The objective of this monograph is a numerical analysis of the well-accepted models of Landau, Lifshitz and Gilbert for (electrically conducting) ferromagnets. Part I discusses convergence behavior of different finite element schemes for solving the stationary problem. Part II deals with numerical analyses of different penalization / projection strategies in nonstationary micromagnetism; it closes with a chapter on nematic liquid crystals to show applicability of these new methods to further applications.
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.
The definitive guide to the bats of Britain and Europe. This concise and definitive guide presents all 45 bat species that regularly occur in Europe (of which 17 are known to breed in the British Isles). The extensive introduction details the remarkable biology of bats and explores the latest findings in bat evolution, behaviour and echolocation. This is followed by in-depth species accounts covering life history, conservation status and identification of families and genera, including echolocation characteristics, and complemented by accurate distribution maps, with the book illustrated throughout with almost 700 superb colour photographs. Suitable for beginners, students, professionals or conservationists alike, Bats of Britain and Europe is the authoritative field guide for bat watchers – an essential reference for every bat enthusiast.
The objective of this monograph is a numerical analysis of the well-accepted models of Landau, Lifshitz and Gilbert for (electrically conducting) ferromagnets. Part I discusses convergence behavior of different finite element schemes for solving the stationary problem. Part II deals with numerical analyses of different penalization / projection strategies in nonstationary micromagnetism; it closes with a chapter on nematic liquid crystals to show applicability of these new methods to further applications.
In his site-specific installations, ecological artist Tue Greenfort, winner of the 2012 GASAG Art Prize, addresses the special features of his exhibition locations, in this case the Berlinische Galerie.In the former premises of a glass warehouse, the participant in dOCUMENTA 13 spins a network of relationships out of glass, with its manifold properties, and gas, an invisible, volatile substance.Instead of an exhibition catalogue an interactive artist's book becomes part of the exhibition and the artistic process. Created as an experiment in book form, it can be structured by the reader himself or herself as they wish, supplemented with photographs or re-arranged.English and German text.
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