**About the book:**

This textbook, translated from the third Russian edition, is intended for students at technical schools specializing in the drilling of oil and gas wells. The book outlines the techniques of cementing oil and gas wells, based on current scientific developments and experience gained in applying advanced methods by the Soviet oil-industry specialists, and offers a description of cementing outfit, plugging cements, and chemicals used for their

treatment. It also surveys the properties of plugging mixtures (slurries) and cement stone under a variety of geological and technical conditions.One of the merits of the text is that it describes the composition of plugging cements and techniques employed in their preparation, which is of great importance in training technical personnel at oil fields.

The book will be of particular value in countries where oil is being produced with the participation of the Soviet specialists and with use of the Soviet-made equipment.

The book was translated from the Russian by *S. Kittell* and was published by Mir in 1985 (Second Edition).

Many thanks to *Akbar Azimi* for the scans.

**Contents**

Preface. 8

Introduction. 9

Chapter I. Methods of Casing Cementing. 13

1.1. Primary Cementing Methods. 13

1.2. Secondary (Remedy) Cementing Methods. 22

Chapter 2. Technology of Cementing Wells. 21

2.1. Flow Properties of Slurries. 24

2.2. Idea of Slurry Flow. 28

2.3. Preparation of Well Bore for Casing and Cementing. 30

2.4. Determining Well Bore Configuration and Volume. 35

2.5. Improving the Quality of Well Cementing. 38

2.6. Technological Parameters. 39

2.7. Spacer (Displacement) Fluids. 42

Chapter 3. Cementing Units and Cement Mixers. 44

3.1. Cementing Units. 44

3.2. Cementing Units of Special Construction. 55

3.3. Improvement of Cementing Units. 57

3.4. Citnent Mixers. 59

3.5. Cementing Process Control Station and Self-Propelled Manifold Unit.68

3.6. Cementing Process Calculations. 71

Chapter 4. Cementing Conditions and Requirements for the Quality of Cement Slurries and Stone. 85

