Displaying similar documents to “On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes”

Existence of skyrmions

Schmitt, Andreas

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Summary: We give an introduction to the Skyrme model from a mathematical point of view. Hereby, we show that it is difficult to solve the field equation even by means of the classical ansatz, the so-called hedgehog ansatz. Our main result is an extended existence proof for solutions of the field equation in the hedgehog ansatz.

Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges, Karine Beauchard (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

On Equations y² = xⁿ+k in a Finite Field

A. Schinzel, M. Skałba (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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Solutions of the equations y² = xⁿ+k (n = 3,4) in a finite field are given almost explicitly in terms of k.