Publications of Rafail Abramov

Rafail V. Abramov.  Linear response of the Lyapunov exponent to a small constant perturbation.  Physical Review E, 16 pp., 2014.
Rafail V. Abramov.  A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling.  Multiscale Model. Simul., 11(1):134--151, 2013. MR3032827
Rafail V. Abramov.  A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling.  Multiscale Modeling and Simulation, 11(1):134--151, 2013.
Rafail V. Abramov.  A simple stochastic parameterization for reduced models of multiscale dynamics.  Journal of Computational Dynamics, 23 pp., 2013.
Rafail V. Abramov and Marc P. Kjerland.  The response of reduced models of multiscale dynamics to small external perturbations .  Communications in Mathematical Sciences, 20 pp., 2013.
Rafail V. Abramov.  Improved linear response for stochastically driven systems.  Front. Math. China, 7(2):199--216, 2012. MR2897702
Rafail V. Abramov.  Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling.  Commun. Math. Sci., 10(2):595--624, 2012. MR2901322
Rafail V. Abramov.  A simple linear response closure approximation for slow dynamics of a multiscale system with linear coupling.  Multiscale Model. Simul., 10(1):28--47, 2012. MR2902597
Rafail V. Abramov and Andrew J. Majda.  Low frequency climate response of quasigeostrophic wind-driven ocean circulation.  Journal of Physical Oceanography, 42:243--260, 2012.
Rafail V. Abramov.  Climate change: is it more predictable than we think?.  Modern Climatology, ISBN 978-953-51-0095-9:289--308, 2012. Book chapter. 
Andrew J. Majda, Rafail Abramov and Boris Gershgorin.  High skill in low-frequency climate response through fluctuation dissipation theorems despite structural instability.  Proc. Natl. Acad. Sci. USA, 107(2):581--586, 2010. MR2608649
Rafail V. Abramov.  The multidimensional maximum entropy moment problem: a review on numerical methods.  Commun. Math. Sci., 8(2):377--392, 2010. MR2664456
Rafail V. Abramov.  Approximate linear response for slow variables of dynamics with explicit time scale separation.  J. Comput. Phys., 229(20):7739--7746, 2010. MR2674299
Rafail V. Abramov.  The multidimensional moment-constrained maximum entropy problem: a BFGS algorithm with constraint scaling.  J. Comput. Phys., 228(1):96--108, 2009. MR2464069
Rafail V. Abramov.  Short-time linear response with reduced-rank tangent map.  Chin. Ann. Math. Ser. B, 30(5):447--462, 2009. MR2601480
Rafail V. Abramov and Andrew J. Majda.  A new algorithm for low frequency climate response.  Journal of the Atmospheric Sciences, 66(2):286--309, 2009.
Rafail V. Abramov and Andrew J. Majda.  New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems.  J. Nonlinear Sci., 18(3):303--341, 2008. MR2411381
Rafail V. Abramov.  An improved algorithm for the multidimensional moment-constrained maximum entropy problem.  J. Comput. Phys., 226(1):621--644, 2007. MR2356853
Rafail V. Abramov and Andrew J. Majda.  Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems.  Nonlinearity, 20(12):2793--2821, 2007. MR2368326
Rafail Abramov.  A practical computational framework for the multidimensional moment-constrained maximum entropy principle.  J. Comput. Phys., 211(1):198--209, 2006. MR2168875
Rafail Abramov, Andrew Majda and Richard Kleeman.  Information theory and predictability for low-frequency variability.  J. Atmospheric Sci., 62(1):65--87, 2005. MR2114468
Kyle Haven, Andrew Majda and Rafail Abramov.  Quantifying predictability through information theory: small sample estimation in a non-Gaussian framework.  J. Comput. Phys., 206(1):334--362, 2005. MR2135840
Andrew J. Majda, Rafail V. Abramov and Marcus J. Grote.  Information theory and stochastics for multiscale nonlinear systems, volume 25 of CRM Monograph Series.  American Mathematical Society, Providence, RI, 2005. MR2166171
Rafail V. Abramov and Andrew J. Majda.  Quantifying uncertainty for non-Gaussian ensembles in complex systems.  SIAM J. Sci. Comput., 26(2):411--447 (electronic), 2004. MR2116354
Rafail V. Abramov, Gregor Kovačič and Andrew J. Majda.  Hamiltonian structure and statistically relevant conserved quantities for the truncated Burgers-Hopf equation.  Comm. Pure Appl. Math., 56(1):1--46, 2003. MR1929441
Rafail V. Abramov and Andrew J. Majda.  Statistically relevant conserved quantities for truncated quasigeostrophic flow.  Proc. Natl. Acad. Sci. USA, 100(7):3841--3846 (electronic), 2003. MR1963812
Rafail V. Abramov and Andrew J. Majda.  Discrete approximations with additional conserved quantities: deterministic and statistical behavior.  Methods Appl. Anal., 10(2):151--189, 2003. MR2074746
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