The Science of Hysteresis

Description

Volume 1 covers:

* Mathematical models

* Differential equations

* Stochastic aspects of hysteresis

* Binary detection using hysteresis

* Models of unemployment in economics

Volume 2 covers:

* Physical models of magnetic hysteresis

* All aspects of magnetisation dynamics

Volume 3 covers:

* Hysteresis phenomena in materials

* Over 2100 pages, rich with supporting illustrations, figures and equations

* Contains contributions from an international list of authors, from a wide-range of disciplines

* Covers all aspects of hysteresis - from differential equations, and binary detection, to models of unemployment and magnetisation dynamics

Front Cover 2
The Science of Hysteresis 5
Copyright Page 6
Contents 7
Preface 11
Contributors 13
Chapter 1. Mathematical Models of Hysteresis 15
- 1.1 Hysteresis Operators 17
- 1.2 The Duhem Model 27
- 1.3 Rheological Models of Elasto-plasticity 31
- 1.4 Discontinuous Hysteresis 49
- 1.5 Micromagnetism 59
- 1.6 Models of Hysteresis with Internal Variables 70
- 1.7 Genesis of Hysteresis and Coupling with PDEs 76
- 1.8 A Transport Equation with Hysteresis 83

Front Cover 2
The Science of Hysteresis 5
Copyright Page 6
Contents 7
Preface 11
Contributors 13
Chapter 1. Mathematical Models of Hysteresis 15
- 1.1 Hysteresis Operators 17
- 1.2 The Duhem Model 27
- 1.3 Rheological Models of Elasto-plasticity 31
- 1.4 Discontinuous Hysteresis 49
- 1.5 Micromagnetism 59
- 1.6 Models of Hysteresis with Internal Variables 70
- 1.7 Genesis of Hysteresis and Coupling with PDEs 76
- 1.8 A Transport Equation with Hysteresis 83
- 1.9 A Quasilinear Parabolic PDE with Hysteresis 92
- 1.10 A Quasilinear Hyperbolic PDE with Hysteresis 105
- 1.11 Hysteresis in Porous-Media Filtration 112
- 1.12 Conclusions 119
- 1.13 Appendix. Elements of Convex Calculus 121
- Acknowledgement 128
- References 129
Chapter 2. Differential Equations with Hysteresis via a Canonical Example 139
- 2.1 Hysteresis Phenomena 139
- 2.2 Numerical Experiments 150
- 2.3 Examples of Rigorous Conclusions 166
- 2.4 Examples of Technical Toolboxes 249
- Acknowledgement 292
- References 293
Chapter 3. Scalar Preisach Models of Hysteresis 307
- 3.1 The Classical Preisach Model of Hysteresis 307
- 3.2 Generalized Scalar Preisach Models of Hysteresis 374
- References 457
Chapter 4. Vector Preisach Models of Hysteresis 461
- 4.1 Classical Stoner–Wohlfarth Model Vector Hysteresis 461
- 4.2 Definition of Vector Preisach Models of Hysteresis and their Numerical Implementation 472
- 4.3 Some Basic Properties of Vector Preisach Hysteresis Models 481
- 4.4 Identification Problem for Isotropic Vector Preisach Models 499
- 4.5 Identification Problem for Anisotropic Vector Preisach Models 508
- 4.6 Dynamic Vector Preisach Models of Hysteresis 518
- 4.7 Generalized Vector Preisach Models of Hysteresis. Experimental Testing 525
- References 540
Chapter 5. Stochastic Aspects of Hysteresis 543
- 5.1 Preisach Model with Stochastic Input as a Model of Thermal Relaxations 543
- 5.2 Experimental Testing. Scaling and Data Collapse in Magnetic Viscosity 555
- 5.3 Preisach Model Driven by Continuous-Time Noise. Origin of the Universality of Long-Time Thermal Relaxations 564
- 5.4 Noise in Hysteretic Systems and Stochastic Processes on Graphs 576
- 5.5 Analysis of Spectral Noise Density of Hysteretic Systems Driven by Stochastic Processes 587
- 5.6 Modeling of Temperature-Dependent Hysteresis within the Framework of Randomly Perturbed Fast Dynamical Systems 592
- 5.7 Functional (Path) Integration Models of Hysteresis 601
- References 615
Chapter 6. Control of Systems with Hysteresis 619
- 6.1 Introduction 619
