portada Stochastic Ferromagnetism: Analysis and Numerics (en Inglés)

Stochastic Ferromagnetism: Analysis and Numerics (en Inglés)

Formato

Libro Físico

Autor

Editorial

Idioma

Inglés

N° páginas

248

Encuadernación

Tapa Dura

Dimensiones

24.4x17x1.6 cm

Peso

0.60 kg.

ISBN13

9783110306996

Categorías

Cálculo diferencial y ecuaciones
Probabilidad y estadística
Matemáticas aplicadas

Stochastic Ferromagnetism: Analysis and Numerics (en Inglés)

Lubomir Banas (Autor) · Zdzislaw Brzezniak (Autor) · Mikhail Neklyudov (Autor) · de Gruyter · Tapa Dura

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Reseña del libro "Stochastic Ferromagnetism: Analysis and Numerics (en Inglés)"

This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). The first part of the book studies the role of noise in finite ensembles of nanomagnetic particles: we show geometric ergodicity of a unique invariant measure of Gibbs type and study related properties of approximations of the SLLG, including time discretization and Ginzburg-Landau type penalization. In the second part we propose an implementable space-time discretization using random walks to construct a weak martingale solution of the corresponding stochastic partial differential equation which describes the magnetization process of infinite spin ensembles. The last part of the book is concerned with a macroscopic deterministic equation which describes temperature effects on macro-spins, i.e. expectations of the solutions to the SLLG. Furthermore, comparative computational studies with the stochastic model are included. We use constructive tools such as e.g. finite element methods to derive the theoretical results, which are then used for computational studies. The numerical experiments motivate an interesting interplay between inherent geometric and stochastic effects of the SLLG which still lack a rigorous analytical understanding: the role of space-time white noise, possible finite time blow-up behavior of solutions, long-time asymptotics, and effective dynamics.