Selected Publications

Papers


  1. "On the convergence of formally diverging neural net-based classifiers” (with P.-E. Jabin), Comptes Rendus Mathematique, 356(4), 395-405 (2018), pdf.
  2. "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.
  3. "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.
  4. "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.
  5. "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.
  6. "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.
  7. "Vortex phase separation in mesoscopic superconductors" (with O. Iaroshenko, V. Rybalko, V. M. Vinokur), Scientific Reports: Nature Publishing Group 3 (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. "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.
  10. "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.
  11. "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.
  12. "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.
  13. "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.
  14. "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.
  15. "Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System" (with J.Wehr), Communications in Mathematical Physics, 185, 73-92 (1997), pdf.
  16. "Large Time Asymptotics of Solutions to a Model Combustion System with Critical Nonlinearity" (with J. Xin), Nonlinearity, 8:161-178 (1995), pdf.
  17. "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.