Full Publication List


  1. "Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents" (with Y. Almog, D. Golovaty, I. Shafrir), submitted to SIAM Journal of Mathematical Analysis, (2018), pdf.
  2. "The effect of randomness on the distribution of multiple Ginzburg-Landau vortices pinned by small holes" (with V. Mityushev, S.D. Ryan), accepted to IMA Journal of Applied Mathematics, (2018), pdf.
  3. "On the convergence of formally diverging neural net-based classifiers” (with P.-E. Jabin), Comptes Rendus Mathematique, 356(4), 395-405 (2018), pdf.
  4. "Bifurcation of traveling waves in a Keller-Segel type free boundary model of cell motility” (with J. Fuhrmann, V. Rybalko), accepted to Communications in Mathematical Sciences, (2018), pdf.
  5. "Focusing of Active Particles in a Converging Flow" (with I. Aranson, A. Kaiser, M. Potomkin), New Journal of Physics, Vol. 19, p. 115005 (2017), pdf.
  6. "Minimal Model of Directed Cell Motility on Patterned Substrates” (with I. Aranson, M. Mizuhara), Physical Review E, 96(5) p. 052408 (2017), pdf.
  7. "On approximation of Ginzburg-Landau minimizers by S1-valued maps in domains with vanishingly small holes"(with D. Golovaty, O. Iaroshenko, V. Rybalko), Journal of Differential Equations, Vol. 264 no. 2, pp. 1317 - 1347 (2017), pdf.
  8. "Flagella bending affects macroscopic properties of bacterial suspensions” (with M. Potomkin, M. Tournus, and I. Aranson), Journal of the Royal Society Interface, Vol. 14 no. 130, p.20161031 (2017), pdf.
  9. "A two scale Gamma-convergence approach for random non-convex homogenization" (with E. Sandier and S. Serfaty), Journal of Calculus of Variations and PDEs No. 6, p. 156 (2017), pdf.
  10. "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.
  11. "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.
  12. "Phase-Field Model of Cell Motility: Traveling Waves and Sharp Interface Limit" (with M. Potomkin and V. Rybalko), Comptes Rendus Mathematique, 354(10), pp. 986-992 (2016), pdf.
  13. "Sharp interface limit in a phase field model of cell motility” (with V. Rybalko, M. Potomkin), Network and Heteregeneous Media, Vol. 12, Number 4, pp. 551-590 (2017), pdf.
  14. "Multiple Ginzburg-Landau Vortices Pinned by Randomly Distributed Small Holes" (with V. Mityushev and S. D. Ryan), submitted (2016), pdf.
  15. "On an evolution equation in a cell motility model" (with M.S. Mizuhara, V. Rybalko, L. Zhang), Physica D, 318-319, pp. 12-25 (2016), pdf.
  16. "Rayleigh Approximation for ground states of the Bose and Coulomb glasses" (with S. D. Ryan, V. Mityushev, and V. M. Vinokur), Scientific Reports: Nature Publishing Group, 5, 7821 (2015), pdf.
  17. "Flexibility of bacterial flagella in external shear results in complex swimming trajectories" (with M. Tournus, A. Kirshtein, and I. Aranson), Journal of the Royal Society Interface 12 (102) (2014), pdf.
  18. "Minimax Critical Points in Ginzburg-Landau Problems with Semi-stiff Boundary Conditions: Existence and Bubbling" (with P. Mironescu, V. Rybalko, E. Sandier), Comm. in PDEs 39(5) pp. 946-1005 (2014), pdf.
  19. "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.
  20. "Vortex phase separation in mesoscopic superconductors" (with O. Iaroshenko, V. Rybalko, V. M. Vinokur), Scientific Reports: Nature Publishing Group 3 (2013), pdf.
  21. "Collective dynamics in semidilute bacterial suspensions" (with S.D. Ryan, A. Sokolov, I.S. Aranson), New Journal of Physics 15 105021 (2013), pdf.
  22. "Effective viscosity of puller-like microswimmers: a renormalization approach" (with S. Gluzman and D.A. Karpeev), J. Royal Society Interface 10:89 (2013), pdf.
  23. "A kinetic model for semi-dilute bacterial suspensions" (with S.D. Ryan, B.M. Haines, D.A. Karpeev), SIAM MMS 11:4, pp. 1176-1196 (2013), pdf.
