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In this paper, we consider two-scale limits obtained with increasing homogenization periods, each period being an entire multiple of the previous one. We establish that, up to a measure preserving rearrangement, these two-scale limits form a martingale which is bounded: the rearranged two-scale limits themselves converge both strongly in L and almost everywhere when the period tends to +∞. This limit, called the Two-Scale Shuffle limit, contains all the information present in all the two-scale...
We study the homogenization process of
ferromagnetic multilayers in the presence of surface energies:
super-exchange, also called interlayer exchange coupling,
and surface anisotropy. The two main difficulties are the non-linearity
of the Landau-Lifshitz equation and the absence of a good sequence
of extension operators for the multilayer geometry.
First, we consider the case when surface anisotropy
is the dominant term, then the case when the magnitude of the super-exchange
interaction is...
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