4.1. Temperature and Pressure In Wells. 86

4.2. Stratal Waters. 88

4.3. Requirements to the Quality ot Plugging Mixture and Stone. 89

Chapter 5. Composition and Basic Properties of Portland Cement. 97

5.1. Classification of Plugging (Oil-Well) Cements and Mixtures. 97

5.2. Plugging Portland Cement. 99

5.3. Clinker Composition. 99

5.4. Quantitative Characteristics of Clinker. 101

5.5. Saturation Coefficient and Moduli of Portland Cement. 101

5.6. Estimated and Actual Mineralogical Composition of Portland Cement Clinker. 102

5.7. Brief Information on the Technology of Portland Cement Production. 104

5.8. Properties of Dry Cement Flour. 106

5.9. Active Mineral Additives io Binders. 107

5.10. Heat Liberation During Hardening of Plugging Mixtures. 108

Chapter 6. Properties of Cement Slurry and Cement Stone. 123

6.1. Sedimentation Stability of Cement Slurries. 123

6.2. Water Loss of Cement Slurry. 124

6.3. Thickening of Cement Slurry. 126

6.4. Setting Time of Cement Slurries. 127

6.5. Density of Cement Slurry. 129

6.6. Intemingling of Mud Fluids and Plugging Mixtures. 129

6.7. Contraction Effect in Hydration of Cement and in Hardening of Cement Slurry. 131

6.8. Mechanical Strength of Cement Stone. 132

6.9. Permeability of Cement Stone. 135

6.10. Adhesion of Cement Stone to Casing String Metal and to Rocks. 137

6.11. Changes in Volume of Plugging Cements (Slurries and Stone). 138

Chapter 7. Plugging Cement. 142

7.1. Definition and Composition of Plugging Cement. 142

7.2. Specifications for Granulated Coke-Smelting Blast-Furnace Slags. 143

7.3. Specifications for Plugging Cement. 143

7.4. Acceptance Rules. 144

7.5. Test Methods. 145

7.6. Transportation and Storage. 159

7.7. Determining the Permeability of Cement Stone. 159

Chapter 8. Adjusting the Properties of Cement Slurry and Cement Stone. 162

8.1. Cement Setting Retardants. 162

Chapter 9. Plugging Cements for High-Temperature Wells. 169

9.1. Cement-Sand Slurries. 169

9.2. Choice of Sand. 171

9.3. Proportioning of Cement-Sand Slurries. 173

9.4. Permeability of Cement-Sand Stone. 175

9.5. Slag-Sand Cements. 176

9.6. Setting Time and Mechanical Strength of Slag-Sand Slurries and Stone. 178

9.7. Slag-Sand Cements for Wells with Bottom-Hole Temperatures above 200 °C and Pressures up to 100 MPa. 182

9.8. Slag-Sand Cements with Sand of Natural Size. 182

9.9. Plugging Cements Based on Ferromanganese Slag. 184

9.10. Jointly Ground Slag-Sand Cements. 184

9.11. Separate and Combined Effects of Temperature and Pressure on Properties of Slag Slurries. 185

9.12. Effect of Storage Time on Properties ot Slag Cements. 185

9.13. Water Loss of Slag Slurries. 186

9.14. Adhesion of Slag Cements to Metal. 187

9.15. Slag Portland Cement. 187

9.16. Lime-Sand Slurries. 189

9.17. Belite-SIlica Cement. 190

Chapter 10. Cements for Low-Density Slurries and Weighted Cements. 191

10.1. Lightened Plugging Mixtures with Finely Ground Silica Additives. 197

10.2. Lightened Slag Slurries. 198

10.3. Weighted Cement Slurries. 200

10.4. Weighted Slag Slurries. 204

10.5. Aerated Cement Slurries. 204

Chapter 11. Cement Slurries Prepared with Concentrated Saline Solutions (Brines) 208

11.1. Dissolution of Saliferous Rocks in Plugging Mixtures. 209

11.2. Preparation of Salinized (Brine) Plugging Mixtures. 210

11.3. Effect of Salts on Pheological Properties of Plugging Mixtures. 212

11.4. Water Loss of Salinized (Brine) Plugging Mixtures. 213

11.5. Adhesion of Cement Stone to Salts. 214

11.6. Corrosion of Plugging Cement Stone. 214

11.7. Features Specific to Cementing of Wells in Permafrost Areas. 215

Chapter 12. Plugging Materials for Controlling Loss of Circulation. 219

12.1. Plugging Mixtures for Controlling Loss of Circulation in Drilling. 220

12.2. Quick-Setting Mixtures. 221

12.3. Gel-Cements. 223

12.4. Features Specific to the Setting of Quick-Taking Plugging Mixtures. Selection of Mixtures for Concrete Conditions. 223

Chapter 13. Special Plugging Cements and Mixtures. 225

13.1. Corrosion-Proof Plugging Cements. 225

13.2. Expanding Plugging Cements. 230

13.3. Gypsum as a Plugging Material. 231

13.4. Hydrophobic Cements. 233

13.5. Oil-Cement Slurries. 233

13.6. Organic and Organic-Mineral Materials for Cementing Wells. 235

Chapter 14. Facilities and Structures for Transporting, Mixing, and Storage of Plugging Materials. 248

14.1. Plugging Cement Storage Regulations.252

14.2. Arrangement, Operating Principle, and Technical Data of Railwayside Mechanized Plugging Cement Store. 254

14.3. GROZNEFT Installation for Preparing Dry Plugging Mixtures. 258

14.4. KRASNODARNEFTEGAZ Installation for Preparing Plugging Mixtures. 259

14.5. Laboratory Control over Plugging Materials. 260

Chapter 15. Organization of Cementing Jobs. Complications and Safety Engineering in Cementing of Wells. 268

