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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.

Ferromagnetism --- Magnetization --- Magnetism --- Mathematics. --- Mathematical models. --- Ginzburg-Landau type penalization. --- Macroscopic deterministic equation. --- Macrospin magnetization dynamics. --- Magnetization dynamics. --- Stochastic Landau-Lifshitz-Gilbert equation.

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"Addressed to both in-training and established radiologists and clinicians, Musculoskeletal MRI Structured Evaluation: How to Practically Fill the Reporting Checklist, written by experts in musculoskeletal imaging, offers the structured checklists for interpreting and reporting musculoskeletal MRI examinations. It describes the "how to" of using these templates and incorporating them into the clinical practice. Each chapter is dedicated to a separate joint or specific group of entities, and includes the reporting template along with a step-by-step description and imaging examples of the entire spectrum of the corresponding pathology"--Provided by publisher.

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