Preface ........................................................ xv
About the Authors ............................................. xxi
1 Introduction ................................................. 1
1.1 Analyzing Materials and Events, Analyzing Quantities,
and the System of Science ............................... 3
1.2 What Quantities Are and Where They Are From ............ 10
1.3 Rotational Movements ................................... 13
1.4 What Time Is ........................................... 14
1.5 Irregular Information and Digital Structuralization .... 16
Acknowledgments ............................................ 21
2 Embryonic Deficits of Quantitative Analysis Systems ......... 23
2.1 Concepts on the Concept of Determinacy ................. 27
2.2 Randomness and Quantitative Comparability .............. 31
2.2.1 Some Background Information ..................... 31
2.2.2 The Problem of Randomness ....................... 32
2.2.3 Random Walk and Denial of Randomness ............ 34
2.2.4 Sample Size and Stable "Roving" ................. 37
2.2.5 Digitization of Irregular Information:
A Process Physics Principle and End of
Quantitative Comparability ...................... 38
2.2.5.1 Digital Structurization of Irregular
Humidity Information and Forecast of
Torrential Rains ....................... 38
2.2.5.2 End of Quantitative Comparability ...... 41
2.3 Equations of Dynamics and Complexity ................... 45
2.3.1 Well-Posed Transformations of Systems of
Nonadiabatic Equations .......................... 49
2.3.2 Characteristic Equations and Eigenvalues ........ 52
2.3.2.1 The Case with Heat Insulation .......... 55
2.3.2.2 The Case without Heat Insulation ....... 58
2.3.3 Transformation between a Phase Trajectory
Equation and a Phase Trajectory of a Center
Point ........................................... 61
Acknowledgments ............................................. 68
3 Attributes and Problems of Numbers and Their Morphological
Transformations ............................................. 69
3.1 Incompleteness of Quantities ........................... 76
3.1.1 Indeterminacy of Quantities Themselves .......... 80
3.1.2 Artificiality of Quantities ..................... 80
3.1.3 The Problem of Computational Inaccuracy of
Quasi-Equal Quantities .......................... 82
3.1.4 Regularization and Large Probabilitization of
Quantitative Variables .......................... 84
3.1.5 The Problem of Nonisomorphic Equal Quantities ... 87
3.1.6 The Problem of Nondimensionalization ............ 89
3.2 Folding and Sharp Turning in Mathematical Models ....... 93
3.2.1 Indeterminacy in Mathematical Descriptions of
Linear Reciprocating Points and Practical
Significance of Corresponding Figurative
Comparability ................................... 93
3.2.2 Transformation of the Shapes and Quantities of
Sharp Turning ................................... 95
3.3 Blown-Ups of Quadratic Nonlinear Models and Dynamic
Spatial Transformations ................................ 96
3.3.1 The Implicit Transformation between a Circle
and a Tangent Line .............................. 99
3.3.2 The Implicit Transformation between a Circle
and a Secant Line ............................... 99
3.3.2.1 Movement on the Minor Arch ............ 100
3.3.2.2 Movement on the Major Arch ............ 100
3.3.3.1 Implicit Transformation between
a Circle and a Disjoint Line .......... 101
3.4 The Dynamic Implicit Transformation of the Riemann
Ball .................................................. 102
3.5 Whole Evolution of Bifurcation Mathematical Models
and Nonlinear Elasticity Models ....................... 104
3.5.1 Standard Bifurcation ........................... 104
3.5.2 The Standard Bifurcation Model of Saddle,
Node Points .................................... 105
3.5.3 The Standard Hofe Bifurcation Model ............ 105
3.5.4 Nonlinear Elasticity Models .................... 106
3.6 Eight Theorems on Mathematical Properties of
Nonlinearity .......................................... 108
3.6.1 Fundamental Characteristics of General
