Publications

Homogenization theory


  1. "Complexity reduction in many particles systems with random initial data" (with P.E. Jabin, M. Potomkin), SIAM/ASA Journal of Uncertainty Quantification, 4(1), pp. 446-474 (2016), pdf.
  2. "Effective rheological properties in semidilute bacterial suspensions" (with M. Potomkin and S. D. Ryan), Bulletin of Mathematical Biology, 78(3), pp. 580-615 (2016), pdf.
  3. "A two scale Gamma-convergence approach for random non-convex homogenization" (with E. Sandier and S. Serfaty), submitted (2016), pdf.
  4. "Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization" (with H. Owhadi, L. Zhang), ESAIM: Mathematical Modelling and Numerical Analysis. Special issue, 48 (2), pp. 517-552 (2014), pdf.
  5. "Vortex phase separation in mesoscopic superconductors" (with O. Iaroshenko, V. Rybalko, V. M. Vinokur), Scientific Reports: Nature Publishing Group 3 (2013), pdf.
  6. "Effective viscosity of puller-like microswimmers: a renormalization approach" (with S. Gluzman and D.A. Karpeev), J. Royal Society Interface 10:89 (2013), pdf.
  7. "Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes" (with V. Rybalko), special issue NHM 8:1 pp.115-130 (2013), pdf.
  8. "Effective viscosity of bacterial suspensions: A three-dimensional PDE model with stochastic torque" (with B.M. Haines, I.S. Aranson, D.A. Karpeev),  Comm. Pure Appl. Anal., v. 11(1), pp. 19-46 (2012), pdf.
  9. "Viscosity of bacterial suspensions: Hydrodynamic interactions and self-induced noise" (with S.D. Ryan, B.M. Haines, F. Ziebert, I.S. Aranson), Rapid Communication to Phys. Rev. E, 83 050904(R) (2011), pdf.
  10. "Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations" (with V. Gyrya, K. Lipnikov, I. Aranson), J. Math. Biology , v. 62 (5), pp. 707-740 (2011), pdf.
  11. "Global Energy Matching Method for Atomistic to Continuum Modeling of Self-Assembling Biopolymer Aggregates" (with Lei Zhang, M.V. Fedorov, H. Owhadi), Multiscale Model. Simul. v. 8, n. 5, pp. 1958-1980 (2010), pdf.
  12. "Flux norm approach to finite dimensional homogenization approximations with non-separated scales and high contrast" (with H. Owhadi), Arch. Rat. Mech. Anal. , v. 198, n. 2, pp. 677-721 (2010), pdf.
  13. "A three-dimensional model for the effective viscosity of bacterial suspensions" (with B.M. Haines, A. Sokolov, I.S. Aranson, D.A. Karpeev), Physical Review E, v. 80, pp.041922 (2009), pdf.
  14. "Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a 2D Model of Concentrated Suspensions" (with Y. Gorb and A. Novikov), Arch. Rat. Mech. Anal., v. 193, n. 3, pp. 585-622, (2009), DOI:10.1007/s00205-008-0152-2, pdf.
  15. "Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain" (with P. Mironescu), Networks and Heterogenous Media, v.3, n.3, pp. 461-487 (2008), pdf.
  16. "Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model" (with B. Haines, I. Aronson, and D. Karpeev), Physical Biology, 5:4, 046003 (9pp) (2008), pdf.
  17. "The Homogenized Model of Small Oscillations of Complex Fluids" (with M. Berezhnyy and E. Khruslov), Networks and Heterogenous Media, v.3, n.4, pp. 831-862 (2008), pdf.
  18. "Strong and weak blow up of the viscous dissipation rates for concentrated suspensions" (with A. Panchenko), Journal of Fluid Mechanics, v. 578, pp. 1-34 (2007), pdf.
  19. "Asymptotic analysis of an array of absolutely conducting holes" (with G. Cardone, Y. Gorb, and G. Panasenko), Networks and Heterogenous Media, 1:3, pp. 353-377 (2006), pdf.
  20. "Continuum limit for three-dimensional mass-spring networks and discrete Korn's inequality" (with M. Berezhnyy), Journal of Mechanics and Physics of Solids, 54:3, pp. 635-669 (2006), pdf.
  21. "Network approximation for effective viscosity of concentrated suspensions with complex geometry" (with L. Borcea and A. Panchenko), SIAM Journal on Mathematical Analysis, 36:5, pp 1580-1628 (2005), pdf.
  22. "Asymptotics of the Effective Conductivity of Composites with Closely Spaced Inclusions of Optimal Shape" (with Y. Gorb), Quarterly Journal of Mechanics and Applied Mathematics, 58 (1), pp. 83-106 (2005), pdf.
  23. "Homogenization of a Ginzburg-Landau functional" (with D. Cioranescu and D. Golovaty), C. R. Acad. Sci., Paris, 340/1 pp 87-92 (2005), pdf.
  24. "Network approximation for effective viscosity of concentrated suspensions with complex geometry" (with L. Borcea and A. Panchenko), SIAM Journal on Mathematical Analysis, 36:5, pp 1580-1628 (2005), pdf.
  25. "Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity" (with V. Mityushev), Journal of Statistical Physics, 118, 3/4 pp 481-509 (2005), pdf.
  26. "Homogenization of a Ginzburg-Landau model for a nematic liquid crystal with inclusions" (with D. Cioranescu and D. Golovaty), Journal des Mathematiques Pures et Appliquees, 84:1, pp. 97-136 (2005), pdf.