15.1. Organization of Cementing Jobs 268

15.2. Complications in Cementing of Wells. 272

15.3. Accident Prevention in Handling Free-Flowing and Dusty Materials. 278

15.4. Accident Prevention in Cementing Jobs. 280

15.5. Safety in Handling Radioactive Isotopes. 282

15.6. Safety Regulations to be Observed when Working in Gaseous Environment and Handling Chemicals.283

15.7. Safety Regulations to be Observed when Working in Winter Time. 283

15.8. General Safety Rules. 284

Chapter 16. Cementing Quality Check. 285

Index 292

]]>**About the book**

This study aid follows the course on linear algebra with elementary analytic geometry and is intended for technical school students specializing in applied mathematics. The text deals with the elements of analytic geometry, the theory of matrices and determinants, systems of linear equations, vectors, and Euclidean spaces. The material is presented in an informal manner. Many interesting examples will help the reader to grasp the material easily.

The book was translated from the Russian by Tamara Baranovskaya and was published by Mir in 1990.

Original colour scan by Folkscanomy Mathematics.

**CONTENTS**

Preface 8

Part One. ANALYTIC GEOMETRY 10

Chapter 1. VECTORS IN THE PLANE AND IN SPACE. CARTESI AN COORDINATE SYSTEM 10

1.1. Vectors 10

1.2. Vector Basis in the Plane and in Space 20

1.3. Cartesian Coordinate System on a Straight Line, in the Plane, and in Space 28

Exercises to Chapter 1 35

Chapter 2. RECTANGULAR CARTESIAN COORDINATES. SIMPLE PROBLEMS IN ANALYTIC GEOMETRY 37

2.1. Projection of a Vector on an Axis 37

2.2. Rectangular Cartesian Coordinate System 40

2.3. Scalar Product of Vectors 47

2.4. Polar Coordinates 54

Exercises to Chapter 2 55

Chapter 3. DETERMINANTS 57

3.1. Second-Order Determinants. Cramer’s Rule 57

3.2. Third-Order Determinants 60

3.3. n-th-Order Determinants 62

3.4. Transposition of a Determinant 67

3.5. Expansion of a Determinant by Rows and Columns 69

3.6. Properties of nth-Order Determinants 71

3.7. Minors. Evaluation of nth-Order Determinants 77

3.8. Cramer’s Rule for an n x n System 82

3.9. A Homogeneous n x n System 86

3.10. A Condition for a Determinant to Be Zero 91

Exercises to Chapter 3 95

Chapter 4. THE EQUATION OF A LINE IN THE PLANE. A STRAIGHT LINE IN THE PLANE 100

4.1. The Equation of a Line 100

4.2. Parametric Equations of a Line 105

4.3. A Straight Line in the Plane and Its Equation 107

4.4. Relative Position of Two Straight Lines in the Plane 122

4.5. Parametric Equations of a Straight Line 124

4.6. Distance Between a Point and a Straight Line 125

4.7. Half-Planes Defined by a Straight Line 127

Exercises to Chapter 4 128

Chapter 5. CONIC SECTIONS 131

5.1. The Ellipse 131

5.2. The Hyperbola 140

5.3. The Parabola 148

Exercises to Chapter 5 153

Chapter 6. THE PLANE IN SPACE 156

6.1. The Equation of a Surface in Space. The Equation of a Plane 156

6.2. Special Forms of the Equation of a Plane 163

6.3. Distance Between a Point and a Plane. Angle Between Two Planes 168

6.4. Half-Spaces 169 Exercises to Chapter 6 171

Chapter 7. A STRAIGHT LINE IN SPACE 174

7.1. Equations of a Line in Space. Equations ofa Straight Line 174

7.2. General Equations of a Straight Line 178

7.3. Relative Position of Two Straight Lines 183

7.4. Relative Position of a Straight Line anda Plane 186

Exercises to Chapter 7 189

Chapter 8. QUADRIC SURFACES 192

8.1. The Ellipsoid 192

8.2. The Hyperboloid 195

8.3. The Paraboloid 198

Part Two. LINEAR ALGEBRA 202

Chapter 9. SYSTEMS OF LINEAR EQUATIONS 203

9.1. Elementary Transformations of a System of Linear Equations 203

9.2. Gaussian Elimination 205

Exercises to Chapter 9 216

