CHORIN, ALEXANDRE J. / Mathematics / Researchers

International Center for Scientific Research

Researchers

Mathematics / CHORIN, ALEXANDRE J.

chorinmath.berkeley.edu

Position

Department of Mathematics, University of California, Berkeley CA, US.

Research interests

Applied mathematics, Numerical methods, Hydrodynamics

His work has stimulated important developments across the entire spectrum from practical engineering applications to convergence proofs for numerical methods. In computational fluid dynamics he is responsible for the introduction of the Projection Method and the Vortex Method, which have had a huge impact on numerous applied fields, including biomedical fluid dynamics and combustion. In statistical mechanics, novel computational methods for the accurate evaluation of Wiener integrals were introduced. In turbulence Chorin has analyzed the blow-up of errors in finite difference calculations involving turbulent flow. He has established the long-sought quantitative link between statistical mechanics and turbulence. Chorin’s most recent work goes by
the name of “optimal prediction”, and entirely new statistical approach to the problem of under resolved computation. From the 1960s to the present day, Chorin has led and inspired applied mathematicians everywhere to tackle the most difficult real-world problems and to make full use of the combined power of advanced computers and sophisticated mathematical analysis.

Prizes and awards

Prof. Chorin received numerous awards including the National Academy of Sciences Award in Applied Mathematics and Numerical Analysis in 1989 (became a member in 1991), Fellow of the American Academy of Arts and Sciences in 1991, the 2000 Norbert Wiener Prize of the American Mathematical Society and the Society for Industrial and Applied Mathematics in recognition of his seminal work in computational fluid dynamics, statistical mechanics and turbulence, and an Honorary Doctor of Science from the Technion, Israel Institute of Technology.

Publications

Turbulence cascades across equilibrium spectra Phys Rev E pp. 2616-2619 (1996)

Partition functions and equilibrium measures in two-dimensional and quasi-three-dimensional turbulence Phys Fluids 8 pp. 2656-2660 (1996)

Analysis of Kosterlitz-Thouless transition models Physica D 99 pp. 442-470 (1997) (with O. H. Hald)

Scaling laws and zero viscosity limits for wall-bounded shear flows and for local structure in developed turbulence Comm. Pure Appl. Math, 50 pp.381-398 (1997) (with G. I. Barenblatt)

Scaling laws and vanishing viscosity limits in turbulence theory Proc. Symposia Appl. Math. AMS, 54, pp. 1-25 (1998) (with G. I. Barenblatt)

Scaling laws for fully developed turbulent flow in pipes: Discussion of experimental data Proc. Natl. Acad. Sci. 94, pp. 773-776 (1997) (with G. I. Barenblatt and V. M. Prostokishin)

Scaling laws for fully developed turbulent flow in pipes Appl. Mech. Rev. 50 pp. 413-429 (1997) (with G. I. Barenblatt and V. M. Prostokishin)

New perspectives in turbulence: Scaling laws, asymptotics and intermittencySIAM Rev. 40, pp.265-291 (1998) (with G. I. Barenblatt)

Structure of the zero-pressure-gradient turbulent boundary layer Proc. Nat. Acad. Sci. 94 (1997), pp. 7817-7819 (with G. I. Barenblatt, O. H. Hald and V. M. Prostokishin)

Optimal prediction of underresolved dynamics Proc. Nat. Acad. Sci. USA, 95 (1998), pp. 4094-4098. (with A. Kast and R. Kupferman)

New perspectives in turbulence Quart. Appl. Math., 56, (1998), pp. 767-785.

New perspectives in turbulence Berkeley Math. Newsletter 1998 (with G. I. Barenblatt)

Scaling of the intermediate region in wall-bounded turbulence: The power law(with G. I. Barenblatt) Phys. Fluids 10 (1998) pp. 1043-1044.

The influence of the flow of the reacting gas on the conditions for a thermal explosion Proc. Nat. Acad. Sci. USA, 94, pp. 12762-12764 (1997)(with G. I. Barenblatt and A. Kast)

One-sided polarization and renormalization flow in the Kosterlitz-Thouless phase transition (with R. Kupferman) SIAM J. Appl. Math., 59, (1999) pp. 1843-1866.

