# Papers

**"Stability for the Training of Deep Neural Networks and Other Classifiers”**(with P.-E. Jabin and C. A. Safsten), submitted (2020) pdf.-
**"Stability of steady states and bifurcation to traveling waves in a free boundary model of cell motility"**(with V. Rybalko),__submitted, available on arxiv.org__(2019), pdf **"A kinetic approach to active rod dynamics in confined domains"**(with P.-E. Jabin, M. Potomkin, E. Ratajczyk),__accepted to SIAM Multiscale Modeling and Simulations,__(2019), pdf.**"Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents"**(with Y. Almog, D. Golovaty, I. Shafrir),__SIAM Journal of Mathematical Analysis,__51/2, 873-912 (2019), pdf.**"The effect of randomness on the distribution of multiple Ginzburg-Landau vortices pinned by small holes"**(with V. Mityushev, S.D. Ryan),__IMA Journal of Applied Mathematics__, 83/6, 977-1006 (2018), pdf.**"On the convergence of formally diverging neural net-based classifiers”**(with P.-E. Jabin),__Comptes Rendus Mathematique,__356(4), 395-405 (2018), pdf.**"Bifurcation of traveling waves in a Keller-Segel type free boundary model of cell motility”**(with J. Fuhrmann, V. Rybalko),__Communications in Mathematical Sciences,__16/3, 735-762 (2018), pdf.**"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.**"Minimal Model of Directed Cell Motility on Patterned Substrates”**(with I. Aranson, M. Mizuhara),__Physical Review E__, 96(5) p. 052408 (2017), pdf.-
**"On approximation of Ginzburg-Landau minimizers by S**(with D. Golovaty, O. Iaroshenko, V. Rybalko),^{1}-valued maps in domains with vanishingly small holes"__Journal of Differential Equations__, Vol. 264 no. 2, pp. 1317 - 1347 (2017), pdf. **"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.**"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.**"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.**"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.**"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.**"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.**"Multiple Ginzburg-Landau Vortices Pinned by Randomly Distributed Small Holes"**(with V. Mityushev and S. D. Ryan),*submitted*(2016), pdf.**"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.**"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.**"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.**"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.**"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.**"Vortex phase separation in mesoscopic superconductors"**(with O. Iaroshenko, V. Rybalko, V. M. Vinokur),__Scientific Reports: Nature Publishing Group__**3**(2013), pdf.**"Collective dynamics in semidilute bacterial suspensions"**(with S.D. Ryan, A. Sokolov, I.S. Aranson),__New Journal of Physics__**15**105021 (2013), pdf.**"Effective viscosity of puller-like microswimmers: a renormalization approach"**(with S. Gluzman and D.A. Karpeev),__J. Royal Society Interface__**10**:89 (2013), pdf.**"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.**"Collision of microswimmers in viscous fluid"**(with M. Potomkin, V. Gyrya, I. Aranson),__Physical Review E__**87**053005 (2013), pdf.**"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.**"Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes"**(with V. Rybalko), special issue__NHM__**8**:1 pp.115-130 (2013), pdf.**"Renormalized Ginzburg-Landau energy and location of near boundary vortices"**(with V. Rybalko, N.K. Yip),__NHM__, 7:1 (online publication) (2012), pdf.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"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.-
**"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), pdf.**"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.**"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.**"Homogenization of a Ginzburg-Landau functional"**(with D. Cioranescu and D. Golovaty),__C. R. Acad. Sci.__, Paris, 340/1 pp 87-92 (2005), pdf.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"Ginzburg-Landau Minimizers with Prescribed Degrees: Dependence on Domain"**(with P. Mironescu)__C. R. Acad. Sci__, Paris, 337 (6), pp. 375-380 (2003), pdf.-
**"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), pdf.**"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.**"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.**"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.**"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.**"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.**"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.**"Frequency-dependent acoustics of composites with interfaces"**(with M. Avellaneda and J. Clouet),__SIAM Journal of Applied Mathematics__, 60:6, 2143-2181 (2000), pdf.**"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.**"Homogenization of the Ginzburg-Landau functional with a surface energy term"**,__Asymptotic Analysis__, 37-59, 21 (1999), pdf.**"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.**"Homogenization of harmonic maps and superconducting composites"**(with E. Ya. Khruslov),__SIAM Journal of Applied Mathematics__, 59, 5 pp. 1892-1916 (1999), pdf.**"Effective Properties of Superconducting and Superfluid Composites"**,__International Journal of Modern Physics B__, 12, 29, 3063-3073 (1999), pdf.**"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.**"Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System"**(with J.Wehr),__Communications in Mathematical Physics__, 185, 73-92 (1997), pdf.**"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.**"Large Time Asymptotics of Solutions to a Model Combustion System with Critical Nonlinearity"**(with J. Xin),__Nonlinearity__, 8:161-178 (1995), pdf.**"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.**"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.**"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.**"Exact Result for the Effective Conductivity of a Continuum Percolation Model"**(with K. Golden),__Physical Review B__, 50 (4):2114-2117 (1994), pdf.**"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.**"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.**"The localization problem for a random elastic continuum with dispersion"**(with S. Molchanov),__Mathematics Notes, USSR Academy__, 49, No. 3:346-348 (1991), pdf.**"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.-
**"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). **"Getting Acquainted with Homogenization and Multiscale"**(with V. Rybalko), Birkhauser series Compact Textbooks in Mathematics, Springer (2018).**"Introduction to Network Approximation for Materials Modeling"**(with A. Kolpakov and A. Novikov), Cambridge University Press (2012), pdf.