Chapter 10. VECTOR SPACES 218

10.1. Arithmetic Vectors and Operations with Them 218

10.2. Linear Dependence of Vectors 222

10.3. Properties of Linear Dependence 227

10.4. Bases in Space R^n 230

10.5. Abstract Vector Spaces 233

Exercises to Chapter 10 239

Chapter 11. MATRICES 241

11.1. Rank of a Matrix 242

11.2. Practical Method for Finding the Rank of a Matrix 245

11.3. Theorem on the Rank of a Matrix 247

11.4. Rank of a Matrix and Systems of Linear Equations 249

11.5. Operations with Matrices 250

11.6. Properties of Matrix Multiplication 253

11.7. Inverse of a Matrix 255

11.8. Systems of Linear Equations in Matrix Form 259

Exercises to Chapter 11 263

Chapter 12. EUCLIDEAN VECTOR SPACES 266

12.1. Scalar Product. Euclidean Vector Spaces 266

12.2. Simple Metric Concepts in Euclidean Vector Spaces 269

12.3. Orthogonal System of Vectors. Orthogonal Basis 271

12.4. Orthonormal Basis 274

Exercises to Chapter 12 275

Chapter 13. AFFINE SPACES. CONVEX SETS AND POLYHEDRONS 277

13.1. The Affine Space A^n 277

13.2. Simple Geometric Figures in A^n 279

13.3. Convex Sets of Points in A^n. Convex Polyhedrons 282

Exercises to Chapter 13 286

Index 288

]]>

About the book

The aim of the present collection of problems is to illustrate the theory of partial differential equations as it is given in various textbooks.

The problems of this collection are divided in three paragraphs. The first paragraph contains introductory excercizes on the reduction of partial differential equations to canonical form. The second paragraph deals mainly with problems, the general solution of which can be formed by means of the method of characteristics e.g. Cauchy’s (or also Goursat’s) and mixed problems.In the third paragraph the most important method is presented, namely the separation of variables. This is done for mixed problems (for hyperbolic and parabolic equations) and for boundary value problems (elliptic equations).

The solutions of all excercizes are given. Most of the problems are accompanied by an explanation of the solution method used: so that this problem book can also be used for self study.

The book was published by Nordoff in 1967 and was translated from the Russian by W. I. M. Wils.

CONTENTS

**Part I. Problems 7**

**1. Reduction of partial differential equations with two independent variables to canonical form 7**

1. Equations of hyperbolic type 7

2. Equations of parabolic type 8

3. Equations of elliptic type 8

**2. The method of characteristics 9**

**3. Separation of variables 23**

1. Equations of hyperbolic type 26

2. Equations of parabolic type 33

3. Equations of elliptic type 38

**Part.II. Solutions and hints 43**

About the book

The book is a collection of folk tales from the Baltic region. The Soviet Baltic republics, Latvia, Lithuania and Lstonia, are closely bound up with the sea. And the people who live there are what you would expect sea tolk to be, tall, tough and strong. This is a land of fishermen, ship-builders and farmers. Lach republic also has a highly developed industry. The radios, transmitters, etc. made in Latvia and Estonia are known throughout the world.

Baltic folk tales have absorbed much of the world around them, of course. They seem to smell of dry wood, resin, sea and forest. Many of the characters in the old songs and legends resemble the people of today who live in these parts: the wise fishermen, the skilled craftsmen, the sturdy, brave young men and the gentle, faithful women. The forces of evil in these stories take the form of terrible monsters, catastrophies and disasters which the heroes have to combat and overcome.

The book was translated from the Russian by and was published by Raduga in 1986.