- 6.2 Optimal Control of Systems with Simple Hysteretic Elements 621
- 6.3 Optimal Control of Systems with Hysteron-Type Operators 628
- 6.4 Optimal Control of Systems with Preisach Hysteresis 636
- 6.5 Hysteresis from Optimal Control, and Hysteresis for Optimal Control 646
- References 648
Chapter 7. Binary Detection and Rectangular Hysteresis Operators 653
- References 648
- 7.1 Introduction 653
- 7.2 General System Description and Outline 655
- 7.3 Input Process and Mid-Span Repeater 658
- 7.4 Receiver Integrator Output: Probability Density Function Calculation 660
- 7.5 Summary 676
- 7.6 Concluding Remarks 677
Chapter 8. Hysteresis and Unemployment: A Preliminary Investigation 681
- 8.1 Introduction 681
- 8.2 Hysteresis 683
- 8.3 An Illustrative Model 684
- 8.4 Computing the Hysteresis Variable 691
- 8.5 Hysteresis and UK Unemployment 699
- 8.6 Concluding Remarks 701
- Appendix 701
- References 710
Index 715
- Front Cover 720
- The Science of Hysteresis: Physical Modeling, Micromagnetics, and Magnetization Dynamics 723
- Copyright Page 724
- Contents 725
- Preface 729
- Contributors 731
- Chapter 1. Thermodynamics, Hysteresis, and Micromagnetics 733
  - 1.1 Introduction 733
  - 1.2 Classical and Nonequilibrium Thermodynamics 737
  - 1.3 Thermodynamic Aspects of Hysteresis 761
  - 1.4 From Micromagnetics to Magnetic Hysteresis 807
  - References 832
- Chapter 2. Random-Field Ising Models of Hysteresis 839
  - 2.1 Introduction 839
  - 2.2 Models 844
  - 2.3 The Renormalization Group and Scaling 849
  - 2.4 Critical Exponents, Scaling Functions 854
  - 2.5 Measuring Universal Properties 860
  - 2.6 Exponent Relations 873
  - 2.7 Finite Sweep Rate 876
  - 2.8 Subloops and History-Induced Critical Behavior 877
  - 2.9 Real Experiments 881
  - 2.10 Unsolved Problems 890
  - Acknowledgement 891
  - Appendix. Derivation of the Scaling Forms and Corrections 892
  - References 899
- Chapter 3. The Barkhausen Effect 913
  - Appendix. Translation of the Original Paper by Barkhausen 725
  - 3.1 Introduction 913
  - 3.2 Experiments and Materials 916
  - 3.3 Experimental Results 922
  - 3.4 Models and Theories of Magnetization Dynamics 943
  - 3.5 Discussion of Theoretical Results 971
  - 3.6 Conclusions and Perspectives 983
  - Acknowledgements 985
  - References 989
- Chapter 4. Recent Analytical Developments in Micromagnetics 1001
  - 4.1 Introduction 1001
  - 4.2 The Energy Functional and Pattern Formation 1005
  - 4.3 Bulk Scalings 1010
  - 4.4 A Hierarchy of Thin-Film Models 1014
  - 4.5 A Two-Dimensional Model for Large Soft Films 1022
  - 4.6 Higher-Order Terms and Wall Structures 1032
  - 4.7 Pattern Formation in Micromagnetics: Mathematical Context 1069
  - 4.8 Beyond Low-Energy States 1078
  - Appendix A. Magnetostatics 1098
  - Appendix B. F-Convergence 1099
  - Appendix C. Frequently Used Symbols 1104
  - References 1106
  - Acknowledgements 1106
- Chapter 5. Computational Aspects of Micromagnetics 1115
  - 5.1 Introduction 1115
  - 5.2 Magnetic Memory and Sensors 1116
  - 5.3 Micromagnetics 1118
  - 5.4 Examples 1126
  - 5.5 Langevin Dynamics 1137
  - 5.6 Energy Barrier: The Path Method 1143
  - 5.7 Applications 1153
  - 5.8 Energy Barriers in Magnetic Random Access Memory Elements 1156
  - References 1161
- Chapter 6. Nonlinear Magnetization Dynamics. Switching and Relaxation Phenomena 1167
  - 6.1 Introduction 1167
  - 6.2 Landau–Lifshitz–Gilbert (LLG) Equation 1170
  - 6.3 Geometrical and Analytical Techniques for LLG Equation in Uniformly Magnetized Bodies 1194
  - 6.4 Magnetization Switching and Relaxation 1220
  - 6.5 Spin-Torque-Driven Magnetization Dynamics 1256
  - Appendix A. LLG Equation in Different Systems of Coordinates 1281
  - Acknowledgements 1281