  27. "The Effective Conductivity of Densely Packed High Contrast Composites with Inclusions of Optimal Shape" (with Y. Gorb) Proceedings of Continuum Models and Discrete Systems (CMDS10) Conference, Tel-Aviv, Israel (2004), pdf.
  28. "Homogenized Non-Newtonian Viscoelastic Rheology of a Suspension of Interacting Particles in a Viscous Newtonian Fluid" (with E. Ya. Khruslov) SIAM Journal of Applied Mathematics, 64:3, pp. 1002-1034 (2004), pdf.
  29. "Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions" (with Y. Gorb and A. Novikov), in Lecture Notes in Computational Science and Engineering, editors B. Engquist, P. Lotstedt and O. Runborg, Springer Verlag (2004), pdf.
  30. "Homogenized Non-Newtonian Viscoelastic Rheology of a Suspension of Interacting Particles in a Viscous Newtonian Fluid" (with E. Ya. Khruslov) SIAM Journal of Applied Mathematics, 64:3, pp. 1002-1034 (2004), pdf.
  31. "Geometric patterns and effective conductivity of highly packed two-phase composites" (with A. Novikov), Homogenization 2001, (Naples), 113-129 GAKUTO Internat. Ser. Math. Sci. Appl, 18, Tokyo (2003).
  32. "Error of the network approximation for densely packed composites with irregular geometry" (with A. Novikov), SIAM Journal on Mathematical Analysis, 34(2), pp. 385-408 (2002), pdf.
  33. "Network Approximation in the Limit of Small Interparticle Distance of the Effective Properties of a High-Contrast Random Dispersed Com- posite" (with A. Kolpakov), Archive for Rational Mechanics and Analysis, 159, pp. 179-227 (2001), pdf.
  34. "Homogenization of harmonic maps with large number of vortices and applications in superconductivity and superfluidity" (with E. Ya. Khruslov), Advances in Differential Equations, v. 6/2, pp. 229-256 (2001), pdf.
  35. "Homogenization. In Memory of Sergei Kozlov." Edited by V. Berdichevsky, V. Jikov and G. Papanicolaou", Series on Advances in Mathematics for Applied Sciences, 50, pp. xiv+418 (1999), pdf.
  36. "Homogenization of the Ginzburg-Landau functional with a surface energy term", Asymptotic Analysis, 37-59, 21 (1999), pdf.
  37. "Homogenization of harmonic maps and superconducting composites" (with E. Ya. Khruslov), SIAM Journal of Applied Mathematics, 59, 5 pp. 1892-1916 (1999), pdf.
  38. "Effective Properties of Superconducting and Superfluid Composites", International Journal of Modern Physics B, 12, 29, 3063-3073 (1999), pdf.
  39. "Renormalization Group Technique for Asymptotic Behavior of a Thermal Diffusive Model with Critical Nonlinearity" (with J. Xin), in Pitman Research Notes, No. 324 "Recent Development in Evolution Equations", 76-85 (1995), pdf.
  40. "Effective Elastic Moduli of a Soft Medium with Hard Polygonal Inclusions and Extremal Behavior of Effective Poisson's Ratio" (with K.S. Promislow), Journal of Elasticity, 40:1, 45-73 (1995), pdf.
  41. "Exact Result for the Effective Conductivity of a Continuum Percolation Model" (with K. Golden), Physical Review B, 50 (4):2114-2117 (1994), pdf.
  42. "Asymptotics of the Homogenized Moduli for the Elastic Chess-Board Composite" (with S. Kozlov), Archive for Rational Mechanics and Analysis, 118, 95-112 (1992), pdf.
  43. "The averaging of the diffusion equation in porous medium with weak absorption" (with M. Goncharenko), Journal of Soviet Mathematics, 53, No. 5:3428-3435 (1990), pdf.
  44. "Operational separation of variables in problems of short wave asymptotic behavior for differential equations with fast oscillating coefficients" (with S. Yu. Dobrokhotov), Sov. Phys. Dokl., 32 (9):714-716 (1987).
  45. "Homogenization and short wave asymptotics for solutions of an initial value problem for the Schroedinger equation with a rapidly oscillating potential" (with S. Yu. Dobrokhotov), Uspekhy Mat. Nauk., 41 (4):195-196 (in Russian, 1986).
  46. "Asymptotic behavior of solutions of the Dirichlet boundary value problem in elasticity for domains with fine-grained boundaries" Uspekhy Mat. Nauk., 38, No. 6 (234), 107-108 (in Russian, 1983).
  47. "Averaging of elasticity equations in domains with fine-grained boundaries, Part 1-2", Functional theory, functional analysis and applications, Kharkov, 39:16-25 - Part 1; 40:16-23 - Part 2 (in Russian, 1983).
  48. "An asymptotic description for a thin plate with a large number of small holes", Ukrainian Academy of Science Reports, Ser. A., No. 10:5-8 (in Russian, 1983).
  49. "Averaging of boundary value problems for higher order differential operators in domains with holes" (with I. Yu. Chudinovich), Soviet Math. Dokl., 28, No. 2:427-430 (1983).
  50. "An averaged description of an elastic medium with a large number of small absolutely solid inclusions" (with A. Okhotsimskii), Soviet Phys. Dokl., 28 (1):81-84 (1983).
  51. "On the vibration of an elastic body with a large number of small holes" Ukrainian Academy of Science reports, Ser. A, 2:3-5 (in Russian, 1983).