Professor Doering’s research is focused on the analysis of mathematical models with the aim of extracting reliable, rigorous, and useful predictions. These models range from stochastic, dynamical systems arising in biology, chemistry and physics, to systems of nonlinear partial differential equations such as those that (ostensibly) describe turbulent fluid flows. The techniques employed range from the development of exact solutions to the application of modern mathematical methods including rigorous estimation, careful numerical computations and simulations, and the use of abstract functional and probabilistic analysis --- often a combination of all three approaches.
Professor Doering received a Bachelor’s degree in mathematics and physics from Antioch College, a Master’s in physics from the University of Cincinnati, and a Doctorate in mathematical physics from The University of Texas at Austin. He held positions at the Center for Nonlinear Studies at Los Alamos National Laboratory and at Clarkson University prior to joining the Michigan faculty in 1996. Among other recognitions, Professor Doering has received the NSF Presidential Young Investigator Award, the University of Michigan’s College of Literature, Science & the Arts Excellence in Education Award, a Fulbright Scholarship, and a Humboldt Research Award. He is a Fellow of the American Physical Society and of the Society of Industrial and Applied Mathematics.
Low-dimensional Models from Upper Bound Theory, (G.P. Chini, N. Dianati, Z. Zhang, and C.R. Doering), Physica D 240, 241-248 (2011).
Variations on Kolmogorov Flow: Turbulent Energy Dissipation and Mean Flow Profiles, (B. Rollin, Y. Dubief, and C.R. Doering), Journal of Fluid Mechanics 670, 204-213 (2011).
Symmetric Factorization of the Conformation Tensor in Viscoelastic Fluid Flows, (N. Balci, B. Thomases, M. Renardy, and C.R. Doering), Journal of Non-Newtonian Fluid Mechanics 166, 546-553 (2011).
Optimal Stirring Strategies for Passive Scalar Mixing, (Z. Lin, J.-L. Thiffeault, and C.R. Doering), Journal of Fluid Mechanics 675, 465-476, (2011).
Noise-induced Statistically Stable Oscillations in a Deterministically Divergent Dynamical System, (K. Bodova and C.R. Doering), Communications in Mathematical Sciences (in press, 2011).
“Ultimate State” of Two-dimensional Rayleigh-Bénard Convection Between Free-slip Fixed-Temperature Boundaries, (J.P. Whitehead and C.R. Doering), Physical Review Letters (in press, 2011).