Nonlinear Equations ............................ 108
3.6.1.1 Second-Degree Polynomials ............. 108
3.6.2 Eight Theorems about Third- and Second-Degree
Nonlinear Models ............................... 112
3.6.2.1 The Third-Order Nonlinear Model ....... 112
3.6.2.2 Second-Order Nonlinear Models ......... 116
3.6.2.3 The Nonlinear Problem of nth-Degree
Polynomial and Theorem 8 .............. 118
3.6.3 Some Explanations .............................. 121
3.7 Conclusions ........................................... 122
Acknowledgments ............................................ 123
4 Achievements and Problems of the Dynamic System of Wave
Motions .................................................... 125
4.1 The Classical Vibration and Wave Motion System ........ 128
4.2 Mathematical Waves and Related Problems ............... 142
4.2.1 Transformation between Mathematical
Hyperbolic Wave Motions and Nonlinear Flows .... 143
4.2.1.1 Nonlinear One-Dimensional Flows and
Their Transitional Changes ............ 143
4.2.1.2 Nonlinear Two-Dimensional Flows and
Their Transitional Changes ............ 148
4.2.2 Mathematical Dispersive Wave Motions ........... 151
4.2.3 The General Dispersive Relationship ............ 155
4.3 Linearization or Weak-Linearization of Nonlinear
Equations ............................................. 160
4.3.1 Rossby Equation and Theory of Rossby Waves of
Fluid Mechanics ................................ 160
4.3.1.1 The Fundamental Characteristics of
Spinning Fluids ....................... 160
4.3.2 Linearization of the Euler Equation and
Problems with Rossby Waves ..................... 163
4.3.2.1 Fundamental Characteristics of
Spinning Fluids ....................... 163
4.3.2.2 The Rossby Equation and the Theory
of Rossby Waves ....................... 167
4.4 Nondimensionalization of the Two-Dimensional
Navier—Stokes—Coriolis Equation and the Problem of
Solving the Rossby Equation ........................... 175
4.4.1 The Nondimensionalization of the
Two-Dimensional Navier—Stokes—Coriolis
Equation ....................................... 175
4.4.2 Problems with Nondimensionalization ............ 177
4.5 The Problem of Integrability of the KdV and Burgers'
Equations ............................................. 188
4.5.1 The Modeling Problem of the KdV Equation ....... 189
4.5.2 The Problem of Solving the KdV Equation ........ 195
4.5.2.1 The Generality of the Solution of
the KdV Equation ...................... 195
4.5.2.2 Backlind Transformation and the
Problem of Solving the KdV Equation ... 198
4.5.2.3 Direct Integration and the Solitary
Waves of the KdV Equation ............. 199
4.5.3 Mathematical Properties of the KdV Equation
and Its Conservation Laws of Energy ............ 200
4.5.3.1 Representation of Conservation Laws
of Energy in Modern Science ........... 201
4.5.3.2 The KdV Equation and Its
Conservation Laws ..................... 202
4.5.4 Mathematical Properties and Problems of
Physics of the Conservation Laws of the KdV
Equation ....................................... 207
4.5.4.1 Mathematical Properties of the
Conservation Laws of the KdV
Equation .............................. 208
4.5.4.2 The Problems of Physics Regarding
the KdV Equation ...................... 209
4.5.5 General Properties and Integrability of the
Burgers' Equation .............................. 210
4.5.5.1 The General Properties of the
Burgers' Equation ..................... 210
4.5.5.2 Integrability of the Burgers'
Equation .............................. 214
4.6 Summary ............................................... 216
Acknowledgments ............................................ 219
5 The Circulation Theorem and Generalization of the Mystery
of Nonlinearity ............................................ 221
5.1 Bjerknes's Circulation Theorem ........................ 227
5.2 Generalized Meaning of Nonlinearity ................... 231
5.2.1 The Universal Gravitational Effects of the
Circulation Theorem ............................ 231
5.2.2 Gravitational Effects of the Equation of
