Rafail Abramov

Teaching

Publications and preprints

1. R. Abramov, Turbulence via intermolecular potential: Uncovering the origin, preprint, 2023.
   [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]

Software