Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An effective model for boundary vortices in thin-film micromagnetics   Ferromagnetic materials are governed by a variational principle which is
nonlocal, nonconvex and multiscale. The main object is given by a unit-length
three-dimensional vector field, the magnetization, that corresponds to the
stable states of the micromagnetic energy. Our aim is to analyze a thin film
regime that captures the asymptotic behavior of boundary vortices generated by
the magnetization and their interaction energy. This study is based on the
notion of "global Jacobian" detecting the topological defects that a priori
could be located in the interior and at the boundary of the film. A major
difficulty consists in estimating the nonlocal part of the micromagnetic energy
in order to isolate the exact terms corresponding to the topological defects.
We prove the concentration of the energy around boundary vortices via a
$\Gamma$-convergence expansion at the second order. The second order term is
the renormalized energy that represents the interaction between the boundary
vortices and governs their optimal position. We compute the expression of the
renormalized energy for which we prove the existence of minimizers having two
boundary vortices of multiplicity $1$. Compactness results are also shown for
the magnetization and the corresponding global Jacobian.

1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int