Rafail Abramov

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

Teaching

MATH 210 — Calculus III

Publications and preprints

  1. R. Abramov, Turbulence via intermolecular potential: Uncovering the origin, Communications in Nonlinear Science and Numerical Simulation, 2024, vol. 130, 107727.
    [DOI] [arXiv.org]

  2. R. Abramov, Turbulence via intermolecular potential: Viscosity and transition range of the Reynolds number, Fluids, 2023, vol. 8, no. 3, 101.
    [DOI] [arXiv.org]

  3. R. Abramov, Turbulence via intermolecular potential: A weakly compressible model of gas flow at low Mach number, Physics of Fluids, 2022, vol. 34, no. 12, 125104.
    [DOI] [arXiv.org]

  4. R. Abramov, Creation of turbulence in polyatomic gas flow via an intermolecular potential, Physical Review Fluids, 2022, vol. 7, 054605.
    [DOI] [arXiv.org]

  5. R. Abramov, Turbulence in large-scale two-dimensional balanced hard sphere gas flow, Atmosphere, 2021, vol. 12, no. 11, 1520.
    [DOI] [arXiv.org]

  6. R. Abramov, Macroscopic turbulent flow via hard sphere potential, AIP Advances, 2021, vol. 11, no. 8, 085210.
    [DOI] [arXiv.org] Also see erratum.

  7. R. Abramov, Formation of turbulence via an interaction potential, preprint, 2021.
    [arXiv.org]

  8. R. Abramov, Turbulent energy spectrum via an interaction potential, Journal of Nonlinear Science, 2020, vol. 30, 3057—3087.
    [DOI] [Free view-only version] [arXiv.org]

  9. R. Abramov, A theory of average response to large jump perturbations, Chaos, 2019, vol. 29, 083128.
    [DOI] [arXiv.org]

  10. R. Abramov, The random gas of hard spheres, J, 2019, vol. 2, no. 2, 162—205.
    [DOI] [arXiv.org]

  11. R. Abramov, The effect of the Enskog collision terms on the steady shock transitions in a hard sphere gas, preprint, 2018.
    [arXiv.org]

  12. R. Abramov and J. Otto, Nonequilibrium diffusive gas dynamics: Poiseuille microflow, Physica D, 2018, vol. 371, 13—27.
    [DOI] [arXiv.org]

  13. R. Abramov, Gas near a wall: shortened mean free path, reduced viscosity, and the manifestation of the Knudsen layer in the Navier-Stokes solution of a shear flow, Journal of Nonlinear Science, 2018, vol. 28, no. 3, 833—845.
    [DOI] [arXiv.org]

  14. R. Abramov, A mass diffusion effect in gas dynamics equations, preprint, 2017.
    [arXiv.org]

  15. R. Abramov, Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers, Physica A, 2017, vol. 484, 532—557.
    [DOI] [arXiv.org]

  16. R. Abramov, Leading order response of statistical averages of a dynamical system to small stochastic perturbations, Journal of Statistical Physics, 2017, vol. 166, no. 6, 1483—1508.
    [DOI] [arXiv.org]

  17. R. Abramov, Linear response of the Lyapunov exponent to a small constant perturbation, Communications in Mathematical Sciences, 2016, vol. 14, no. 4, 1155—1167.
    [DOI] [arXiv.org]

  18. R. Abramov, A simple stochastic parameterization for reduced models of multiscale dynamics, Fluids, 2016, vol. 1, no. 1.
    [DOI] [arXiv.org]

  19. R. Abramov and M. Kjerland, The response of reduced models of multiscale dynamics to small external perturbations, Communications in Mathematical Sciences, 2016, vol. 14, no. 3, 831—855.
    [DOI] [arXiv.org]

  20. R. Abramov, Coarse-grained transport of a turbulent flow via moments of the Reynolds-averaged Boltzmann equation, submitted to Journal of Fluid Mechanics, 2015 — oops, rejected. Left as a preprint.
    [arXiv.org]

  21. 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] [DOI] [arXiv.org]

  22. 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] [DOI] [arXiv.org]

  23. 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] [DOI] [arXiv.org]

  24. 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]

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

  26. 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]

  27. 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]

  28. 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]

  29. 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]

  30. 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]

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

  32. 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]

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

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

  35. 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]

  36. 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]

  37. 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]

  38. 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]

  39. 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]

  40. 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]

  41. 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]

  42. 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.
A new, better version of the maxent algorithm
I am working on a better version of what I wrote years ago. The new code is aimed at use in various applications with different moment problems. Currently, the code is in its initial stage, and the manual is not yet available.

Last modified: Tue Jan 18 20:19:12 CST 2022