Physics of Asymmetric Continuum: Extreme and Fracture Processes: Earthquake Rotation and Soliton Waves / Edition 1

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More About This Textbook

Overview

The monograph summarizes some fundamental theories of continua, in particular those with defect content, and develops asymmetric theory of continuum; the idea of spin and twist motions, the latter related to the shear axes oscillations, leads to the complex rotation field governed by the equations analogues to electromagnetic field.
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Product Details

  • ISBN-13: 9783540683544
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 9/26/2008
  • Edition description: 2008
  • Edition number: 1
  • Pages: 293
  • Product dimensions: 6.60 (w) x 9.60 (h) x 0.80 (d)

Table of Contents

Part I Introduction to Asymmetric Continuum and Experimental Evidence of Rotation Motions 1

1 Introduction to Asymmetric Continuum: Fundamental Point Deformations Roman Teisseyre Marek Gorski 3

1.1 Introduction 3

1.2 Self-Field Nuclei: Deviations from Classical Elasticity 8

1.3 Basic Deformations and Simple Motions in an Asymmetric Continuum 10

1.4 Conclusions 13

2 Measurement of Short-Period Weak Rotation Signals Leszek R. Jaroszewicz Jan Wiszniowski 17

2.1 Definition of Rotation and a Review of the Measurement Methods 17

2.2 Classification of Rotation Measurements and Requirements for Recording Instruments 25

2.3 The Influence of Recording Error on the Computed Rotation Signal 27

2.4 Direct Detection of the Rotational Component 37

2.5 Conclusions 42

3 Buildings as Sources of Rotational Waves Mihailo D. Trifunac 49

3.1 Introduction 49

3.2 Soil-Foundation Interaction - Near Field 51

3.3 Soil-Foundation Interaction - Far Field 62

3.4 Summary 62

4 Two-Pendulum Systems for Measuring Rotations Vladimir Graizer 67

4.1 Introduction 67

4.2 Theory 68

4.3 Testing and Measurements 73

4.4 Discussion and Conclusions 73

5 Theory and Observations: Some Remarks on Rotational Motions Roman Teisseyre 77

5.1 Ten Motions and Deformations 77

5.2 Recording Spin and Twist 78

5.3 Rotation Motions in the Universe 79

Part II Continuum with Defect Densities and Asymmetry of Fields 83

6 Field Invariant Representation: Dirac Tensors Jan Wiszniowski Roman Teisseyre 85

6.1 Introduction 85

6.2 Axial and Deviatoric Parts of any Symmetric Tensor 85

6.3 Dirac Tensors 86

6.4 Motion Equations: Classical Elasticity 88

6.5 Diagonal andOff-Diagonal Symmetric Tensor Representation 89

6.6 Particular Cases 90

6.7 Conclusion 93

7 Asymmetric Continuum: Standard Theory Roman Teisseyre 95

7.1 Introduction 95

7.2 Standard Asymmetric Theory: Basic Assumptions 97

7.3 Spin and Twist Motions 100

7.4 Defects: Dislocation and Disclination Densities 101

7.5 Balance Laws for the Rotation Field and the EM Analogy 103

Appendix Continuum with Internal Nuclei 104

8 Fracture Processes: Spin and Twist-Shear Coincidence Roman Teisseyre Marek Gorski Krzysztof P. Teisseyre 111

8.1 Introduction 111

8.2 Approaching Fracture: Constitutive Laws for Mylonite Zones 116

8.3 Slip Propagation and Spin Release Hypothesis 118

8.4 Conclusions 122

9 Inplane and Antiplane Fracturing in a Multimode Random Sequence Wojciech Boratynski 123

9.1 Introduction 123

9.2 Standard Asymmetric Theory of Continuum 123

9.3 Dislocation Flow on Slip Plane 126

9.4 Numerical Simulation of Dislocation Flow Pattern 128

9.5 Discussion 136

10 Charged Dislocations and Various Sources of Electric Field Excitation Krzysztof P. Teisseyre 137

10.1 Introduction 137

10.2 Effects of Varying and Transient Polarization Due to Mechanical Stimulation 139

10.3 Electrokinetics and the Properties of Water 144

10.4 Less-Known Mechanisms of Charge Separation 149

10.5 Pre-earthquake Stress Variations as the Source of Rotations and Electric Processes 155

10.6 Charge Separation and the Rise of Current 156

10.7 Large-Scale Electric Circuits 156

10.8 Final Remarks 158

11 Friction and Fracture Induced Anisotropy: Asymmetric Stresses Roman Teisseyre 163

11.1 Introduction 163

11.2 2D Uniform Anisotropy 164

11.3 2D Fracture/Friction Induced Anisotropy 167

11.4 Conclusions 168

12 Asymmetric Fluid Dynamics: Extreme Phenomena Roman Teisseyre 171

12.1 Introduction 171

12.2 Standard Asymmetric Fluid Theory 171

