Improved linear response for stochastically driven systems

Frontiers of Mathematics in China

Volumn 7, Issue 2, 2012, Pages 199-216

  Abramov, Rafail V ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Fluctuation dissipation theorem; linear response; stochastic processes

Indexed keywords

EID: 84858452018     PISSN: 16733452     EISSN: 16733576     Source Type: Journal    
DOI: 10.1007/s11464-012-0192-7     Document Type: Article

References (29)

1. Abramov R. Short-time linear response with reduced-rank tangent map. Chin Ann Math, 2009, 30B(5): 447-462.
2. Abramov R. Approximate linear response for slow variables of dynamics with explicit time scale separation. J Comput Phys, 2010, 229(20): 7739-7746.
3. Abramov R, Majda A. Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems. Nonlinearity, 2007, 20: 2793-2821.
4. Abramov R, Majda A. New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems. J Nonlin Sci, 2008, 18(3): 303-341.
5. Abramov R, Majda A. New algorithms for low frequency climate response. J Atmos Sci, 2009, 66: 286-309.
6. Bell T. Climate sensitivity from fluctuation dissipation: Some simple model tests. J Atmos Sci, 1980, 37(8): 1700-1708.
7. Carnevale G, Falcioni M, Isola S, Purini R, Vulpiani A. Fluctuation-response in systems with chaotic behavior. Phys Fluids A, 1991, 3(9): 2247-2254.
8. Cohen B, Craig G. The response time of a convective cloud ensemble to a change in forcing. Quart J Roy Met Soc, 2004, 130(598): 933-944.
9. Eckmann J, Ruelle D. Ergodic theory of chaos and strange attractors. Rev Mod Phys, 1985, 57(3): 617-656.
10. Evans D, Morriss G. Statistical Mechanics of Nonequilibrium Liquids. New York: Academic Press, 1990.
11. Gritsun A. Fluctuation-dissipation theorem on attractors of atmospheric models. Russ J Numer Math Modeling, 2001, 16(2): 115-133.
12. Gritsun A, Branstator G. Climate response using a three-dimensional operator based on the fluctuation-dissipation theorem. J Atmos Sci, 2007, 64: 2558-2575.
13. Gritsun A, Branstator G, Dymnikov V. Construction of the linear response operator of an atmospheric general circulation model to small external forcing. Num Anal Math Modeling, 2002, 17: 399-416.
14. Gritsun A, Branstator G, Majda A. Climate response of linear and quadratic functionals using the fluctuation dissipation theorem. J Atmos Sci, 2008, 65: 2824-2841.
15. Gritsun A, Dymnikov V. Barotropic atmosphere response to small external actions, theory and numerical experiments. Atmos Ocean Phys, 1999, 35(5): 511-525.
16. Kubo R, Toda M, Hashitsume N. Statistical Physics II: Nonequilibrium Statistical Mechanics. New York: Springer-Verlag, 1985.
17. Kunita H. Stochastic Flows and Stochastic Differential Equations. Cambridge: Cambridge University Press, 1997.
18. Leith C. Climate response and fluctuation-dissipation. J Atmos Sci, 1975, 32: 2022-2025.
19. Lorenz E. Predictability-a problem partly solved. In: Palmer T, Hagedorn R, eds. Predictability of Weather and Climate. Cambridge: Cambridge University Press, 2006.
20. Lorenz E, Emanuel K. Optimal sites for supplementary weather observations. J Atmos Sci, 1998, 55: 399-414.
21. Majda A, Abramov R, Gershgorin B. High skill in low frequency climate response through fluctuation dissipation theorems despite structural instability. Proc Natl Acad Sci, 2010, 107(2): 581-586.
22. Majda A, Abramov R, Grote M. Information Theory and Stochastics for Multiscale Nonlinear Systems. CRM Monograph Series of Centre de Recherches Mathématiques, Université de Montréal, Vol 25. Providence: American Mathematical Society, 2005.
23. Majda A, Gershgorin B. A test model for fluctuation-dissipation theorems with timeperiodic statistics. Physica D, 2010, 239(17): 1741-1757.
24. Majda A, Wang X. Linear response theory for statistical ensembles in complex systems with time-periodic forcing. Commun Math Sci, 2010, 8(1): 145-172.
25. Risken F. The Fokker-Planck Equation. 2nd ed. New York: Springer-Verlag, 1989.
26. Ruelle D. Chaotic Evolution and Strange Attractors. Cambridge: Cambridge University Press, 1989.
27. Ruelle D. Differentiation of SRB states. Comm Math Phys, 1997, 187: 227-241.
28. Ruelle D. General linear response formula in statistical mechanics, and the fluctuationdissipation theorem far from equilibrium. Phys Lett A, 1998, 245: 220-224.
29. Young L-S. What are SRB measures, and which dynamical systems have them? J Stat Phys, 2002, 108(5-6): 733-754.