The book has some amazing full page paintings, done by three different artists one for each set of the tales: Gunars Krollis for Lativia, Jaan Tammsaar for Estonia and Vange Gedmantaitc-Galkuviene for Lithuania. The book was designed by Mikhail Anikst.

Contents

LATVIAN FOLK TALES

The White Deer 6

The Sea Bride 26

ESTONIAN FOLK TALES

The King of the Mushrooms 48

The Forbidden Knot 72

LITHUANIAN FOLK TALE

The Sun Princess and the Prince 96

A book covering various aspects of strength of materials. The topics covered are succinct and with basic definitions and requisite mathematics. Each chapter has a set of “Check Questions” in the end.

The development of the foundations for the design of structural members is the subject matter of a science called the strength of materials.

Without knowledge of the fundamentals of strength of materials it is impossible to construct even a simple machine satisfying the technical requirements placed on each construction.

The book was translated from the Russian by *M. Konyaeva* and was published by Mir in 1978 (second print).

Many thanks to *Akbar Azimi* for the raw scans.

Contents

Introduction. 13

1. Science of Strength of Materials. Concepts of Deformation and of an Elastic Body 13

2. Classification of External Forces 16

3. Basic Types of Deformation 17

4. Method of Sections. Stress 19

5. Check Questions 22

Chapter II. Tension and Compression 23

6. Longitudinal Strain. Stress. Hooke’s Law 23

7. Lateral Strain in Tension and Compression 27

8. Experimental Study of Materials in Tension 29

9. Tension Test Diagram and Its Characteristic Points 31

10. Strain Hardening 38

11. Strain Energy in Tension 40

12. Compression Testing 42

13. Harness 43

14. Check Questions 45

Chapter III. Strength Design for Tension and Compression 47

15. Allowable Stress and Selection of Sections 47

16. Effect of Gravity in Tension and Compression 54

17. Stepped Rod 57

18 Statically Indeterminate Problems in Tension and Compression 60

19. Stresses Due to Temperature Changes 65

20. Design of Statically Indeterminate Systems Based on Allowable Loads, and Limit Design 68

21. Check Questions 74

Chapter IV. Combined Stresses

22. Stresses on Inclined Sections Under Axial Tension or Compression

23. Concept of Principal Stresses

24. Stresses on Inclined Sections Under Tension (Compression) in Two Mutually Perpendicular Directions 79

25. Determination of Principal Stresses 81

26. Strains Under Tension or Compression in Two Mutually Perpendicular Directions. Strain Energy 84

27. Strength Theories 87

28. Design of Thin-Walled Vessels 94

29. Check Questions 98

Chapter V. Shear 99

30. Concept of Shear. Stresses in Shear. Hooke’s Law in Shear 99

31. Pure Shear in a Rod Subjected to Tension and Compression in Two Mutually Perpendicular D irections 101

32. Relation Between Moduli of Elasticity E and G 102

33. Allowable Stress in Shear 104

34. Crushing 106

35. Examples of Design for Shear andCrushing. 107

36. Design of Welded Joints 111

37. Check Questions. 114

Chapter VI. Torsion 116

38. Construction of Twisting Moment Diagrams. Relation Between Torque. Power and Number of Revolutions 116

39. Determination of Stresses and Strains in a Circular Bar Subjected to Torsion 121

40. Polar Moment of Inertia and Section Modulus of a Circle and a Circular Ring 126

41. Design Equations in Torsion 128

42. Elements of Design of Bars of Rectangular Section for Torsional Loads 136

43. Potential Energy in Torsion 139

44. Design of Closely Coiled Helical Springs 140

45. Design of Shafts Based on Allowable Loads 142

46. Check Questions 144

Chapter VII. Static Moments, Centroids and Moments of Inertia of Plane Figures 145

