Stochastic Ferromagnetism PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Stochastic Ferromagnetism PDF full book. Access full book title Stochastic Ferromagnetism by Lubomir Banas. Download full books in PDF and EPUB format.
Author: Lubomir Banas
Publisher: Walter de Gruyter
ISBN: 3110307103
Category : Mathematics
Languages : en
Pages : 248
Get Book
Book Description
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.
Author: Lubomir Banas
Publisher: Walter de Gruyter
ISBN: 3110307103
Category : Mathematics
Languages : en
Pages : 248
Get Book
Book Description
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.
Author: Andreas Eberle
Publisher: Springer
ISBN: 3319749293
Category : Mathematics
Languages : en
Pages : 574
Get Book
Book Description
This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.
Author: Yasushi Ishikawa
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110378078
Category : Mathematics
Languages : en
Pages : 288
Get Book
Book Description
This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener–Poisson space. Solving the Hamilton–Jacobi–Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory. The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: Preface Preface to the second edition Introduction Lévy processes and Itô calculus Perturbations and properties of the probability law Analysis of Wiener–Poisson functionals Applications Appendix Bibliography List of symbols Index
Author: Peter Guttorp
Publisher: CRC Press
ISBN: 135141366X
Category : Mathematics
Languages : en
Pages : 384
Get Book
Book Description
Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.
Author: Nai-li Haung Liu
Publisher: World Scientific
ISBN: 9814550809
Category :
Languages : en
Pages : 278
Get Book
Book Description
On 19 March 1993, Raymond L. Orbach was inaugurated as the eighth Chancellor of the University of California, Riverside. In connection with this occasion, a two-day scientific symposium was held. Invited and contributed papers were presented on subjects related to 2 vital areas of condensed-matter physics in which Chancellor Orbach has made seminal contributions: the effects of disorder on magnetic behavior, and the theory of high-temperature superconductivity. The papers in this book, many of which are by outstanding contributors to these important fields, give an up-to-date overview of recent progress.
Author: Bernard Dieny
Publisher: John Wiley & Sons
ISBN: 111900974X
Category : Science
Languages : en
Pages : 277
Get Book
Book Description
Magnetic random-access memory (MRAM) is poised to replace traditional computer memory based on complementary metal-oxide semiconductors (CMOS). MRAM will surpass all other types of memory devices in terms of nonvolatility, low energy dissipation, fast switching speed, radiation hardness, and durability. Although toggle-MRAM is currently a commercial product, it is clear that future developments in MRAM will be based on spin-transfer torque, which makes use of electrons’ spin angular momentum instead of their charge. MRAM will require an amalgamation of magnetics and microelectronics technologies. However, researchers and developers in magnetics and in microelectronics attend different technical conferences, publish in different journals, use different tools, and have different backgrounds in condensed-matter physics, electrical engineering, and materials science. This book is an introduction to MRAM for microelectronics engineers written by specialists in magnetic materials and devices. It presents the basic phenomena involved in MRAM, the materials and film stacks being used, the basic principles of the various types of MRAM (toggle and spin-transfer torque; magnetized in-plane or perpendicular-to-plane), the back-end magnetic technology, and recent developments toward logic-in-memory architectures. It helps bridge the cultural gap between the microelectronics and magnetics communities.
Author: Challa S.S.R. Kumar
Publisher: Springer
ISBN: 3662527804
Category : Technology & Engineering
Languages : en
Pages : 566
Get Book
Book Description
Sixth volume of a 40 volume series on nanoscience and nanotechnology, edited by the renowned scientist Challa S.S.R. Kumar. This handbook gives a comprehensive overview about Magnetic Characterization Techniques for Nanomaterials. Modern applications and state-of-the-art techniques are covered and make this volume an essential reading for research scientists in academia and industry.
