Center for Interdisciplinary Mathematics
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On Superconducting and Superfluidity

  1. L. Berlyand, Effective Properties of Superconducting and Superfluid Composites, International Journal of Modern Physics B., 12(29), pp. 3063-3073(1999).
  2. L. Berlyand, and E. Khruslov, Homogenization of harmonic maps and superconducting composites, SIAM Journal of Applied Mathematics, 59(5), pp. 1892-1916 (1999).
  3. L. Berlyand, Homogenization of the Ginzburg-Landau functional with a surface energy term, Asymptotic Analysis, 37-59, 21 (1999)
  4. L. Berlyand, and K. Voss, Symmetry Breaking in Annular Domains for a Ginzburg-Landau Superconductivity Model, Proceedings of IUTAM 99/4 Symposium, Sydney, Australia, January, Kluwer Academic Publishers, 189-200 (2001).
  5. L. Berlyand, and E. Khruslov, Homogenization of harmonic maps with large number of vortices and applications in superconductivity and superfluidity, Advances in Differential Equations., 6(2), pp. 229-256 (2001).
  6. D. Golovaty, and L. Berlyand, On uniqueness of vector-valued minimizers of the Ginzburg-Landau functional in annular domains, Calculus of Variations, 14, pp. 213-232 (2002).
  7. L. Berlyand, and E. Khruslov, Competition between the surface and the boundary layer energies in a Ginzburg-Landau model of a liquid crystal composite, Asymptotic Analysis, 29, pp. 185-219 (2002).
  8. L. Berlyand, and P. Mironescu, Ginzburg-Landau Minimizers with Prescribed Degrees: Dependence on Domain, C. R. Acad. Sci. Paris., 337(6), pp, 375-380 (2003).
  9. L. Berlyand, D. Cioranescu, and D. Golovaty, Homogenization of a Ginzburg-Landau model for a nematic liquid crystal with inclusions, Journal des Mathematiques Pures et Appliquees, 84(1), pp. 97-136(2005).
  10. M. Berezhnyy, and L. Berlyand, Continuum limit for three-dimensional mass-spring networks and discrete Korn's inequality, C. R. Acad. Sci. Paris., 340(1), pp. 87-92 (2005).
  11. L. Berlyand, and E. Khruslov, Ginzburg-Landau model of a liquid crystal with random inclusions, Journal of Mathematical Physics, 46, pp. 095107:1-15 (2005).
  12. L. Berlyand, and P. Mironscu, Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices, J. Functional Analysis, 239(1), pp. 76-99 (2006).
  13. L. Berlyand, D. Golovaty, and V. Rybalko, Nonexistence of Ginzburg-Landau minimizers with prescribed degree on the boundary of a doubly connected domain, C. R. Acad. Sci. Paris., 343(1), pp. 63-68 (2006).
  14. L. Berlyand and P. Mironescu, Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain, Networks and Heterogenous Media, 3(3), pp 461-487 (2008).
  15. Y. Almog, L. Berlyand, D. Golovaty, and I. Shafrir, Global minimizers for a p-Ginzburg-Landau-type energy in R2, J. Func. Analysis, 256(7), pp. 2268-2290 (2009).
  16. L. Berlyand, and V. Rybalko, Solutions with Vortices of a Semi-Stiff Boundary Value Problem for the Ginzburg-Landau Equation, J. European Math. Society, 12(6), pp.1497-1531 (2009).
  17. L. Berlyand, O. Misiats, and V. Rybalko, Near boundary vortices in a magnetic Ginzburg-Landau model: their locations via tight energy bounds, J. Func. Analysis, 258, pp. 1728-1762 (2010).
  18. L. Berlyand, O. Misiats, and V. Rybalko, Minimizers of the magnetic Ginzburg-Landau functional in simply connected domain with prescribed degree on the boundary, Communications in Contemporary Mathematics, 13(1), pp. 53-66 (2011).
  19. L. Berlyand, V. Rybalko, and N. Yip, Renormalized Ginzburg-Landau energy and location of near boundary vortices, NHM, 7(1) (online publication) (2012).
  20. L. Berlyand, and V. Rybalko, Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes, NHM special isssue, 8(1), pp.115-130 (2013).
  21. Y. Almog, L. Berlyand, D. Golovaty, and I. Shafrir, On the limit p to infinity of global minimizers for a p-Ginzburg-Landau-type energy, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 30(6), pp.1159-1174 (2013)
  22. O. Iaroshenko, V. Rybalko, V. Vinokur, and L. Berlyand, Vortex phase separation in mesoscopic superconductors, Scientific Reports: Nature Publishing, Group 3, 2013.
  23. L. Berlyand, P. Mironescu, V. Rybalko, and E. Sandier, Minimax Critical Points in Ginzburg-Landau Problems with Semi-stiff Boundary Conditions: Existence and Bubbling, Comm. in PDEs 39(5) pp. 946-1005 (2014)
  24. S. D. Ryan, V. Mityushev, V. M. Vinokur, and L. Berlyand, Rayleigh Approximation for ground states of the Bose and Coulomb glasses, Scientific Reports: Nature Publishing Group, 5, 7821 (2015)
  25. M.S. Mizuhara, L. Berlyand, V. Rybalko, and L. Zhang, On an evolution equation in a cell motility model, Physica D (2015)
  26. L. Berlyand, V. Mityushev, and S. D. Ryan, Multiple Ginzburg-Landau Vortices Pinned by Randomly Distributed Small Holes, submitted (2016).
  27. L. Berlyand, E. Sandier, and S. Serfaty, A two scale Gamma-convergence approach for random non-convex homogenization, Calculus of Variations and PDEs, accepted, (2017).
  28. L. Berlyand, D. Golovaty, O. Iaroshenko, and V. Rybalko, On approximation of Ginzburg-Landau minimizers by S1-valued maps in domains with vanishingly small holes, submitted, (2017).