# Superconductivity and Superfluidity

**"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.**"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.-
**"On approximation of Ginzburg-Landau minimizers by S**(with D. Golovaty, O. Iaroshenko, V. Rybalko),^{1}-valued maps in domains with vanishingly small holes"__Journal of Differential Equations__, Vol. 264 no. 2, pp. 1317 - 1347 (2017), pdf. **"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.**"Multiple Ginzburg-Landau Vortices Pinned by Randomly Distributed Small Holes"**(with V. Mityushev and S. D. Ryan),*submitted*(2016), pdf.**"On an evolution equation in a cell motility model"**(with M.S. Mizuhara, V. Rybalko, L. Zhang),__Physica D__(2015), 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.**"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.**"Vortex phase separation in mesoscopic superconductors"**(with O. Iaroshenko, V. Rybalko, V. M. Vinokur),__Scientific Reports: Nature Publishing Group__**3**(2013), pdf.**"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.**"Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes"**(with V. Rybalko), special issue__NHM__**8**:1 pp.115-130 (2013), pdf.**"Renormalized Ginzburg-Landau energy and location of near boundary vortices"**(with V. Rybalko, N.K. Yip),__NHM__, 7:1 (online publication) (2012), pdf.**"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.**"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.**"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.**"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.**"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.**"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.**"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.**"Ginzburg-Landau model of a liquid crystal with random inclusions"**(with E. Khruslov),__Journal of Mathematical Physics__, 46, pp. 095107:1-15 (2005), pdf.**"Homogenization of a Ginzburg-Landau functional"**(with D. Cioranescu and D. Golovaty),__C. R. Acad. Sci.__, Paris, 340/1 pp 87-92 (2005), pdf.**"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.**"Ginzburg-Landau Minimizers with Prescribed Degrees: Dependence on Domain"**(with P. Mironescu)__C. R. Acad. Sci__, Paris, 337 (6), pp. 375-380 (2003), pdf.**"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.**"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.**"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.**"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.**"Homogenization of the Ginzburg-Landau functional with a surface energy term"**,__Asymptotic Analysis__, 37-59, 21 (1999), pdf.**"Homogenization of harmonic maps and superconducting composites"**(with E. Ya. Khruslov),__SIAM Journal of Applied Mathematics__, 59, 5 pp. 1892-1916 (1999), pdf.**"Effective Properties of Superconducting and Superfluid Composites"**,__International Journal of Modern Physics B__, 12, 29, 3063-3073 (1999), pdf.