Full Text
 Nolen, J, & Xin, J. (2004). MinMax Variational Principles and Fronts Speeds in Random Shear Flows. Methods and Applications of Analysis , 11 (4), 635644. (Academic Article) Link to Item
 Nolen, J, & Xin, J. (2003, January). ReactionDiffusion Front Speeds in SpatiallyTemporally Periodic Shear Flows. Multiscale Modeling & Simulation , 1 (4), 554570. Full Text
 Boye, DM, Silversmith, AJ, Nolen, J, Rumney, L, Shaye, D, Smith, BC, & Brewer, KS. (2001, December 1). Redtogreen upconversion in Erdoped SiO2 and SiO2TiO2 solgel silicate glasses. Journal of Luminescence , 9495 , 279282. Full Text
 Nolen, J, Roquejoffre, JM, & Ryzhik, L. Refined longtime asymptotics for Fisher–KPP fronts(Published online). Communications in Contemporary Mathematics ,, 18500721850072. 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 340: Advanced Introduction to Probability 2019
 MATH 641: Probability 2019
 MATH 740: Advanced Introduction to Probability 2019
 MATH 79090: Minicourse in Advanced Topics 2019
 MATH 356: Elementary Differential Equations 2018
 BIOLOGY 490: Topics in Biology 2017
 MATH 490: Topics in Mathematics 2017
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