Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes

Leonid Berlyand, Volodymyr Rybalko

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider a homogenization problem for the magnetic Ginzburg-Landau 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 of variational problems. This stands in sharp contrast with homogeneous superconductors, where all vortices are known to be simple. The proof is based on the G-convergence approach applied to a coupled continuum/discrete variational problem: continuum in the induced magnetic field and discrete in the unknown finite (quantized) values of multiplicity of vortices pinned by holes.

Original languageEnglish (US)
Pages (from-to)115-130
Number of pages16
JournalNetworks and Heterogeneous Media
Issue number1
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Engineering
  • Computer Science Applications
  • Applied Mathematics


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