47. Static Moments of Plane Figures 145

48. Moments of Inertia of Plane Figures 148

49. Transformation Formulas for Moments of Inertia in the Case of Parallel Transfer of Axes 149

50. Moments of Inertia of Some Simple Figures 151

51. Determination of Moments of Inertia of Figures Composed of Simple Figures 155

52. Transformation Formulas for Moments of Inertia in the Case of Rotation of Axes 157

53. Concept of Principal Axes of Inertia and Determination of Their Position 160

54. Determination of Principal Moments of Inertia 163

55. Check Questions 167

Chapter VIII. Bending of a Straight Rod, Bending Moment and Shearing Force 168

56. General Considerations 168

57 Supports and Reactions at Supports of Beams 171

58. Determination of Reactions at Supports of Beam 173

59 Shearing Force and Bending Moment 176

60. Relations Between Load Intensity, Shearing Force and Bending Moment 178

61. Construction of Bending Moment and Shearing Force Diagram? 179

62. Check Questions 197

Chapter IX. Stresses in Bending and Design of Beams for Strength 198

63. Determination of Normal Stresses in Bending 198

64. Section Moduli for Common Sections 198

65. Design Flexure Formulas. Examples of Designing Beams 204

66. Shearing Stresses in a Beam of Rectangular Section. Jourawski’s Formula 211

67. Shearing Stresses in an I-Beam 216

68. Verification of the Strength of a Beam on the Basis of Principal Stresses 218

69. Design of Beams Based on Allowable Loads, and Limit Design 221

70. Check Questions 224

Chapter X The Elastic Curve of a Beam 226

71. The Elastic Curve of a Beam 226

72 Derivation of the Generalized Equation of the Elastic Curve 230

73. Special Cases of Determining Displacements of Beams from the Generalized Equation of the Elastic Curve 233

74. Mohr’s Method and Vereshchagin’s Rule 241

75. Beams of Uniform Resistance to Bending 246

76. Check Questions 252

Chapter XI. Statically Indeterminate Beams 253

77. Concept of Statically Indeterminate Beams 253

78. A Beam Fixed at One End and Simply Supported at the Other 253

79. A Beam with Both Ends Fixed 259

80. A Beam on Three Supports 263

81. Check Questions 268

Chapter XII Complex Resistance 269

82. Oblique Bending 269

83. Bending Combined with Tension or Compression 276

84. Eccentric Compression 278

85. The General Case of Eccentric Compression or Tension. 279

86. Concept of Core of Section. 282

87. Combined Bending and Torsion. 284

88. Combined Torsion and Tension or Compression 290

89. Check Questions 291

Chapter XIII. Buckling 292

90. Concept of Buckling. 292

91. Euler’s Formulas 294

92. Limitations of Euler’s Formulae able for Column Design 298

93. Examples of Design for Buckling Strength. 300

94. Check Questions. 306

Chapter XIV. Strength Under Dynamic and Repeated Loading 307

95. Concepts of Dynamic and Repeated Loading 307

97. The Stress and Strain in a Rod Subjected to Impact Loading 308

96. Design of a Uniformly 310

98. Impact Testing of Metals 313

99. Fatigue of Metals 314

100. Fatigue Testing of Materials 317

101. Endurance Limit for Fluctuating Stress Cycle 320

102. Effect of Overall Dimensions of Parts on Endurance Limit 321

103. Strength Design for Completely Reversed Stresses 323

104. Determination of Factor of Safety in the Case of Fluctuating Stresses 326

105. Construction of Approximate Fatigue Strength Diagram and Determination of Factor of Safety from It 328

106. Determination of Factor of Safety in the Case of Combined Varying 336 Stresses 336

107. Examples of Design for Varying Stresses 336

108. Improvement of Fatigue Strength 338

109. Check Questions 341

Appendices 343

Index 356

About the book

This book is designed to be used as an aid to solving elasticity problems in college and university courses in engineering.

The book covers all subjects of the mathematical theory of elasticity. It contains material which forms the basis for structural analysis and design. Numerous problems illustrate the text and somewhat complete it. Along with classical problems, they include cases of practical significance.

The author does not emphasize any particular procedure of solution, but instead considerable emphasis is placed on the solution of problems by the use of various methods. Most of the problems are worked out and those which are left as an exercise to the student are provided with answers or references to the original works.

