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A Model for Mixtures of Micromagnetic Mate-allowing Existence and Regularity

Summary: A Model for Mixtures of Micromagnetic Mate-
allowing Existence and Regularity
Emilio Acerbi
Abstract. In this paper a realistic model for mixtures of magnetic materials
is presented, and an application to an optimal design problem is also given.
1. Energies involved
In the Weiss-Landau-Lifschitz model of the micromagnetic theory (which we do
not want to discuss here in detail, referring the reader e.g. to [6]), the total energy
associated with a single crystal (or "grain") of a magnetic material is given by the
sum of several contributions. Every point (every atom in the real, discrete world)
in the body R3
is magnetized, i.e., it generates a magnetic field, and we may
describe it with a vector field
m : R3
called magnetization. Below a certain temperature characteristic of the material
(Curie temperature) the modulus of the magnetization is constant,
|m| ms
in ,
where the magnetic saturation intensity ms


Source: Acerbi, Emilio - Dipartimento di Matematica, UniversitÓ degli Studi di Parma


Collections: Mathematics