**Publications**

- "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). - "Vortex phase separation in mesoscopic superconductors"
(with O. Iaroshenko, V. Rybalko, V. M. Vinokur),
__Scientific Reports: Nature Publishing Group__**3**(2013). - "Collective dynamics in semidilute bacterial suspensions"
(with S.D. Ryan, A. Sokolov, I.S. Aranson),
__New Journal of Physics__**15**105021 (2013) - "Effective viscosity of puller-like microswimmers: a renormalization approach"
(with S. Gluzman and D.A. Karpeev),
__J. Royal Society Interface__**10**:89 (2013) -
"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). - "Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization"
(with H. Owhadi, L. Zhang), accepted to
__ESAIM: Mathematical Modelling and Numerical Analysis.__**Special issue**(2013). - "Collision of microswimmers in viscous fluid"
(with M. Potomkin, V. Gyrya, I. Aranson),
__Physical Review E__**87**053005 (2013). -
"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). -
"Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes"
(with V. Rybalko), special issue
__NHM__**8**:1 pp.115-130 (2013). -
"Renormalized Ginzburg-Landau energy and location of near boundary vortices"
(with V. Rybalko, N.K. Yip),
__NHM__, 7:1 (online publication) (2012). -
"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). -
"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). , v. 13:1, pp. 53-66 (2011).__"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__-
"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). -
"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). -
"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).__ __"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).__"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).__"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).__"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).__"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).__"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.__"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).__"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).__"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).__"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).__"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).__"Nonlinear Dielectric Response of Periodic Composite Materials" (with A. Kolpakov, A. Tagantsev, and A. Kanareikin),____J. of Electroceramics__, v.18, pp. 129-137 (2007).__"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).__"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).__"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).__"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).__"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).__"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).__"Ginzburg-Landau model of a liquid crystal with random inclusions" (with E. Khruslov),____Journal of Mathematical Physics__, 46, pp. 095107:1-15 (2005).__"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).__"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).__"Homogenization of a Ginzburg-Landau functional" (with D. Cioranescu and D. Golovaty),____C. R. Acad. Sci.__, Paris, 340/1 pp 87-92 (2005).__"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).__"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).__"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).__"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).__"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).__"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).-
__"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). __"Ginzburg-Landau Minimizers with Prescribed Degrees: Dependence on Domain" (with P. Mironescu)____C. R. Acad. Sci__, Paris, 337 (6), pp. 375-380 (2003).__"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).__"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).__"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).__"On uniqueness of vector-valued minimizers of the Ginzburg-Landau functional in annular domains" (with D. Golovaty),____Calculus of Variations__, 14, 213-232 (2002).__"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).__"Generalized Clausius-Mosotti formula for random composite with circular fibers" (with V. Mityushev),____Journal of Statistical Physics__, 102, 1/2 pp. 115-145 (2001).__"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).__"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).__"Frequency-dependent acoustics of composites with interfaces" (with M. Avellaneda and J. Clouet),____SIAM Journal of Applied Mathematics__, 60:6, 2143-2181 (2000).__"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).__"Homogenization of the Ginzburg-Landau functional with a surface energy term",____Asymptotic Analysis__, 37-59, 21 (1999).__"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).__"Homogenization of harmonic maps and superconducting composites" (with E. Ya. Khruslov),____SIAM Journal of Applied Mathematics__, 59, 5 pp. 1892-1916 (1999).__"Effective Properties of Superconducting and Superfluid Composites",____International Journal of Modern Physics B__, 12, 29, 3063-3073 (1999).__"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).__"Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System" (with J.Wehr),____Communications in Mathematical Physics__, 185, 73-92 (1997).__"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).__"Large Time Asymptotics of Solutions to a Model Combustion System with Critical Nonlinearity" (with J. Xin),____Nonlinearity__, 8:161-178 (1995).__"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).__"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).__"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).-
__"Exact Result for the Effective Conductivity of a Continuum Percolation Model" (with K. Golden),____Physical Review B__, 50 (4):2114-2117 (1994). __"Asymptotics of the Homogenized Moduli for the Elastic Chess-Board Composite" (with S. Kozlov),____Archive for Rational Mechanics and Analysis__, 118, 95-112 (1992).__"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).__"The localization problem for a random elastic continuum with dispersion" (with S. Molchanov),____Mathematics Notes, USSR Academy__, 49, No. 3:346-348 (1991).__"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).__"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).-
__"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). __"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).__"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).__"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).__"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).__"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).-
__"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). __"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).

**Recent Preprints and Submitted Papers (PostScript/PDF files)**

- "Sharp interface limit in a phase field model of cell motility" (with V. Rybalko, M. Potomkin),
__arXiv__submitted (2013) - "Complexity reduction in many particles systems with random initial data"
(with P.E. Jabin, M. Potomkin),
__arXiv__submitted (2013)