Author: William T Coffey
Publisher: World Scientific
ISBN: 981448380X
Category : Science
Languages : en
Pages : 852
Get Book
Book Description
This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles. Contents:Historical Background and Introductory ConceptsLangevin Equations and Methods of SolutionBrownian Motion of a Free Particle and a Harmonic OscillatorRotational Brownian Motion About a Fixed Axis in N-Fold Cosine PotentialsBrownian Motion in a Tilted Periodic Potential: Application to the Josephson Tunnelling JunctionTranslational Brownian Motion in a Double-Well PotentialNon-inertial Rotational Diffusion in Axially Symmetric External Potentials: Applications to Orientational Relaxation of Molecules in Fluids and Liquid CrystalsAnisotropic Non-inertial Rotational Diffusion in an External Potential: Application to Linear and Nonlinear Dielectric Relaxation and the Dynamic Kerr EffectBrownian Motion of Classical Spins: Application to Magnetization Relaxation in SuperparamagnetsInertial Effects in Rotational and Translational Brownian Motion for a Single Degree of FreedomInertial Effects in Rotational Diffusion in Space: Application to Orientational Relaxation in Molecular Liquids and FerrofluidsAnomalous Diffusion and Relaxation Readership: Advanced undergraduates, postgraduates, academics and researchers in statistical physics, condensed matter physics and magnetism, chemical physics, theoretical chemistry and applied mathematics. Keywords:Brownian Motion;Historical Development;Analogy with Financial Systems;Translational and Rotational Diffusion;Stochastic Differential Equations;Langevin Equation;FokkerâPlanck Equation;Characteristic Times of Relaxation Processes;Escape Rate Theory;Kramers Turnover Problem;Matrix Continued Fraction Solution of Evolution Equtions;Kerr Effect;Microwave (Debye) and Far-Infrared (Poley) Absorption;Dielectric Relaxation in Liquids and Nematic Liquid Crystals;Classical Spins;Superparamagnetism;Néel-Brown Model;Dynamic Magnetic Hysteresis;Switching Fields;Stoner-Wohlfarth Astroids;Ferromagnetic Resonance;Ferrofluids;Josephson Effect;Ring Laser;Magnetic Resonance Imaging;Stochastic Resonance;Anomalous Diffusion;Continuous Time Random Walk;Fractional Langevin Equation;Fractional FokkerâPlanck EquationKey Features:This volume is the third edition of the first elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion in a potential with particular emphasis on modern applications in the natural sciences, electrical engineering, etc.It has been extensively enlarged to cover in a reasonably succinct manner using a synergetic approach a number of new topics such as anomalous diffusion, continuous time random walks, stochastic resonance, superparamagnetism, magnetic resonance imaging, etc. which are of major current interest in view of the large number of disparate systems which exhibit these phenomenaThe book is written in a manner such that all the material should be accessible to an advanced undergraduate or beginning graduate studentReviews: “This book is devoted to a detailed presentation of Langevin's idea and does this almost perfectly. Successive topics considered in this book are presented in a detailed manner giving the general impression that this book is a comprehensive compendium of knowledge. This book should be a very valuable addition to libraries of many experienced scientists and also beginners (e.g., students) presenting solutions of many stochastic phenomena.” Zentralblatt MATH Reviews of the First and Second Editions: “I found this book a valuable addition to my library. It will be of interest to researchers and advanced students and the material could be used as the text for a course for advanced undergraduates and graduate students.” Irwin Oppenheim MIT “This enlarged and updated second edition of the book: 'The Langevin equation presents an extremely useful source for the practitioners of stochastic processes and its applications to physics, chemistry, engineering and biological physics, both for the experts and the beginners. It gives a valuable survey of solvable paradigms that rule many diverse stochastic phenomena. As such, it belongs onto the desk of all engaged in doing research and teaching in this area.” Peter Hanggi University of Augsburg “This is a timely update of the theory and applications of the Langevin equation, which skillfully combines the elementary approaches with most recent developments such as anomalous diffusion and fractional kinetics. Both experts and beginners will benefit from this well-written textbook.” Joseph Klafter Tel Aviv University
Author: Ekkes Bruck
Publisher: Academic Press
ISBN: 0323986021
Category : Science
Languages : en
Pages : 82
Get Book
Book Description
Handbook of Magnetic Materials, Volume 31 highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely and field specific topics, each contributed to by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Magnetic Materials series
Author: Kalmykov Yuri P
Publisher: World Scientific
ISBN: 9813222018
Category : Science
Languages : en
Pages : 928
Get Book
Book Description
Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker–Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.