The Kolmogorov-Obukhov exponent in the inertial range of turbulence: A reexamination of experimental data (with G. I. Barenblatt and V. M. Prostokishin) Physica D, 127 (1999), pp. 105-110.

Unresolved computation and optimal predictions (with A. Kast and R. Kupferman) Comm. Pure Appl. Math., 52 (1999), pp. 1231-1254.

On the prediction of large scale dynamics using unresolved computations (with A. Kast and R. Kupferman) Contemp. Math. AMS, 238 (1999), pp. 53-75.

A new formulation of the near-equilibrium theory of turbulence(with G.I. Barenblatt) www.emath.fr/Maths/Proc (1999), pp. 22-35.

Self-similar intermediate structures in turbulent boundary layers at large Reynolds numbers (with G. I. Barenblatt and V. M. Prostokishin) J. Fluid Mech. 97 (2000), pp. 263-283.

Optimal prediction for Hamiltonian partial differential equations (with R. Kupferman and D. Levy) J. Comp. Phys., 162 (2000), pp. 267-297.

Optimal prediction and the Mori-Zwanzig representation of irreversible processes (with O. H. Hald and R. Kupferman) Proc. Nat. Acad. Sci. USA, 97 (2000), pp. 2968-2973.

Characteristic length scale of the intermediate structure in zero-pressure-gradient boundary layer flow (with G. I. Barenblatt and V. M. Prostokishin) Proc. Nat. Acad. Sci. USA, 97 (2000), pp. 3799-3802.

Stochastic optimal prediction with application to averaged Euler equations (with J. Bell and W. Crutchfield). Proc. 7th Nat. Conf. CFD, Taiwan (2000), pp. 1-13.

Non-Markovian optimal prediction (with O. H. Hald and R. Kupferman). Monte Carlo Meth. & Appl. 7 (2001) pp. 99-109.

Optimal prediction with memory (with O. H. Hald and R. Kupferman). Physica D, 166 (2002), pp. 239-257.

A model of a turbulent boundary layer with a non-zero pressure gradient (with G. I. Barenblatt and V. M. Prostokishin). Proc. Nat. Acad. Sci. USA, 99 (2002), pp. 5772-5776.

Conditional expectations and renormalization. Multiscale Modeling and Simulation, 1 (2003) pp. 105-118.

Stochastic Tools for Mathematics and Science (with O. H. Hald) (book).

Averaging and renormalization for the Korteveg-deVries-Burgers equation Proc.Nat. Acad. Sci. USA 100 (2003), pp. 9674-9679.

Prediction from partial data, renormalization, and averaging (with O.H. Hald and R. Kupferman). J. Sc. Comput. 28 (2006), pp. 245-261.

A mathematical model for the scaling of turbulence (with G.I. Barenblatt). Proc. Nat. Acad. Sc. USA 101 (2004),pp. 15023-15026.

Dimensional reduction for a Bayesian filter (with P. Krause). Proc. Nat. Acad. Sc. USA 101 (2004), pp. 15013-15016.

Viscosity-dependent inertial spectra of the Burgers and the KdVB equations (with O.H. Hald). Proc. Nat. Acad. Sc. USA 102 (2005), pp. 3921-3923.

Problem reduction, renormalization, and memory (with P. Stinis). Comm. Appl. Math. Comp. Sc. 1 (2005), pp. 1-27.

The turbulent wall jet: a triple-layered structure and incomplete similarity (with G.I. Barenblatt and V.M. Prostokishin). Proc. Nat. Acad. Sc. USA 102 (2005), pp. 8850-8853.

A note concerning the Lighthill ``sandwich model\\\" of tropical cyclones (with G.I. Barenblatt and V.M. Prostokishin). Proc. Nat. Acad. Sc. USA 102 (2005), pp. 11148-11150.

On the existence and scaling of structure functions in turbulence according to the data (with A. Arenas). Proc. Nat. Acad. Sc. (USA) 103 (2006), pp. 4352-4355.

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