Unresolved computation and optimal predictions

Communications on Pure and Applied Mathematics

Volumn 52, Issue 10, 1999, Pages 1231-1254

  Chorin, Alexandre J ^a   Kast, Anton P ^a   Kupferman, Raz ^a  

^a LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033459243     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(199910)52:10<1231::AID-CPA3>3.0.CO;2-C     Document Type: Article

References (22)

1. Adrian, R. Stochastic estimation of sub-grid scale motions. Appl. Mech. Rev. 43 (1990), S214-S218.
2. Barenblatt, G. I. Scaling, self-similarity and intermediate asymptotics. Cambridge University Press, Cambridge, 1996.
3. Barenblatt, G. I.; Chorin, A. J. New perspectives in turbulence: scaling laws, asymptotics, and intermittency. SIMM Rev. 40 (1998), no. 2, 265-291.
4. Barenblatt, G. I.; Chorin, A. J. Scaling laws and vanishing viscosity limits in turbulence theory. Recent Advances in Partial Differential Equations Venice 1996, 1-25. Proceedings of Symposia in Applied Mathematics No. 54, American Mathematical Society, Providence, R.I., 1998.
5. Bennett, A. F. Inverse methods in physical oceanography. Cambridge University Press, Cambridge, 1992.
6. Binder, K.; Heermann, D. W. Monte-Carlo simulation in statistical physics. An introduction. 2nd ed., Springer Series in Solid-State Sciences, 80. Springer-Verlag, Berlin-New York, 1992.
7. Boucher, C.; Turkington, B. Derivation of maximum entropy principles in two dimensional turbulence via large deviations. Preprint, University of Massachusetts, Amherst, 1998.
8. Chorin, A. J. Vortex methods. Mécanique des fluides numérique (Les Hauches, 1993), 65-109. North-Holland, Amsterdam, 1996.
9. Chorin, A. J.; Kast, A. P.; Kupferman, R. Optimal prediction of underresolved dynamics. Proc. Natl. Acad. Sci. USA 95 (1998), no. 8, 4094-4098.
10. Dembo, A.; Zeitouni, O. Large deviations techniques and applications. Jones and Bartlett, Boston, 1993.
11. Feynman, R. P.; Hibbs, A. R. Quantum mechanics and path integrals. McGraw-Hill, New York, 1965.
12. Goldenfeld, N.; McKane, A.; Hou, Q. Block spins for partial differential equations. J. Statist. Phys. 93 (1998), no. 3-4, 699-714.
13. Kleinert, H. Gauge fields in condensed matter. World Scientific, Singapore-Teaneck, N.J., 1989.
14. McComb, W. D.; Watt, A. G. Conditional averaging procedure for the elimination of the smallscale modes from incompressible fluid turbulence at high Reynolds numbers. Phys. Rev. Lett. 65 (1990), 3281-3284.
15. McKean, H. P. Statistical mechanics of nonlinear wave equations. IV. Cubic Schrödinger. Comm. Math. Phys. 168 (1995), 479-491.
16. Miller, R.; Carter, E.; Blue, S. Data assimilation into nonlinear stochastic models. Tellus, to appear.
17. Papoulis, A. Probability, random variables, and stochastic processes. 3rd ed. McGraw-Hill, New York, 1991.
18. Risken, H. The Fokker-Planck equation. Methods of solution and applications. Springer Series in Synergetics, 18. Springer-Verlag, Berlin-New York, 1984.
19. Rozovskiǐ, B. L. Stochastic evolution systems. Linear theory and applications to nonlinear filtering. Translated from the Russian by A. Yarkho. Mathematics and Its Applications (Soviet Series), 35. Kluwer Academic, Dordrecht, 1990.
20. Scotti, A.; Meneveau, C. Fractal model for coarse-grained partial differential equations. Phys. Rev. Lett. 78 (1997), 867-870.
21. Turkington, B. Statistical equilibrium measures and coherent states in two-dimensional turbulence. Comm. Pure Appl. Math. 52 (1999), no. 7, 781-809.
22. Turkington, B.; Whitaker, N. Statistical equilibrium computations of coherent structures in turbulent shear layers. SIAM J. Sci. Comput. 17 (1996), no. 6, 1414-1433.