12.3 Conclusions 174

13 Fracture Band Thermodynamics Roman Teisseyre 175

13.1 Introduction 175

13.2 Earthquake Dislocation Theory 176

13.3 Fracture Band Model 178

13.4 Earthquake Thermodynamics 179

13.5 Conclusions 184

14 Interaction Asymmetric Continuum Theory Roman Teisseyre 187

14.1 Introduction 187

14.2 Thermal Interaction Field 189

14.3 Dislocation Related Polarization: Polarization Gradient Theory 189

14.4 Conclusion 191

15 Fracture Physics Based on a Soliton Approach Eugeniusz Majewski 193

15.1 Introduction 193

15.2 The Dilaton Mechanism 193

15.3 The Nonlinear Klein-Gordon Equation 194

15.4 Coupled Klein-Gordon Equations Applied to Modeling a Two-Layer Model 196

15.5 The Generalized Korteweg-de Vries (KdV) Equation 198

15.6 The Spin and Twist Strain Solitions 199

15.7 Splitting the Spin Strain Solitons Propagating along the Fracture Surface into the Fracture-Zone Related Part and the Elastic Part 200

15.8 The Sine-Gordon Model of Moving Dislocations 201

15.9 Soliton Ratchets 202

15.10 The Generalized Sine-Gordon Model of Rock Fracture 203

15.11 Links Between Solitons and Moving Cracks 204

15.12 Fracture Solitions in Polymer Chains 204

15.13 Chaos of Soliton Systems 204

15.14 The Soliton Complexes 204

15.15 The Soliton Arrays 205

15.16 Conclusions 206

16 Canonical Approach to Asymmetric Continua Eugeniusz Majewski 209

16.1 Introduction 209

16.2 Hamilton's Principle 210

16.3 Action of Spin and Twist Fields 211

16.4 The Euler-Lagrange Equations 212

16.5 Additive Decomposition of the Lagrangian 214

16.6 The Canonical Equations (Hamilton's Equations) 214

16.7 Conclusions 217

Part III Deformations in Riemannian Geometry 219

17 Continuum Theory of Defects: Advanced Approaches Hiroyuki Nagahama Roman Teisseyre 221

17.1 Geometry of Deformation 221

17.2 Deformation Measures and Incompatibility 225

17.3 Evolution Equations for Stresses and Dislocations 228

17.4 Source/Sink Functions of Dislocation Density 229

17.5 Virtual Tearing (Kondo 1964) 231

17.6 High-Order Spaces and Non-Locality of Deformation 233

17.7 Interaction Between Microscopic and Macroscopic Fields: Comparison Between the Different Approaches 235

17.8 Asymmetric and Anholonomic Deformation 237

17.9 Micromorphic Continuum with Defects 239

17.10 Taylor-Bishop-Hill Model 240

18 Spinors and Torsion in a Riemann-Cartan Approach to Elasticity with a Continuous Defect Distribution and Analogies to the Einstein-Cartan Theory of Gravitation Eugeniusz Majewski 249

18.1 Introduction 249

18.2 The Riemann-Cartan Geometry 252

18.3 Spinors and Spin-Spaces 254

18.4 Elastic Crystal with a Continuous Defect Distribution 254

18.5 The Disclination-Curvature Analogy 256

18.6 The Dislocation-Torison Analogy 257

18.7 The Rotational and Translational Strain Tensors 257

18.8 Description of Moving Defects in 4D 260

18.9 Rotational Metric 260

18.10 Complex Vielbein, Rotational Field, and Metric 261

18.11 Disclination Density and Current Tensor 261

18.12 Dislocation Density and Current Tensor 262

18.13 Additive Decomposition of the Total Strain Tensors 263

18.14 The Einstein-Cartan Theory 264

18.15 The Analogy Between the Disclination Density Tensor and the Einstein Tensor 265

18.16 The Evolution Equation for the Disclination Density 266

18.17 The Evolution Equation for the Disclocation Density 267

18.18 Spin Energy Potential 267

18.19 Degenerate Asymmetric Continuum in Terms of Spinors: Analogy to Maxwell's Equations 268

18.20 Conclusions 268

19 Twistors as Spin and Twist Solitons Eugeniusz Majewski 273

19.1 Introduction 273

19.2 The Twistor Equation 273

19.3 Twistor Definition 274

19.4 Twistor Quantization Theory Applied to Spin and Twist Solitons 274

19.5 The Spin Operator 277

19.6 The Twist Operator 278

19.7 Spin and Twist Solitons Described by the Nonlinear Schrodinger Equation 278

19.8 The Fracture Solitons 281

19.9 The Robinson Congruences 282

19.10 Conclusions 283

20 Potentials in Asymmetric Continuum: Approach to Complex Relativity Roman Teisseyre 285

20.1 Introduction 285

20.2 Natural Potentials 286

20.3 Spin and Twist Fields in the Riemannian Space 288

20.4 Natural Potentials: Analogy to Electromagnetic Field 289

20.5 Complex Relativity Theory 290

20.6 Concluding Remarks 290

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