James H. Nolen
- Associate Professor of Mathematics
Research Areas and Keywords
PDE & Dynamical Systems
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.
Nolen, J. "Normal approximation for a random elliptic equation." Probability Theory and Related Fields 159.3-4 (2014): 661-700. Full Text
Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, and Skwerer, S. "Sticky central limit theorems on open books." The Annals of Applied Probability 23 (2013): 2238-2258. (Academic Article) Full Text Open Access Copy
Nolen, J. "Normal approximation for a random elliptic equation." Probability Theory and Related Fields (2013): 1-40. Full Text
Nolen, J, Roquejoffre, J-M, Ryzhik, L, and Zlatoš, A. "Existence and Non-Existence of Fisher-KPP Transition Fronts." Archive for Rational Mechanics and Analysis 203.1 (2012): 217-246. Full Text
Hamel, F, Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "A short proof of the logarithmic Bramson correction in Fisher-KPP equations (Accepted)." Networks and Heterogeneous Media (2012). (Academic Article)
Matic, I, and Nolen, J. "A Sublinear Variance Bound for Solutions of a Random Hamilton-Jacobi Equation." Journal of Statistical Physics 149.2 (2012): 342-361. Full Text
Cardaliaguet, P, Nolen, J, and Souganidis, PE. "Homogenization and Enhancement for the G—Equation." Archive for Rational Mechanics and Analysis 199.2 (February 2011): 527-561. Full Text
Nolen, J, and Novikov, A. "Homogenization of the G-equation with incompressible random drift in two dimensions." Communications in Mathematical Sciences 9.2 (2011): 561-582.
Nolen, J. "An invariance principle for random traveling waves in one dimension." SIAM Journal on Mathematical Analysis 43.1 (2011): 153-188. Full Text