Elsevier S & T

Mathematical Models of Hysteresis and their Applications

Mayergoyz, Isaak D.

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Table of contents
  • Cover
  • Contentsvii
  • Dedicationv
  • Prefaceix
  • Introductionxiii
  • Chapter 1. The Classical Preisach Model of Hysteresis1
  • 1.1 Definition of the Classical Preisach Model1
  • 1.2 Geometric Interpretation and Main Properties of the Preisach Model8
  • 1.3 Identification Problem for the Preisach Model. Representation Theorem20
  • 1.4 Numerical Implementation of the Preisach Model37
  • 1.5 The Preisach Model and Hysteretic Energy Losses49
  • Chapter 2. Generalized Scalar Preisach Models of Hysteresis65
  • 2.1"Moving" Preisach Model of Hysteresis65
  • 2.2 Preisach Model of Hysteresis with Input-dependent Measure73
  • 2.3"Restricted" Preisach Models of Hysteresis93
  • 2.4 Dynamic Preisach Models of Hysteresis108
  • 2.5 Preisach Model of Hysteresis with Accommodation117
  • 2.6 Magnetostrictive Hysteresis and Preisach Models with Two Inputs124
  • 2.7 Experimental Testing of Preisach-Type Models of Hysteresis132
  • Chapter 3. Vector Preisach Models of Hysteresis149
  • 3.1 Classical Stoner–Wohlfarth Model of Vector Hysteresis149
  • 3.2 Definition of Vector Preisach Models of Hysteresis and Their Numerical Implementation158
  • 3.3 Some Basic Properties of Vector Preisach Hysteresis Models167
  • 3.4 Identification Problem For Isotropic Vector Preisach Models183
  • 3.5 Identification Problem for Anisotropic Vector Preisach Models190
  • 3.6 Dynamic Vector Preisach Models of Hysteresis201
  • 3.7 Generalized Vector Preisach Models of Hysteresis. Experimental Testing207
  • Chapter 4. Stochastic Aspects of Hysteresis225
  • 4.1 Preisach Model with Stochastic Input as a Model for Viscosity225
  • 4.2 Experimental Testing. Scaling and Data Collapse in Magnetic Viscosity236
  • 4.3 Preisach Model Driven by Continuous-Time Noise. Origin of the Universality of Long-Time Thermal245
  • 4.4 Noise in Hysteretic Systems and Stochastic Processes on Graphs256
  • 4.5 Analysis of Spectral Noise Density of Hysteretic Systems Driven By Stochastic Processes267
  • 4.6 Modeling of Temperature Dependent Hysteresis Within the Framework of Randomly Perturbed Fast Dyn272
  • 4.7 Functional (Path) Integration Models of Hysteresis281
  • Chapter 5. Superconducting Hysteresis299
  • 5.1 Superconductors With Sharp Resistive Transitions299
  • 5.2 Experimental Testing of the Preisach Modeling of Superconducting Hysteresis313
  • 5.3 Nonlinear Diffusion in Superconductors with Gradual Resistive Transitions (Linear Polarization)331
  • 5.4 Nonlinear Diffusion in Isotropic Superconductors with Gradual Resistive Transitions (Circular Po348
  • 5.5 Nonlinear Diffusion in the Case of Elliptical Polarizations and Anisotropic Media359
  • Chapter 6. Eddy Current Hysteresis. Core Losses377
  • 6.1 Eddy Current Analysis in the Case of Abrupt (Sharp) Magnetic Transitions377
  • 6.2 Eddy Current Hysteresis and the Preisach Model397
  • 6.3 Eddy Current Losses in Magnetic Conductors with Abrupt Magnetic Transitions. Excess Hysteresis L411
  • 6.4 Eddy Current Analysis in the Case of Gradual Magnetic Transitions424
  • 6.5 Eddy Current Analysis in the Case of Circularly Polarized Electromagnetic Fields. Rotational Edd443
  • Subject Index469
Book details
  • Vendor Elsevier S & T
  • SKU 9780124808737
  • ISBN-13 9780080535890
  • Author Mayergoyz, Isaak D.
  • Edition 2nd
  • Category Mathematics
  • Subject Applied

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Description eBook delivery & access Reviews
This new edition has been significantly revised and updated to reflect advances in the field since the publication of the first edition, such as the systematic experimental testing of Preisach models of hysteresis. The author has, however, retained the two most salient features of the original, the emphasis on the universal nature of mathematical models of hysteresis and their applicability to the description of hysteresis phenomena in various areas of science, technology and economics and its accessibility to a broad audience of researchers, engineers, and students.

· Provides a unique emphasis on the development of universal mathematical models of hysteresis
· Accessibility to a broad audience, using simple and complex mathematical tools, application to various areas of science.
· Presents new theoretical and experimental results