Publications

Superconductivity and Superfluidity


  1. "On approximation of Ginzburg-Landau minimizers by S1-valued maps in domains with vanishingly small holes"(with D. Golovaty, O. Iaroshenko, V. Rybalko), submitted, (2017), pdf.
  2. "A two scale Gamma-convergence approach for random non-convex homogenization" (with E. Sandier and S. Serfaty), accepted to Calculus of Variations and PDEs, (2017), pdf.
  3. "Multiple Ginzburg-Landau Vortices Pinned by Randomly Distributed Small Holes" (with V. Mityushev and S. D. Ryan), submitted (2016), pdf.
  4. "On an evolution equation in a cell motility model" (with M.S. Mizuhara, V. Rybalko, L. Zhang), Physica D (2015), 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. "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.
  7. "Vortex phase separation in mesoscopic superconductors" (with O. Iaroshenko, V. Rybalko, V. M. Vinokur), Scientific Reports: Nature Publishing Group 3 (2013), pdf.
  8. "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.
  9. "Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes" (with V. Rybalko), special issue NHM 8:1 pp.115-130 (2013), pdf.
  10. "Renormalized Ginzburg-Landau energy and location of near boundary vortices" (with V. Rybalko, N.K. Yip), NHM, 7:1 (online publication) (2012), pdf.
  11. "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.
  12. "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.
  13. "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.
  14. "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.
  15. "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.
  16. "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.
  17. "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.
  18. "Ginzburg-Landau model of a liquid crystal with random inclusions" (with E. Khruslov), Journal of Mathematical Physics, 46, pp. 095107:1-15 (2005), pdf.
  19. "Homogenization of a Ginzburg-Landau functional" (with D. Cioranescu and D. Golovaty), C. R. Acad. Sci., Paris, 340/1 pp 87-92 (2005), pdf.
  20. "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.
  21. "Ginzburg-Landau Minimizers with Prescribed Degrees: Dependence on Domain" (with P. Mironescu) C. R. Acad. Sci, Paris, 337 (6), pp. 375-380 (2003), pdf.
  22. "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.
  23. "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.
  24. "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.
  25. "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.
  26. "Homogenization of the Ginzburg-Landau functional with a surface energy term", Asymptotic Analysis, 37-59, 21 (1999), pdf.
  27. "Homogenization of harmonic maps and superconducting composites" (with E. Ya. Khruslov), SIAM Journal of Applied Mathematics, 59, 5 pp. 1892-1916 (1999), pdf.
  28. "Effective Properties of Superconducting and Superfluid Composites", International Journal of Modern Physics B, 12, 29, 3063-3073 (1999), pdf.