Page 235 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 235
ARIATIONAL AND EVOLUTIONARY MODELS INVOLVING LOCAL/NONLOCAL
INTERACTIONS (MS-58)
alternating magnetization, are infinite volume ground states. Our proof is based on localization
bounds combined with reflection positivity. (Joint work with Alessandro Giuliani.)
Domain walls in thin ferromagnetic strips
Valeriy Slastikov, valeriy.slastikov@bristol.ac.uk
University of Bristol, United Kingdom
Coauthors: Matteo Novaga, Cyrill Muratov, Massimiliano Morini
We present a characterization of the domain wall solutions arising as minimizers of an energy
functional obtained in a suitable asymptotic regime of micromagnetics for infinitely long thin
film ferromagnetic strips in which the magnetization is forced to lie in the film plane. For
the considered energy, we provide existence, uniqueness, monotonicity, and symmetry of the
magnetization profiles in the form of 180 and 360 degree walls. We also demonstrate how this
energy arises as a Gamma-limit of the reduced two-dimensional thin film micromagnetic energy
that captures the non-local effects associated with the stray field.
Long time behaviour of discrete volume preserving mean curvature flows
Emanuele Spadaro, spadaro@mat.uniroma1.it
Università La Sapienza, Italy
Coauthors: Massimiliano Morini, Marcello Ponsiglione
Volume preserving mean-curvature flow is a model for coarsening phenomena in physical sys-
tems exhibiting a combination of local effects driven by curvature and nonlocal ones driven by
the volume constraint. In this talk I will analyse the Euler implicit scheme for the volume pre-
serving mean curvature flow, following the scheme introduced by Almgren-Taylor-Wang and
Luckhaus-Sturzenhecker for the flat flows, and I will show the exponential convergence of the
scheme to a finite union of disjoint balls with equal volume for any bounded initial set with
finite perimeter.
233
INTERACTIONS (MS-58)
alternating magnetization, are infinite volume ground states. Our proof is based on localization
bounds combined with reflection positivity. (Joint work with Alessandro Giuliani.)
Domain walls in thin ferromagnetic strips
Valeriy Slastikov, valeriy.slastikov@bristol.ac.uk
University of Bristol, United Kingdom
Coauthors: Matteo Novaga, Cyrill Muratov, Massimiliano Morini
We present a characterization of the domain wall solutions arising as minimizers of an energy
functional obtained in a suitable asymptotic regime of micromagnetics for infinitely long thin
film ferromagnetic strips in which the magnetization is forced to lie in the film plane. For
the considered energy, we provide existence, uniqueness, monotonicity, and symmetry of the
magnetization profiles in the form of 180 and 360 degree walls. We also demonstrate how this
energy arises as a Gamma-limit of the reduced two-dimensional thin film micromagnetic energy
that captures the non-local effects associated with the stray field.
Long time behaviour of discrete volume preserving mean curvature flows
Emanuele Spadaro, spadaro@mat.uniroma1.it
Università La Sapienza, Italy
Coauthors: Massimiliano Morini, Marcello Ponsiglione
Volume preserving mean-curvature flow is a model for coarsening phenomena in physical sys-
tems exhibiting a combination of local effects driven by curvature and nonlocal ones driven by
the volume constraint. In this talk I will analyse the Euler implicit scheme for the volume pre-
serving mean curvature flow, following the scheme introduced by Almgren-Taylor-Wang and
Luckhaus-Sturzenhecker for the flat flows, and I will show the exponential convergence of the
scheme to a finite union of disjoint balls with equal volume for any bounded initial set with
finite perimeter.
233
