Rafail Abramov

Department of Mathematics, Statistics and Computer Science
University of Illinois at Chicago
851 S. Morgan St.
Chicago, IL 60607
E-mail: abramov@math.uic.edu
Phone: (312) 413 7945

Teaching

MATH 210 — Calculus III
MATH 480 — Applied Differential Equations

Publications

  1. R. Abramov, Linear response of the Lyapunov exponent to a small constant perturbation, submitted to Physical Review E, 2014.
    [arXiv.org]

  2. R. Abramov, A simple stochastic parameterization for reduced models of multiscale dynamics, submitted to Journal of Computational Dynamics, 2013.
    [arXiv.org]

  3. R. Abramov and M. Kjerland, The response of reduced models of multiscale dynamics to small external perturbations, submitted to Communications in Mathematical Sciences, 2013.
    [arXiv.org]

  4. R. Abramov, A simple closure approximation for slow dynamics of a multiscale system: Nonlinear and multiplicative coupling, Multiscale Modeling and Simulation, 2013, vol. 11, no. 1, 134—151.
    [PDF] [PDF preprint] [arXiv.org]

  5. R. Abramov, A simple linear response closure approximation for slow dynamics of a multiscale system with linear coupling, Multiscale Modeling and Simulation, 2012, vol. 10, no. 1, 28—47.
    [PDF] [PDF preprint] [arXiv.org]

  6. R. Abramov, Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling, Communications in Mathematical Sciences, 2012, vol. 10, no. 2, 595—624.
    [PDF] [PDF preprint] [arXiv.org]

  7. R. Abramov & A. Majda, Low Frequency Climate Response of Quasigeostrophic Wind-Driven Ocean Circulation, Journal of Physical Oceanography, 2012, vol. 42, no. 2, 243—260.
    [PDF] [PDF preprint]

  8. R. Abramov, Improved linear response for stochastically driven systems, Frontiers of Mathematics in China, 2012, vol. 7, no. 2, 199—216.
    [PDF] [arXiv.org]

  9. 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]

  10. 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.
    [PDF]

  11. 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]

  12. R. Abramov, Short-time linear response with reduced-rank tangent map, Chinese Annals of Mathematics series B, 2009, vol. 30B, no. 5, 447—462.
    [PDF]

  13. 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]

  14. R. Abramov & A. Majda, A new algorithm for low frequency climate response, Journal of the Atmospheric Sciences, 2009, vol. 66, 286—309.
    [DOI link]

  15. 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.
    [PDF]

  16. R. Abramov & A. Majda, Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems, Nonlinearity, 2007, vol. 20, 2793—2821.
    [PDF]

  17. R. Abramov, An improved algorithm for the multidimensional moment-constrained maximum entropy problem, Journal of Computational Physics, 2007, vol. 226, 621—644.
    [DOI link]

  18. 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]

  19. 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]

  20. 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]

  21. 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]

  22. 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.
    [PDF]

  23. 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.
    [PDF]

  24. 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.
    [PDF]

  25. 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]

Ph.D. Rensselaer Polytechnic Institute, Department of Mathematics, 2002.
Thesis title: Statistically relevant and irrelevant conserved quantities for the equilibrium statistical description of the truncated Burgers-Hopf equation and the equations for barotropic flow.
[PDF]

Software

The multidimensional moment-constrained maximum entropy algorithm
The library for the PC and some other platforms is there with few examples in C, C++ and FORTRAN (see file maxent_dist.tar.gz). A short manual is included.
Last modified: Fri Mar 28 12:23:36 CDT 2014