Fluid Movement ................................. 232
5.2.3 The Problem of Terrain and Nonlinearity ........ 233
5.2.3.1 The Topographic Coordinate System ..... 233
5.2.3.2 The Nonlinear Effect of Terrains ...... 235
5.3 Mystery of Nonlinearity ............................... 238
5.4 Einstein's General Relativity Theory and the Problem
of Gravitational Waves ................................ 244
5.4.1 The Law of Governance of the Slaving Energy
of the Newtonian First Push and the
Mass—Energy Formula of Mutual Reactions ........ 245
5.4.1.1 The Law of Governance of the Slaving
Energy of the Newtonian First Push .... 245
5.4.1.2 Mutual Reactions and Einstein's
Mass-Energy Formula ................... 247
5.4.2 General Relativity Theory and Problems with
Irrotational Curvature Spaces .................. 248
5.4.3 Problems with Energy-Momentum Tensors .......... 249
5.4.4 Irrotational Kinetic Energy and Problems with
Energy Transformations ......................... 249
5.4.5 Irrotational Riemann Geometry and the Problem
of Linearization ............................... 251
5.4.6 Rotationality and Universal Gravitation ........ 255
5.5 Probabilistic Waves of the Schrödinger Equation and
Transmutation of High-Speed Flows ..................... 258
5.5.1 Flow-Wave Duality of Microscopic Material
Flows and Quantumization ....................... 259
5.5.2 Nonprobabilistic Annotation of Uneven Wave
Functions ...................................... 261
5.5.3 Non-Initial-Value Transformation of Energy
and Momentum and Transmutation of High-Speed
Flows .......................................... 267
5.5.3.1 The Problem of the Classical
Low-Speed Flows of Particles .......... 267
5.5.3.2 High-Speed Flows of Particles of
Relativity Theory ..................... 268
5.6 Numerical Experiments on Probabilistic Waves and
Torsion of Quantum Effects ............................ 271
5.6.1 The Fundamental Equation ....................... 272
5.6.1.1 The Original Schrodinger Equation ..... 272
5.6.1.2 An Altered But Equivalent
Schrodinger Equation .................. 272
5.6.1.3 The Difference Equation of the
Altered Schrodinger Equation .......... 273
5.6.2 The Numerical Experiments ...................... 275
5.6.2.1 The Function of the Quantum Effects ... 275
5.6.2.2 The Combined Impact of the Intensity
Pushing of Potential Field and
Quantum Effects ....................... 275
5.6.2.3 Numerical Experiments on the Impact
of Quantum Effects .................... 276
5.6.2.4 Pushing of Potential Field Intensity
and Combined Quantum Effects .......... 279
5.6.2.5 Numerical Experiments with Changing
Unit Volume Density ................... 284
5.7 Summary ............................................... 288
Acknowledgments ............................................ 291
6 Nonlinear Computations and Experiments ..................... 293
6.1 Mathematical Properties and Numerical Computability
of Nonlinearity ....................................... 298
6.1.1 Computational Instability of Nonlinearity ...... 299
6.1.2 Errors of Initial Values ....................... 300
6.1.3 Infinitesimal Difference of Large Quantities ... 301
6.2 Computational Stability Analysis of Nonconservative
and Conservative Schemes of Nonlinear Fluid
Equations ............................................. 303
6.2.1 Desired Quantitative Stability ................. 304
6.2.2 Energy Conservation and Quantitative Growth .... 305
6.3 The Form of Computational Stability of the
Conservative Scheme ................................... 307
6.4 Principal Problems in the Quantitative Computations
of Harmonic Wave Analysis of Spectral Expansions ...... 313
6.4.1 The Basic Computational Formula ................ 314
6.4.2 Numerical Experiments .......................... 314
6.4.2.1 Quasi-Equal Quantities ................ 315
6.4.2.2 Invariant Initial Value and
Parameters with Adjusted Time Steps ... 315
6.4.2.3 Impacts of the Initial Value and
Parameters ............................ 317
6.5 Lorenz's Chaos Doctrine and Related Computational
Schemes ............................................... 320
