James H. Nolen, Professor
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.  Contact Info:
Teaching (Fall 2021):
 MATH 69070.01, TOPICS IN APPLIED MATH
Synopsis
 Physics 205, TuTh 12:00 PM01:15 PM
 MATH 69070.11, TOPICS IN APPLIED MATH
Synopsis
 Online ON, TuTh 12:00 PM01:15 PM
 Office Hours:
 Mondays 1:303:00pm
Wednesdays 1:303:00pm
 Education:
Ph.D.  University of Texas, Austin  2006 
B.S.  Davidson College  2000 
 Specialties:

Analysis
Probability Applied Math
 Research Interests: Partial differential equations, stochastic processes, random media, applied mathematics, 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.
 Areas of Interest:
partial differential equations stochastic processes asymptotic analysis homogenization theory front propagation reactiondiffusion equations
 Current Ph.D. Students
(Former Students)
 Representative Publications
(More Publications)
 Nolen, J, Normal approximation for a random elliptic equation,
Probability Theory and Related Fields, vol. 159 no. 34
(2013),
pp. 140, Springer Nature, ISSN 01788051 [pdf], [doi] [abs]
 J. Lu and J. Nolen, Reactive trajectories and the transition path process.,
Probability Theory and Related Fields
(January, 2014) [1744], [doi]
 Nolen, J, A central limit theorem for pulled fronts in a random medium,
Networks and Heterogeneous Media, vol. 6 no. 2
(2011),
pp. 167194, American Institute of Mathematical Sciences (AIMS), ISSN 15561801 [pdf], [doi] [abs]
 Nolen, J; Ryzhik, L, Traveling waves in a onedimensional heterogeneous medium,
Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 26 no. 3
(2009),
pp. 10211047, Elsevier BV, ISSN 02941449 [pdf], [doi] [abs]
 Mellet, A; Nolen, J; Roquejoffre, JM; Ryzhik, L, Stability of generalized transition fronts,
Communications in Partial Differential Equations, vol. 34 no. 6
(2009),
pp. 521552, Informa UK Limited, ISSN 03605302 [pdf], [doi] [abs]
 Nolen, J; Xin, J, Asymptotic spreading of KPP reactive fronts in incompressible spacetime random flows,
Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 26 no. 3
(2009),
pp. 815839, Elsevier BV, ISSN 02941449 [pdf], [doi] [abs]
 Cardaliaguet, P; Nolen, J; Souganidis, PE, Homogenization and Enhancement for the GEquation,
Archive for Rational Mechanics and Analysis, vol. 199 no. 2
(2011),
pp. 527561, Springer Nature, ISSN 00039527 [4160], [doi] [abs]
 Selected Grant Support
 Analysis of Fluctuations for PDEs with Random Coefficients, National Science Foundation, DMS1007572.
 CAREER: Research and training in stochastic dynamics, National Science Foundation, DMS1351653.
