Nonlinear Problems of Engineering (eBook)

Front Cover 1
Nonlinear 
4 
Copyright Page 5
Table of Contents 12
Contributors 6
Foreword 8
Preface 10
Chapter 1. 
16 
I. Introduction 16
II. The Comparative Approach 17
III. Classical Approach 17
IV. Discussion 19
V. The New Approach of Invariant 
19 
VI. Discussion 20
VII. Variational Processes 21
VIII. Geodesies 22
IX. Dynamic Programming and the Calculus of Variations 23
X. Approximation in Policy Space 24
XI. Discussion 25
References 25
Chapter 
27 
I. 27
II. 29
III. 32
IV. 33
Chapter 3. 
38 
Text 38
References 42
Chapter 4. 
44 
I. The "Center Problem" in the Iteration of Analytic Functions 44
II. Contexts Leading to Small-Divisor Series 48
III. Generalities Regarding Iteration of Analytic Functions 51
IV. Construction of Singular Iterations zn+1 = f(zn) 57
V. Properties of Singular Iterations 60
References 65
Chapter 5 . 
66 
I. Introduction 66
II. Pure Homogeneous Deformation 67
III. Plane Strain of a Net—Displacement Boundary Conditions 71
IV. Plane Strain of a Net—Force Boundary Conditions 74
V. Further Developments 77
Bibliography 79
Chapter 6. 
80 
Introduction 80
I. Partial Differential Equations Arising in the Theory of Compressible Fluids 82
II. The Determination of the Stream Function of a Vortex in the Subsonic Region 86
III. A Method for Generating Solutions of Equation (1.3.5) 91
References 101
Bibliography 102
Chapter 7. 
105 
A. Melting or Solidification 105
B. Consolidation of an Earth Dam 107
C. Seepage through a Porous Dam 110
D. Lubrication in a Journal Bearing, with Oil Cavitation 113
References 118
General References 118
Chapter 8. 
119 
Nomenclature 119
Introduction 119
The Single Plate-Type Fin 120
Radiant Interaction between Fin and Tube Surfaces 124
Radiant Interaction between Fin Surfaces 131
Radiant Interaction between Fin and Tube and between Neighboring Fins 135
Concluding Remarks 136
References 137
Chapter 9. 
138 
I. A Particular Nonlinear Partial Differential Equation and Its Solution by Means of a Geometrical Construction 139
II. Formulation of a Statistical Problem 143
III. The Solution of the Auxiliary Differential Equation 149
Notes 151
Chapter 10. 
153 
Introduction 153
Symbols 154
Analysis 157
Results 167
Concluding Remarks 175
References 176
Chapter 11. 
178 
I. Introduction 178
II. Fundamentals of Radiant Energy Transfer 179
III. Fundamental Equations of Radiation Gas Dynamics 180
IV. Solutions for Radiation Transfer Equation 183
V. New Parameters of Radiation Gas Dynamics 185
VI. Wave Motions in Radiation Gas Dynamics 188
VII. Shock Waves in Radiation Gas Dynamics 189
VIII. Jet Mixing in Radiation Gas Dynamics 191
IX. Plane Couette Flow in Radiation Magnetogas Dynamics 194
References 198
Chapter 12. 
199 
Introduction 199
List of Symbols 200
1. Two-Dimensional Compressible Flow in the Physical Plane 201
2. Two-Dimensional Compressible Flow in the Hodograph Plane 204
3. Two-Dimensional Compressible Flow about a Closed Body in a Uniform Subsonic Flow 209
4. Two-Dimensional Flow through the Sonic Line 215
References 221
Chapter 13. 
223 
Introduction 223
Information and Communication 224
Symbols and Symbolic Structure 226
Handicaps and Communication 228
Other Observations 230
Concluding Remarks 231
References 231
Chapter 14. 
232 
Text 232
References 233
Chapter 15. 
235 
1. Introduction 235
2. The Difference Equation 236
3. The Linear System 238
4. The Peaceman-Rachford Method 239
5. The Cummutative Case 243
6. Laminar Flow Problem 248
7. Numerical Results and Conclusions 259
References 260
Subject Index 262