6.5.1 Problems with Fundamental Concepts ............. 320
6.5.2 Problems with Lorenz's Model ................... 322
6.5.3 Computational Schemes and Lorenz's Chaos ....... 331
6.5.3.1 The Results of Integration with
Relatively Small Time Steps Using
a Nonsmoothing Scheme ................. 332
6.5.3.2 The Computational Results with
Increased Time Steps .................. 339
6.5.3.3 The Computational Results with
Negative Initial Values ............... 342
6.5.3.4 The Computational Results with an
Adjusted Parameter .................... 343
6.5.3.5 Varying Parameter r ................... 344
6.5.3.6 Varying Parameter σ ................... 344
6.5.3.7 The Truncated Spectral Energy Analysis
of Lorenz's Model ..................... 345
6.5.3.8 Discussions on the Phenomenon of
Lorenz's Chaos ........................ 347
Acknowledgments ............................................ 348
7 Evolution Science .......................................... 349
7.1 Specifics of the Concept of Noninertial Systems ....... 351
7.1.1 Dualism, Materials, Attributes of Materials,
and the Concept of Noninertial Systems ......... 351
7.1.2 Quantitative Formality and Variability of
Events - Existence and Evolution ............... 353
7.1.3 Rotational Movements and Material Evolutions ... 359
7.2 What Is Time? ......................................... 362
7.2.1 The Problem .................................... 362
7.2.2 About the Concept of Time ...................... 364
7.2.2.1 Time in China ......................... 365
7.2.2.2 Time in the West ...................... 366
7.2.3 The Concept of Time ............................ 368
7.3 Stirring Motion and Stirring Energy ................... 372
7.3.1 Rotation and the Problem of Stirring Energy .... 373
7.3.2 Conservation of Stirring Energy and Three-
Ringed Energy Transformation ................... 375
7.3.3 Conservation of Stirring Energy, Process of
Energy Transformation, and Nonconservation of
Stirring Energy and Evolution .................. 379
7.3.4 Conservability of Stirring Energy and
Physical Meaning of Energy Transformation ...... 381
7.4 Physical Quantities, Parametric Dimension, and
Variable Events ....................................... 386
7.4.1 The Physics of Physical Quantities ............. 386
7.4.2 The Physics of Physical Quantities and
Nonquantification of Events .................... 390
7.4.2.1 Problems with the Physics of
Physical Quantities ................... 390
7.4.2.2 Nonquantification of Variable
Events ................................ 392
7.4.3 Material Dimensions and Problems with
Quantitative Parametric Dimensions ............. 398
Acknowledgments ............................................ 401
8 Irregular Information and Regional Digitization ............ 403
8.1 Digitization of Region-Specific Information and
Prediction of Disastrous Weathers ..................... 412
8.1.1 Basic Logic Used in the Design of
Digitization of Regional Disastrous Weather
Conditions ..................................... 413
8.1.1.1 Choice of Heat Analysis ............... 413
8.1.1.2 Order of Information and the
Reversed Order Structure .............. 414
8.1.1.3 The V-3θ Graph of Digitized Regional
Information and Explanations .......... 416
8.2 The Digital Design and Functions of the V-3θ Graphs ... 424
8.3 Structural Characteristics of Major Disastrous
Weathers .............................................. 432
8.3.1 Severe Convective Weathers ..................... 432
8.3.1.1 Hailstone Disastrous Weathers ......... 433
8.3.2 Local Severe Rainfalls and Thundershowers ...... 437
8.3.2.1 Local Severe Rainfalls ................ 437
8.3.2.2 Thundershowers ........................ 439
8.3.3 Predicting the Amount of Rainfalls ............. 441
8.3.3.1 Predicting the Amounts of General
Rainfalls ............................. 443
8.3.3.2 Predicting the Precipitations of
Torrential Rains ...................... 445
8.3.3.3 Strong Winds and Sand-Dust Storms ..... 447
8.3.3.4 High-Temperature Weathers ............. 449
8.3.3.5 Dense Fog Weathers .................... 451
