Science of Hysteresis (eBook)

Front Cover 1
The Science of Hysteresis 4
Copyright Page 5
Contents 6
Preface 10
Contributors 12
Chapter 1. Mathematical Models of Hysteresis 14
1.1 Hysteresis Operators 16
1.2 The Duhem Model 26
1.3 Rheological Models of Elasto-plasticity 30
1.4 Discontinuous Hysteresis 48
1.5 Micromagnetism 58
1.6 Models of Hysteresis with Internal Variables 69
1.7 Genesis of Hysteresis and Coupling with PDEs 75
1.8 A Transport Equation with Hysteresis 82
1.9 A Quasilinear Parabolic PDE with Hysteresis 91
1.10 A Quasilinear Hyperbolic PDE with Hysteresis 104
1.11 Hysteresis in Porous-Media Filtration 111
1.12 Conclusions 118
1.13 Appendix. Elements of Convex Calculus 120
Acknowledgement 127
References 128
Chapter 2. Differential Equations with Hysteresis via a Canonical Example 138
2.1 Hysteresis Phenomena 138
2.2 Numerical Experiments 149
2.3 Examples of Rigorous Conclusions 165
2.4 Examples of Technical Toolboxes 248
Acknowledgement 291
References 292
Chapter 3. Scalar Preisach Models of Hysteresis 306
3.1 The Classical Preisach Model of Hysteresis 306
3.2 Generalized Scalar Preisach Models of Hysteresis 373
References 456
Chapter 4. Vector Preisach Models of Hysteresis 460
4.1 Classical Stoner–Wohlfarth Model Vector Hysteresis 460
4.2 Definition of Vector Preisach Models of Hysteresis and their Numerical Implementation 471
4.3 Some Basic Properties of Vector Preisach Hysteresis Models 480
4.4 Identification Problem for Isotropic Vector Preisach Models 498
4.5 Identification Problem for Anisotropic Vector Preisach Models 507
4.6 Dynamic Vector Preisach Models of Hysteresis 517
4.7 Generalized Vector Preisach Models of Hysteresis. Experimental Testing 524
References 539
Chapter 5. Stochastic Aspects of Hysteresis 542
5.1 Preisach Model with Stochastic Input as a Model of Thermal Relaxations 542
5.2 Experimental Testing. Scaling and Data Collapse in Magnetic Viscosity 554
5.3 Preisach Model Driven by Continuous-Time Noise. Origin of the Universality of Long-Time Thermal Relaxations 563
5.4 Noise in Hysteretic Systems and Stochastic Processes on Graphs 575
5.5 Analysis of Spectral Noise Density of Hysteretic Systems Driven by Stochastic Processes 586
5.6 Modeling of Temperature-Dependent Hysteresis within the Framework of Randomly Perturbed Fast Dynamical Systems 591
5.7 Functional (Path) Integration Models of Hysteresis 600
References 614
Chapter 6. Control of Systems with Hysteresis 618
6.1 Introduction 618
6.2 Optimal Control of Systems with Simple Hysteretic Elements 620
6.3 Optimal Control of Systems with Hysteron-Type Operators 627
6.4 Optimal Control of Systems with Preisach Hysteresis 635
6.5 Hysteresis from Optimal Control, and Hysteresis for Optimal Control 645
References 647
Chapter 7. Binary Detection and Rectangular Hysteresis Operators 652
7.1 Introduction 652
7.2 General System Description and Outline 654
7.3 Input Process and Mid-Span Repeater 657
7.4 Receiver Integrator Output: Probability Density Function Calculation 659
7.5 Summary 675
7.6 Concluding Remarks 676
References 647
Chapter 8. Hysteresis and Unemployment: A Preliminary Investigation 680
8.1 Introduction 680
8.2 Hysteresis 682
8.3 An Illustrative Model 683
8.4 Computing the Hysteresis Variable 690
8.5 Hysteresis and UK Unemployment 698
8.6 Concluding Remarks 700
Appendix 700
References 709
Index 714
Front Cover 719
The Science of Hysteresis: Physical Modeling, Micromagnetics, and Magnetization Dynamics 722
Copyright Page 723
Contents 724
Preface 728
Contributors 730
Chapter 1. Thermodynamics, Hysteresis, and Micromagnetics 732
1.1 Introduction 732
1.2 Classical and Nonequilibrium Thermodynamics 736
1.3 Thermodynamic Aspects of Hysteresis 760
1.4 From Micromagnetics to Magnetic Hysteresis 806
References 831
Chapter 2. Random-Field Ising Models of Hysteresis 838
2.1 Introduction 838
2.2 Models 843
2.3 The Renormalization Group and Scaling 848
2.4 Critical Exponents, Scaling Functions 853
2.5 Measuring Universal Properties 859
2.6 Exponent Relations 872
2.7 Finite Sweep Rate 875
2.8 Subloops and History-Induced Critical Behavior 876
2.9 Real Experiments 880
2.10 Unsolved Problems 889
Acknowledgement 890
Appendix. Derivation of the Scaling Forms and Corrections 891
References 898
Chapter 3. The Barkhausen Effect 912
3.1 Introduction 912
3.2 Experiments and Materials 915
3.3 Experimental Results 921
3.4 Models and Theories of Magnetization Dynamics 942
3.5 Discussion of Theoretical Results 970
3.6 Conclusions and Perspectives 982
Acknowledgements 984