  24. "Collision of microswimmers in viscous fluid" (with M. Potomkin, V. Gyrya, I. Aranson), Physical Review E 87 053005 (2013), pdf.
  25. "On the limit p to infinity of global minimizers for a p-Ginzburg-Landau-type energy" (with Y. Almog, L. Berlyand, D. Golovaty, I. Shafrir), Annales de l'Institut Henri Poincare (c) Analyse Non Lineaire 30(6), pp.1159-1174 (2013), pdf.
  26. "Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes" (with V. Rybalko), special issue NHM 8:1 pp.115-130 (2013), pdf.
  27. "Renormalized Ginzburg-Landau energy and location of near boundary vortices" (with V. Rybalko, N.K. Yip), NHM, 7:1 (online publication) (2012), pdf.
  28. "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.
  29. "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.
  30. "Minimizers of the magnetic Ginzburg-Landau functional in simply connected domain with prescribed degree on the boundary" (with O. Misiats, V. Rybalko), Communications in Contemporary Mathematics, v. 13:1, pp. 53-66 (2011), pdf.
  31. "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.
  32. "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.
  33. "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.
  34. "Near boundary vortices in a magnetic Ginzburg-Landau model: their locations via tight energy bounds" (with O. Misiats, V. Rybalko), J. Func. Analysis, v. 258, pp. 1728-1762 (2010), pdf.
  35. "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.
  36. "A model of hydrodynamic interaction between swimming bacteria" (with V.T. Gyrya, I.S. Aranson, D.A. Karpeev), Bulletin of Mathematical Biology v. 72, pp. 148-183 (2010), pdf.
  37. "Solutions with Vortices of a Semi-Stiff Boundary Value Problem for the Ginzburg-Landau Equation" (with V. Rybalko), J. European Math. Society v. 12 n. 6, pp.1497-1531 (2009), pdf.
  38. "Global minimizers for a p-Ginzburg-Landau-type energy in R2" (with Y. Almog, D. Golovaty, and I. Shafrir), J. Func. Analysis, v.256, n.7, pp. 2268-2290 (2009), pdf.
  39. "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.
  40. "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.
  41. "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.
  42. "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.
  43. "A Network Model of Geometrically Constrained Deformations of Granular Materials" (with K.A. Ariyawansa and A. Panchenko), Networks and Heterogenous Media, v.3, pp. 125-148 (2008), pdf.
  44. "Rise of Correlations of Transformation Strains in Random Polycrystals" (with O. Bruno and A. Novikov), SIAM J. Math. Analysis, v.40, n.4, pp. 15501584 (2008), pdf.
  45. "Nonlinear Dielectric Response of Periodic Composite Materials" (with A. Kolpakov, A. Tagantsev, and A. Kanareikin), J. of Electroceramics, v.18, pp. 129-137 (2007), pdf.
  46. "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.
  47. "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.
  48. "Nonexistence of Ginzburg-Landau minimizers with prescribed degree on the boundary of a doubly connected domain" (with D. Golovaty and V. Rybalko), C. R. Acad. Sci, Paris, 343/1, pp. 63-68 (2006), pdf.
  49. "Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices" (with P. Mironescu), J. Functional Analysis, v. 239, n. 1, pp. 76-99 (2006), pdf.
  50. "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.
  51. "Methodology, theory and practice of sociological analysis of modern society" (with O. Kutsenko and V. Sherstobitov), in collection of papers A theoretical model to explain support of terrorist actions, Kharkov State University, pp 63-69 (2005).
  52. "Ginzburg-Landau model of a liquid crystal with random inclusions" (with E. Khruslov), Journal of Mathematical Physics, 46, pp. 095107:1-15 (2005), pdf.
  53. "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.
  54. "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.
  55. "Homogenization of a Ginzburg-Landau functional" (with D. Cioranescu and D. Golovaty), C. R. Acad. Sci., Paris, 340/1 pp 87-92 (2005), pdf.
  56. "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.
  57. "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.
  58. "Transport properties of densely packed composites. Effects of shapes and spacings of inclusions" (with D. Golovaty, A. Movchan, and J. Phillips) The Quarterly Journal of Mechanics and Applied Mathematics, 57, pp. 495-528 (2004), pdf.
  59. "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.
  60. "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.
  61. "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.
  62. "Random network model for heat transfer in high contrast composite materials" (with D. Gerenrot and J. Phillips), IEEE Transactions on Advanced Packaging, 26:4, pp. 410-417 (2003), pdf.
