Rafail Abramov

Teaching

Publications

1. R. Abramov, A simple linear response closure approximation for slow dynamics of a multiscale system with linear coupling, submitted to Multiscale Modeling and Simulation on August 16, 2011.
   [PDF] (preprint) [arXiv.org]
   
   
2. R. Abramov, Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling, submitted to Communications in Mathematical Sciences on May 16, 2011, accepted on August 12, 2011.
   [PDF] (preprint) [arXiv.org]
   
   
3. R. Abramov & A. Majda, Low Frequency Climate Response of Quasigeostrophic Wind-Driven Ocean Circulation, submitted to Journal of Physical Oceanography on March 10, 2011, accepted on September 2, 2011.
   [PDF] (preprint)
   
   
4. R. Abramov, Improved linear response for stochastically driven systems, submitted to Frontiers of Mathematics in China on February 1, 2011.
   [PDF] [arXiv.org] (preprint available since January 14, 2010)
   
   
5. R. Abramov, Approximate linear response for slow variables of dynamics with explicit time scale separation, Journal of Computational Physics, 2010, vol. 229, no. 20, 7739—7746.
   [DOI link]
   
   
6. A. Majda, R. Abramov & B. Gershgorin, High skill in low frequency climate response through fluctuation dissipation theorems despite structural instability, Proceedings of the National Academy of Sciences, 2010, vol. 107, no. 2, 581—586.
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7. R. Abramov, The multidimensional maximum entropy moment problem: A review on numerical methods, Communications in Mathematical Sciences, 2010, vol. 8, no. 2, 377—392.
   [PDF]
   
   
8. R. Abramov, Short-time linear response with reduced-rank tangent map, Chinese Annals of Mathematics, 2009, vol. 30B, no. 5, 447—462.
   [PDF]
   
   
9. R. Abramov, The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling, Journal of Computational Physics, 2009, vol. 228, 96—108.
   [DOI link]
   
   
10. R. Abramov & A. Majda, A new algorithm for low frequency climate response, Journal of the Atmospheric Sciences, 2009, vol. 66, 286—309.
    [DOI link]
    
    
11. R. Abramov & A. Majda, New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems, Journal of Nonlinear Science, 2008, vol. 18, 303—341.
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12. R. Abramov & A. Majda, Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems, Nonlinearity, 2007, vol. 20, 2793—2821.
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13. R. Abramov, An improved algorithm for the multidimensional moment-constrained maximum entropy problem, Journal of Computational Physics, 2007, vol. 226, 621—644.
    [DOI link]
    
    
14. R. Abramov, A practical computational framework for the multidimensional moment-constrained maximum entropy principle, Journal of Computational Physics, 2006, vol. 211, 198—209.
    [DOI link]
    
    
15. A. Majda, R. Abramov & M. Grote, Information theory and stochastics for multiscale nonlinear systems, vol. 25 of CRM Monograph Series, Centre de Recherches Mathématiques, Université de Montréal. Published by American Mathematical Society, 2005. ISBN 0-8218-3843-1. 141 pp.
    [Amazon] [Barnes & Noble]
    
    
16. K. Haven, A. Majda & R. Abramov, Quantifying predictability through information theory: Small sample estimation in a non-Gaussian framework, Journal of Computational Physics, 2005, vol. 206, 334—362.
    [DOI link]
    
    
17. R. Abramov, A. Majda & R. Kleeman, Information Theory and Predictability for Low Frequency Variability, Journal of Atmospheric Sciences, 2005, vol. 62, no. 1, 65—87.
    [PDF]
    
    
18. R. Abramov & A. Majda, Quantifying uncertainty for non-Gaussian ensembles in complex systems, SIAM Journal on Scientific Computing, 2003, vol. 26, no. 2, 411—447.
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19. R. Abramov & A. Majda, Discrete approximations with additional conserved quantities: Deterministic and statistical behavior, Methods and Applications of Analysis, 2003, vol. 10, no. 2, 151—190.
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20. R. Abramov & A. Majda, Statistically relevant conserved quantities for truncated quasi-geostrophic flow, Proceedings of the National Academy of Sciences, 2003, vol. 100, no. 7, 3841—3846.
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21. R. Abramov, G. Kovačič & A. Majda, Hamiltonian structure and statistically relevant conserved quantities for the truncated Burgers-Hopf equation, Communications in Pure and Applied Mathematics, 2003, vol. 56, 1—46.
    [PDF]

Software