Volodymyr Rybalko

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We study solutions of the 2D Ginzburg-Landau equation −∆u + 1 ε 2 u(|u| 2 − 1) = 0 subject to " semi-stiff " boundary conditions: the Dirichlet condition for the modulus, |u| = 1, and the homogeneous Neumann condition for the phase. The principal result of this work shows there are stable solutions of this problem with zeros (vortices), which are located(More)
Let Ω ⊂ R 2 be a smooth bounded simply connected domain. We consider the simplified Ginzburg-Landau energy E ε (u) = 1 2 ˆ Ω |∇u| 2 + 1 4ε 2 ˆ Ω (1 − |u| 2) 2 , where u : Ω → C. We prescribe |u| = 1 and deg (u, ∂Ω) = 1. In this setting, there are no minimizers of E ε. Using a mountain pass approach, we obtain existence of critical points of E ε for large ε.(More)
We demonstrate that in mesoscopic type II superconductors with the lateral size commensurate with London penetration depth, the ground state of vortices pinned by homogeneously distributed columnar defects can form a hierarchical nested domain structure. Each domain is characterized by an average number of vortices trapped at a single pinning site within a(More)
The results of monitoring the main productivity indices of pigs bred for a long time in the Stavropol krai and presently imported breeds are given. The adaptation level of natural resistance, which indicates better survival of progeny of local genotypes, is established.
We consider the location of near boundary vortices which arise in the study of minimizing sequences of Ginzburg-Landau functional with degree boundary condition. As the problem is not well-posed — minimizers do not exist, we consider a regularized problem which corresponds physically to the presence of a superconducting layer at the boundary. The study of(More)
We consider the location of near boundary vortices which arise in the study of minimizing sequences of Ginzburg-Landau functional with degree boundary condition. As the problem is not well-posed — minimizers do not exist, we consider a regularized problem which corresponds physically to the presence of a superconducting layer at the boundary. The study of(More)
Capacity of a multiply-connected domain and nonexistence of Ginzburg-Landau minimizers with prescribed degrees on the boundary. Abstract Suppose that ω ⊂ Ω ⊂ R 2. In the annular domain A = Ω \ ¯ ω we consider the class J of complex valued maps having degree 1 on ∂Ω and ∂ω. It was conjectured in [5] that the existence of minimizers of the Ginzburg-Landau(More)
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