Volodymyr Rybalko

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Let ω and Ω be bounded simply connected domains in R, and let ω̄ ⊂ Ω. In the annular domain A = Ω \ ω̄ we consider the class J of complex valued maps having degree 1 on ∂Ω and ∂ω. We prove that, when cap(A) < π, there exists a finite threshold value κ1 of the Ginzburg-Landau parameter κ such that the minimum of the Ginzburg-Landau energy Eκ not attained in(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)
We consider a homogenization problem for the magnetic GinzburgLandau functional in domains with a large number of small holes. We establish a scaling relation between sizes of holes and the magnitude of the external magnetic field when the multiple vortices pinned by holes appear in nested subdomains and their homogenized density is described by a hierarchy(More)
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells on a substrate. The key issue is the evolution of the cell membrane (interface curve) which involves shape change and(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)
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 a system of two PDEs introduced in [1] to model motility of eukaryotic cells on substrates. This system consists of the volume preserving Allen-Cahn equation for the scalar phase field function coupled with another parabolic equation for the orientation vector. We study the asymptotic behavior of solutions in the limit of a small parameter(More)
A combined index of reproductive qualities (CIRQ) is used for evaluating the reproductive productivity of sows of different genotypes, the index V 100 * for evaluating young replacement stock, and the index for evaluating fattening qualities. The best crossing variants are revealed as a result of using the index evaluations: Large White of the(More)
The results of analyzing the reproductive qualities of purebred and crossbred pigs obtained from regionalized and imported animals are given. The best two- and three-breed crosses with a high heterotic effect with respect to fattening and meat qualities are revealed.