# Bruce Turkington

Professor Emeritus

Professor Turkington's research lies at the interface between nonlinear partial differential equations and statistical mechanics. His recent work has focused on applying the techniques of statisical mechanics to modeling coherent structures in two-dimensional turbulence, geophysical fluid flows and other complex systems, such as nonintegrable, nonlinear Schr"odinger equations. For instance, he and his collaborators have shown how the observed zonal jets and vortical spots in the atmosphere of Jupiter arise as equilibrium macrostates in a statistical model, and how the statistical properties of the small-scale potential vorticity flucuations determine the features of the stable, large-scale mean flow. In his current work Turkington is developing general stategies of model reduction for complex systems, such as Hamiltonian systems with many degrees of freedom, by adapting ideas from nonequilibrium statistical mechanics, information theory and optimization. His approach has been applied to derive statistical closure of coarse-grained descriptions for the truncated Burgers-Hopf equation, a shell model of turbulence, and two-dimensional ideal flow.

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Education

Ph.D. Stanford University, 1978

M.S. Stanford University, 1976

B.S. University of Victoria, 1974

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RESEARCH INTERESTS

Nonlinear PDE, Applied Mathematics, Fluid Dynamics

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Selected Publications

- S. Thalabard and B. Turkington, Optimal response to nonequilibrium disturbances under truncated Burgers-Hopf dynamics.
*J. Phys. A: Math. Theor.***50**, 175502, 2017. - B. Turkington, Q-Y. Chen and S. Thalabard, Coarse-graining two-dimensional turbulence via dynamical optimization.
*Nonlinearity***29**, 2961-2989, 2016. - S. Thalabard and B. Turkington, Optimal thermalization in a shell model of homogeneous turbulence.
*J. Phys. A: Math. Theor.***49,**165502, 2016**.** - R. Kleeman and B. Turkington, A nonequilibrium statistical model of spectrally truncated Burgers-Hopf dynamics.
*Commun. Pure Appl. Math.***67**, 1905-1946, 2014. - B. Turkington, An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics.
*J. Stat. Phys.***152 (3)**, 569-597, 2013. - B. Turkington, Statistical mechanics of two-dimensional and quasi-geostrophic turbulence. In
*Long-Range Interacting Systems,*Lecture Notes of the Les Houches Summer School,**90,**pp. 159--209. T. Dauxois, S. Ruffo and L.F. Cugliandolo, eds. Oxford U. Press, 2009. - A. Eisner and B. Turkington, Nonequilibrium statistical behavior of nonlinear Schroedinger equations.
*Physica D***213**, 85-97, 2006. - R.S. Ellis, R. Jordan, P. Otto and B. Turkington, A statistical approach to the asymptotic behavior of a generalized class of nonlinear Schroedinger equations.
*Commun. Math. Phys.***244**, 187-208, 2004. - R.S. Ellis, K. Haven and B. Turkington, Nonequivalent statistical equilibrium ensembles and refined stability theorems for most probable flows.
*Nonlinearity***15**, 239-255, 2002. - B. Turkington, A. Majda, K. Haven and M. DiBattista, Statistical equilibrium predictions of the jets and spots on Jupiter.
*Proc. Nat. Acad. Sci.***98**, 12346-12350, 2001. - R.S. Ellis, K. Haven and B. Turkington, Large deviation principles and complete equivalence and nonequivalence results for pure and mixed ensembles.
*J. Stat. Phys.***101**, 999-1064, 2000. - B. Turkington, Statistical equilibrium measures and coherent states in two-dimensional turbulence.
*Commun. Pure Appl. Math.***52**, 781-809, 1999.