  - Appendix B. Poincaré–Melnikov Method 1284
  - Appendix C. Classification of Bifurcations 1289
  - References 1293
- Chapter 7. Nonlinear magnetization Dynamics. Magnetization Modes and Spin Waves under Rotating Fields 1299
  - 7.1 Introduction 1299
  - 7.2 Spatially Uniform Magnetization Modes 1304
  - 7.3 Spin Waves Under Far-From-Equilibrium Conditions References 1340
  - References 1371
- Index 1375
- Front Cover 1382
- The Science of Hysteresis: Hysteresis in Materials 1385
- Copyright Page 1386
- Contents 1387
- Preface 1391
- Contributors 1393
- Chapter 1. Hysteresis in Magnetic Materials 1395
  - 1.1 Introduction 1395
  - 1.2 General Phenomenology of Magnetic Hysteresis 1396
  - 1.3 Energy in a Magnetic System. Domain Walls and Domain Structures 1423
  - 1.4 Magnetization Process and Coercivity 1452
  - 1.5 Rate-Dependent Magnetic Hysteresis 1484
  - 1.6 Hysteresis Modeling 1493
  - 1.7 Experimental Methods 1514
  - References 1577
- Chapter 2. Magnetic Hysteresis in Nanostructured Materials 1585
  - 2.1 Introduction 1585
  - 2.2 Magnetic Hysteresis in Nanocrystalline Systems 1592
  - 2.3 Magnetic Hysteresis in Nanogranular Systems 1622
  - References 1643
- Chapter 3. Superconducting Hysteresis 1651
  - 3.1 Superconductors with Sharp Resistive Transitions 1651
  - 3.2 Experimental Testing of the Preisach Modelling of Superconducting Hysteresis 1666
  - 3.3 Nonlinear Diffusion in Superconductors with Gradual Resistive Transitions (Linear Polarization) 1684
  - 3.4 Nonlinear Diffusion in Isotropic Superconductors with Gradual Resistive Transitions (Circular Polarization) 1701
  - 3.5 Nonlinear Diffusion in the Case of Elliptical Polarizations and Anisotropic Media 1712
  - References 1728
- Chapter 4. Hysteresis in Piezoelectric and Ferroelectric Materials 1731
  - 4.1 Introduction 1731
  - 4.2 Basic Definitions 1735
  - 4.3 Piezoelectric Hysteresis in Linear Systems 1749
  - 4.4 Piezoelectric and Dielectric Hysteresis in Nonlinear Systems under Subswitching Conditions 1781
  - 4.5 Ferroelectric Hysteresis 1825
  - Appendix A. Tensor Notation 1842
  - Appendix B. Thermodynamic Derivation of the Piezoelectric Effect and Piezoelectric Constitutive Equations 1843
  - References 1846
  - Acknowledgement 1846
- Chapter 5. Hysteresis in Shape-Memory Materials 1861
  - 5.1 Introduction 1861
  - 5.2 Martensitic Transformations 1863
  - 5.3 Hysteresis 1884
  - 5.4 Thermodynamics 1901
  - 5.5 Modeling of the Transformation Kinetics 1917
  - 5.6 Hysteresis in Magnetic SMA 1922
  - 5.7 Summary and Perspectives 1934
  - References 1935
  - Acknowledgement 1935
- Chapter 6. Hysteretic Elastic Systems: Geophysical Materials 1949
  - 6.1 Introduction 1949
  - 6.2 Model 1953
  - 6.3 Consequences of the Model 1970
  - 6.4 Thermodynamic Forces 2006
  - 6.5 Experiment 2014
  - 6.6 Conclusion 2050
  - Appendix A. Fluid-Pore Space 2051
  - Appendix B. Models for the Behavior of the Elastic State 2057
  - Appendix C. Inversion for the Density in Preisach Space 2064
  - Appendix D. Lumped-Element Model 2065
  - Appendix E. Projection Procedure 2069
  - Appendix F. Stochastic Equations 2071
  - References 2077
- Chapter 7. Application of the Preisach Model to Soil-Moisture Hysteresis 2083
  - 7.1 Introduction 2083
  - 7.2 The Preisach Model 2087
  - 7.3 Results of Fitting 2100
  - 7.4 Discussion 2127
  - Appendix. Historical Review of Soil-Moisture Hysteresis 2127
  - Acknowledgment 2135
  - References 2136
- Index 2139

Author's affiliation

Giorgio Bertotti: INRIM - Istituto Nazionale di Ricerca Metrolo
Isaak D. Mayergoyz: University of Maryland, ECE Department, Colle

3-volume set

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