8.4 The Problem of Mid- and Long-Term Forecasts ........... 453
8.4.1 Analysis and Forecast of the High-Temperature
Drought of Summer 2006 ......................... 454
8.4.1.1 Layers of East Winds and Subtropical
High Pressures ........................ 456
8.4.2 The January 2008 Snow-Ice Disaster
Experienced in Southern China .................. 469
8.4.2.1 Some Explanations ..................... 469
8.4.2.2 Key Points for Forecasting the 2008
Snow—Ice Disaster ..................... 469
8.5 Examples of Case Studies .............................. 478
8.5.1 The Windstorm in the Bay of Bengal on May 3,
2008 ........................................... 478
8.5.1.2 The Problem of Prediction ............. 481
8.5.2 Changes in Atmospheric Structures for the
Sichuan Earthquake on May 12, 2008 .............. 483
8.5.2.1 Changes in Atmospheric Structures
before the Earthquake ................. 484
8.5.2.2 Severely Instable Atmospheric
Structures and Characteristics of
the Atmospheric Structures along the
Edge of the Epicenter 486
8.5.2.3 Aftershock Rainfalls and Weakening
of Instable Energies .................. 487
8.5.2.4 Some Simplified Explanations .......... 494
Acknowledgments ............................................ 495
9 Digital Transformation of Automatically Recorded
Information ................................................. 497
9.1 Some Briefings ........................................ 498
9.1.1 Quantification of Events and the Problem of
Digitization ................................... 499
9.1.2 Variable Events and Time ....................... 501
9.2 Digitization of Automatically Recorded Information
of Disastrous Weathers ................................ 502
9.2.1 Digital Transformation of Automatically
Recorded Information on Locations of
Torrential Rains ............................... 504
9.2.1.1 Case Studies of Informational
Digitization .......................... 507
9.2.1.2 Digital Transformation of the
Information of Rainfall Locations ..... 507
9.2.1.3 Digitalized Comparison between the
Humidity Evolutional Processes of
the Chengdu and Longquan Stations ..... 509
9.2.2 Digitalized Information and Applications in
the Forecasting of Thunderstorms ............... 515
9.2.2.1 The V-36 Graphic Characteristics of
Strong Convective Thunderstorm
Weathers .............................. 516
9.2.2.2 Digital Transformation of
Automatically Recorded Time Series
Information of Humidity for
Predicting Rainfall Locations ......... 521
9.2.3 Digital Forecasts for the Locations of Fogs
and Hazes ...................................... 522
9.2.3.1 About the Weather Conditions of the
Case Study ............................ 525
9.2.3.2 Digital Transformation of
Automatically Recorded Information
and Forecast of Locations ............. 527
9.3 Examples of Digitizing Seismological Oscillating
Information and Prediction of Earthquakes ............. 545
9.3.1 Digitization Characteristics of Geomagnetic
Information .................................... 545
9.3.2 Digitization Characteristics of the
Information of Normal Conditions ............... 548
9.3.3 Digitization Characteristics of Abnormal
Conditions ..................................... 548
9.3.4 Analysis of Disastrous Events .................. 552
9.3.4.1 Relationship between Abnormality of
Information Digitization and
Earthquakes ........................... 552
9.3.4.2 Structural Abnormality in
Geomagnetic Readings and Several
Kinds of Disasters .................... 554
9.3.5 Test with the Earthquakes of 2005 (as of
November 30,2005) .............................. 554
9.3.5.1 The Data Collection ................... 554
9.3.5.2 Tests of Actual Forecasts (as of the
End of November 2005) ................. 556
Acknowledgments ............................................... 562
Afterword ..................................................... 563
References .................................................... 571
Index ......................................................... 577
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