Superconductivity and Superfluidity

  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 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.
  4. "A two scale Gamma-convergence approach for random non-convex homogenization" (with E. Sandier and S. Serfaty), accepted to Journal of Calculus of Variations and PDEs No. 6, p. 156 (2017), pdf.
  5. "Multiple Ginzburg-Landau Vortices Pinned by Randomly Distributed Small Holes" (with V. Mityushev and S. D. Ryan), submitted (2016), pdf.
  6. "On an evolution equation in a cell motility model" (with M.S. Mizuhara, V. Rybalko, L. Zhang), Physica D (2015), pdf.
  7. "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.
  8. "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.
  9. "Vortex phase separation in mesoscopic superconductors" (with O. Iaroshenko, V. Rybalko, V. M. Vinokur), Scientific Reports: Nature Publishing Group 3 (2013), pdf.
  10. "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.
  11. "Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes" (with V. Rybalko), special issue NHM 8:1 pp.115-130 (2013), pdf.
  12. "Renormalized Ginzburg-Landau energy and location of near boundary vortices" (with V. Rybalko, N.K. Yip), NHM, 7:1 (online publication) (2012), pdf.
  13. "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.
  14. "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.
  15. "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.
  16. "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.
  17. "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.
  18. "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.
  19. "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.
  20. "Ginzburg-Landau model of a liquid crystal with random inclusions" (with E. Khruslov), Journal of Mathematical Physics, 46, pp. 095107:1-15 (2005), pdf.
  21. "Homogenization of a Ginzburg-Landau functional" (with D. Cioranescu and D. Golovaty), C. R. Acad. Sci., Paris, 340/1 pp 87-92 (2005), pdf.
  22. "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.
  23. "Ginzburg-Landau Minimizers with Prescribed Degrees: Dependence on Domain" (with P. Mironescu) C. R. Acad. Sci, Paris, 337 (6), pp. 375-380 (2003), pdf.
  24. "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.
  25. "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.
  26. "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.
  27. "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.
  28. "Homogenization of the Ginzburg-Landau functional with a surface energy term", Asymptotic Analysis, 37-59, 21 (1999), pdf.
  29. "Homogenization of harmonic maps and superconducting composites" (with E. Ya. Khruslov), SIAM Journal of Applied Mathematics, 59, 5 pp. 1892-1916 (1999), pdf.
  30. "Effective Properties of Superconducting and Superfluid Composites", International Journal of Modern Physics B, 12, 29, 3063-3073 (1999), pdf.