  63. "Ginzburg-Landau Minimizers with Prescribed Degrees: Dependence on Domain" (with P. Mironescu) C. R. Acad. Sci, Paris, 337 (6), pp. 375-380 (2003), pdf.
  64. "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).
  65. "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.
  66. "Competition between the surface and the boundary layer energies in a Ginzburg-Landau model of a liquid crystal composite" (with E. Ya. Khruslov), Asymptotic Analysis, 29, pp. 185-219 (2002), pdf.
  67. "On uniqueness of vector-valued minimizers of the Ginzburg-Landau functional in annular domains" (with D. Golovaty), Calculus of Variations, 14, 213-232 (2002), pdf.
  68. "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.
  69. "Generalized Clausius-Mosotti formula for random composite with circular fibers" (with V. Mityushev), Journal of Statistical Physics, 102, 1/2 pp. 115-145 (2001), pdf.
  70. "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.
  71. "Symmetry Breaking in Annular Domains for a Ginzburg-Landau Superconductivity Model" (with K. Voss), Proceedings of IUTAM 99/4 Symposium, Sydney, Australia, January, Kluwer Academic Publishers, 189-200 (2001), pdf.
  72. "Frequency-dependent acoustics of composites with interfaces" (with M. Avellaneda and J. Clouet), SIAM Journal of Applied Mathematics, 60:6, 2143-2181 (2000), pdf.
  73. "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.
  74. "Homogenization of the Ginzburg-Landau functional with a surface energy term", Asymptotic Analysis, 37-59, 21 (1999), pdf.
  75. "Asymmetric Strain-Stress Distribution Function for Crystal with Random Point Defects" In the book Homogenization, ed. V. Berdichevsky, V. Jikov and G. Papanicolaou, World Scientific, 179-192 (1999), pdf.
  76. "Homogenization of harmonic maps and superconducting composites" (with E. Ya. Khruslov), SIAM Journal of Applied Mathematics, 59, 5 pp. 1892-1916 (1999), pdf.
  77. "Effective Properties of Superconducting and Superfluid Composites", International Journal of Modern Physics B, 12, 29, 3063-3073 (1999), pdf.
  78. "First-Passage Percolation, Semi-Directed Bernoulli Percolation, and Failure in Brittle Materials" (with M. Rintoul and S. Torquato) Journal of Statistical Physics, 91, 3/4, 603-623 (1998), pdf.
  79. "Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System" (with J.Wehr), Communications in Mathematical Physics, 185, 73-92 (1997), pdf.
  80. "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.
  81. "Large Time Asymptotics of Solutions to a Model Combustion System with Critical Nonlinearity" (with J. Xin), Nonlinearity, 8:161-178 (1995), pdf.
  82. "The Probability Distribution of the Percolation Threshold in a Large System" (with J. Wehr), Journal of Physics A: Mathematics and General, 28:24, 7127-7133 (1995), pdf.
  83. "The accuracy of O'Doherty-Anstey approximation for wave propagation in highly disordered stratiffied media" (with R. Burridge), Wave Motion, 21:3, 357-373 (1995), pdf.
  84. "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.
  85. "Exact Result for the Effective Conductivity of a Continuum Percolation Model" (with K. Golden), Physical Review B, 50 (4):2114-2117 (1994), pdf.
  86. "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.
  87. "Exactly solvable random model and IR spectroscopy of strained defective lattice" (with N. Chukanov and V. Dubovitskii), Chemical Physics Letters, 181, No. 5:450-454 (1991), pdf.
  88. "The localization problem for a random elastic continuum with dispersion" (with S. Molchanov), Mathematics Notes, USSR Academy, 49, No. 3:346-348 (1991), pdf.
  89. "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.
  90. "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).
  91. "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).
  92. "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).
  93. "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).
  94. "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).
  95. "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).
  96. "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).
  97. "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).
  98. "On convergence of spectral families of operators for Neumann boundary value problems", Function theory, functional analysis and applications, Kharkov, 33:3-8 (in Russian, 1980).

  99. Books

    • "Getting Acquainted with Homogenization and Multiscale" (with V. Rybalko), to appear in Birkhauser series Compact Textbooks in Mathematics (2018).

    • "Introduction to Network Approximation for Materials Modeling" (with A. Kolpakov and A. Novikov), Cambridge University Press (2012), pdf.