# Papers

**"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),*accepted to*__Communications in Mathematical Sciences,__(2018), 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.**"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.**"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.**"Vortex phase separation in mesoscopic superconductors"**(with O. Iaroshenko, V. Rybalko, V. M. Vinokur),__Scientific Reports: Nature Publishing Group__**3**(2013), 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.**"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.**"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.**"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.**"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.**"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.**"Network Approximation in the Limit of Small Interparticle Distance of the Effective Properties of a High-Contrast Random Dispersed Composite"**(with A. Kolpakov),__Archive for Rational Mechanics and Analysis__, 159, pp. 179-227 (2001), 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.**"Large Time Asymptotics of Solutions to a Model Combustion System with Critical Nonlinearity"**(with J. Xin),__Nonlinearity__, 8:161-178 (1995), 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.

# 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.