Appendix. Translation of the Original Paper by Barkhausen 724
References 988
Chapter 4. Recent Analytical Developments in Micromagnetics 1000
4.1 Introduction 1000
4.2 The Energy Functional and Pattern Formation 1004
4.3 Bulk Scalings 1009
4.4 A Hierarchy of Thin-Film Models 1013
4.5 A Two-Dimensional Model for Large Soft Films 1021
4.6 Higher-Order Terms and Wall Structures 1031
4.7 Pattern Formation in Micromagnetics: Mathematical Context 1068
4.8 Beyond Low-Energy States 1077
Appendix A. Magnetostatics 1097
Appendix B. F-Convergence 1098
Appendix C. Frequently Used Symbols 1103
Acknowledgements 1105
References 1105
Chapter 5. Computational Aspects of Micromagnetics 1114
5.1 Introduction 1114
5.2 Magnetic Memory and Sensors 1115
5.3 Micromagnetics 1117
5.4 Examples 1125
5.5 Langevin Dynamics 1136
5.6 Energy Barrier: The Path Method 1142
5.7 Applications 1152
5.8 Energy Barriers in Magnetic Random Access Memory Elements 1155
References 1160
Chapter 6. Nonlinear Magnetization Dynamics. Switching and Relaxation Phenomena 1166
6.1 Introduction 1166
6.2 Landau–Lifshitz–Gilbert (LLG) Equation 1169
6.3 Geometrical and Analytical Techniques for LLG Equation in Uniformly Magnetized Bodies 1193
6.4 Magnetization Switching and Relaxation 1219
6.5 Spin-Torque-Driven Magnetization Dynamics 1255
Acknowledgements 1280
Appendix A. LLG Equation in Different Systems of Coordinates 1280
Appendix B. Poincaré–Melnikov Method 1283
Appendix C. Classification of Bifurcations 1288
References 1292
Chapter 7. Nonlinear magnetization Dynamics. Magnetization Modes and Spin Waves under Rotating Fields 1298
7.1 Introduction 1298
7.2 Spatially Uniform Magnetization Modes 1303
7.3 Spin Waves Under Far-From-Equilibrium Conditions References 1339
References 1370
Index 1374
Front Cover 1381
The Science of Hysteresis: Hysteresis in Materials 1384
Copyright Page 1385
Contents 1386
Preface 1390
Contributors 1392
Chapter 1. Hysteresis in Magnetic Materials 1394
1.1 Introduction 1394
1.2 General Phenomenology of Magnetic Hysteresis 1395
1.3 Energy in a Magnetic System. Domain Walls and Domain Structures 1422
1.4 Magnetization Process and Coercivity 1451
1.5 Rate-Dependent Magnetic Hysteresis 1483
1.6 Hysteresis Modeling 1492
1.7 Experimental Methods 1513
References 1576
Chapter 2. Magnetic Hysteresis in Nanostructured Materials 1584
2.1 Introduction 1584
2.2 Magnetic Hysteresis in Nanocrystalline Systems 1591
2.3 Magnetic Hysteresis in Nanogranular Systems 1621
References 1642
Chapter 3. Superconducting Hysteresis 1650
3.1 Superconductors with Sharp Resistive Transitions 1650
3.2 Experimental Testing of the Preisach Modelling of Superconducting Hysteresis 1665
3.3 Nonlinear Diffusion in Superconductors with Gradual Resistive Transitions (Linear Polarization) 1683
3.4 Nonlinear Diffusion in Isotropic Superconductors with Gradual Resistive Transitions (Circular Polarization) 1700
3.5 Nonlinear Diffusion in the Case of Elliptical Polarizations and Anisotropic Media 1711
References 1727
Chapter 4. Hysteresis in Piezoelectric and Ferroelectric Materials 1730
4.1 Introduction 1730
4.2 Basic Definitions 1734
4.3 Piezoelectric Hysteresis in Linear Systems 1748
4.4 Piezoelectric and Dielectric Hysteresis in Nonlinear Systems under Subswitching Conditions 1780
4.5 Ferroelectric Hysteresis 1824
Appendix A. Tensor Notation 1841
Appendix B. Thermodynamic Derivation of the Piezoelectric Effect and Piezoelectric Constitutive Equations 1842
Acknowledgement 1845
References 1845
Chapter 5. Hysteresis in Shape-Memory Materials 1860
5.1 Introduction 1860
5.2 Martensitic Transformations 1862
5.3 Hysteresis 1883
5.4 Thermodynamics 1900
5.5 Modeling of the Transformation Kinetics 1916
5.6 Hysteresis in Magnetic SMA 1921
5.7 Summary and Perspectives 1933
Acknowledgement 1934
References 1934
Chapter 6. Hysteretic Elastic Systems: Geophysical Materials 1948
6.1 Introduction 1948
6.2 Model 1952
6.3 Consequences of the Model 1969
6.4 Thermodynamic Forces 2005
6.5 Experiment 2013
6.6 Conclusion 2049
Appendix A. Fluid-Pore Space 2050
Appendix B. Models for the Behavior of the Elastic State 2056
Appendix C. Inversion for the Density in Preisach Space 2063
Appendix D. Lumped-Element Model 2064
Appendix E. Projection Procedure 2068
Appendix F. Stochastic Equations 2070
References 2076
Chapter 7. Application of the Preisach Model to Soil-Moisture Hysteresis 2082
7.1 Introduction 2082
7.2 The Preisach Model 2086
7.3 Results of Fitting 2099
7.4 Discussion 2126
Appendix. Historical Review of Soil-Moisture Hysteresis 2126
Acknowledgment 2134
References 2135
Index 2138