Mathematical models of hysteresis and their applications

1. The Classical Preisach Model of Hysteresis......Page 1
Instead of title page......Page 3
Date-line......Page 4
Contents......Page 5
Preface......Page 7
Introduction......Page 11
1.1 Definition of the Classical Preisach Model......Page 25
1.2 Geometric Interpretation and Main Properties of the Preisach Model......Page 32
1.3 Identification Problem for the Preisach Model. Representation Theorem......Page 44
1.4 Numerical Implementation of the Preisach Model......Page 61
1.5 The Preisach Model and Hysteretic Energy Losses......Page 73
2.1 \"Moving\" Preisach Model of Hysteresis......Page 89
2.2 Preisach Model of Hysteresis with Input-dependent Measure......Page 97
2.3 \"Restricted\" Preisach Models of Hysteresis......Page 117
2.4 Dynamic Preisach Models of Hysteresis......Page 132
2.5 Preisach Model of Hysteresis with Accommodation......Page 141
2.6 Magnetostrictive Hysteresis and Preisach Models with Two Inputs......Page 148
2.7 Experimental Testing of Preisach-Type Models of Hysteresis......Page 156
3.1 Classical Stoner-Wohlfarth Model of Vector Hysteresis......Page 173
3.2 Definition of Vector Preisach Models of Hysteresis and Their Numerical Implementation......Page 182
3.3 Some Basic Properties of Vector Preisach Hysteresis Models......Page 191
3.4 Identification Problem For Isotropic Vector Preisach Models......Page 207
3.5 Identification Problem for Anisotropic Vector Preisach Models......Page 214
3.6 Dynamic Vector Preisach Models of Hysteresis......Page 225
3.7 Generalized Vector Preisach Models of Hysteresis. Experimental Testing......Page 231
4.1 Preisach Model with Stochastic Input as a Model for Viscosity......Page 249
4.2 Experimental Testing. Scaling and Data Collapse in Magnetic Viscosity......Page 260
4.3 Preisach Model Driven by Continuous-Time Noise. Origin of the Universality of Long-Time Thermal Relaxations......Page 269
4.4 Noise in Hysteretic Systems and Stochastic Processes on Graphs......Page 280
4.5 Analysis of Spectral Noise Density of Hysteretic Systems Driven By Stochastic Processes......Page 291
4.6 Modeling of Temperature Dependent Hysteresis Within the Framework of Randomly Perturbed Fast Dynamical Systems......Page 296
4.7 Functional (Path) Integration Models of Hysteresis......Page 305
5.1 Superconductors With Sharp Resistive Transitions......Page 323
5.2 Experimental Testing of the Preisach Modeling of Superconducting Hysteresis......Page 337
5.3 Nonlinear Diffusion in Superconductors with Cradual Resistive Transitions (Linear Polarization)......Page 355
5.4 Nonlinear Diffusion in Isotropic Superconductors with Gradual Resistive Transitions (Circular Polarization)......Page 372
5.5 Nonlinear Diffusion in the Case of Elliptical Polarizations and Anisotropic Media......Page 383
6.1 Eddy Current Analysis in the Case of Abrupt (Sharp) Magnetic Transitions......Page 401
6.2 Eddy Current Hysteresis and the Preisach Model......Page 421
6.3 Eddy Current Losses in Magnetic Conductors with Abrupt Magnetic Transitions. Excess Hysteresis Losses......Page 435
6.4 Eddy Current Analysis in the Case of Gradual Magnetic Transitions......Page 448
6.5 Eddy Current Analysis in the Case of Circularly Polarized Electromagnetic Fields. Rotational Eddy Current Losses......Page 467
Subject Index......Page 493