**About the author**

Professor Vladimir Germanovich Rekach, D.Sc., is the Head of the Department of Strength of Materials at the Patrice Lumumba Peoples’ Friendship University in Moscow.

His main scientific interests are structural design, analysis of curved bars and vibration problems. The title of his doctoral thesis was “The Analysis of Spherical Shells”. He is the author of 28 articles and 3 books (3 as coauthor).

The book was translated from the Russian by *M. Konyaeva* and was published by Mir in 1979.

Many thanks to *Akbar Azimi* for the raw scans.

Note: There may be warping in some pages.

CONTENTS

Notation

Chapter 1 Theory of Stress 9

I. Static and Dynamic Equilibrium Equations. 9

II. Surface Conditions. 12

III. State of Stress at a Point Problems. 13

III. Cylindrical Co-ordinates. 15

IV. Spherical Co-ordinates.

Problems. 15

Chapter 2 Theory of Strain 24

I. Strain Equations in Orthogonal Co-ordinates 24

II. State of Strain at a Point 28

III. Cesaro’s Formulas 29

Problems 30

Chapter 3 Basic Equations of the Theory of Elasticity and Their Solution or Special Cases 40

I. Orthogonal Curvilinear Co-ordinates 40

II. Rectangular Co-ordinates 41

III. Cylindrical Co-ordinates 43

IV. Spherical Co-ordinates 44

Problems 46

Chapter 4 General Solutions of the Basic Equations of the Theory of Elasticity. Solution or Three-dimensional Problems 66

I. Harmonic Equation (Laplace’s ) 66

II. Biharmonic Equation 66

III. Boundary Value Problems for the Harmonic and Biharmonic Equations 72

IV. Various Forms of the General Solutions of Lame’s Equations 79

Problems 83

Chapter 5 Plane Problem in Rectangular Co-ordinates 106

I. Plane Stress 106

II. Plane Strain 108

III. Solutions of Basic Equations 109

Problems 119

Chapter 6 Plane Problem in Polar Co-ordinates. 151

I. Plane Stress 153

II. Plane Strain 153

III. Solution of Basic Equations 153

Problems 158

Chapter 7 Torsion of Prismatic and Cylindrical Bars 184

I. Pure Torsion of Bars of Constant Section 184

II. Pure Torsion of Circular Bars (Shafts) of Variable Section 187

Problems 194

Chapter 8 Thermal Problem 210

I. Steady-state Thermal Process 210

II. Transient Thermal Process 216

Problems 217

Chapter 9 Contact Problem. 236

I. The action of punches on an Elastic Half-plane 236

II. The Action of Punches on an Elastic Half-space 239

III. Contact Between Two Elastic Bodies 240

Problems 240

Chapter 10 Dynamic Problem. 267

I. Simple Harmonic Motion 267

II. Propagation of Volume Waves in an Elastic Isotropic Medium 269

III. Wave propagation over the surface of an elastic isotropic body 272

IV. Excitation of Elastic Waves by Body Forces 275

VI. Deformation of solids Under Centrifugal Forces 276

VI. Plane Dynamic Problems 277

VII. Thermodynamic Problem 281

Problems 283

References 302

Author Index 308

Subject Index 310

About the book (from the Preface)

In selecting the material and the order of presentation for this work I have been guided by the definition of electrochemistry, given by Kislyakovsky in 1912, as the science “concerned with the study of the phenomena accompanying the direct conversion of chemical energy into electrical and vice versa”. This definition was taken further by Pisarzhevsky, who was the first to formulate clearly the prerequisites for mutual conversion of chemical and electrical forms of energy and introduce the concept of electrochemical system in which this process is possible. Our presentation is based on the theory of electrochemical systems, their constituent parts and their possible states. It seems to me that these principles permit one to visualize electrochemistry as an integral whole and independent, self-contained discipline and clearly define the boundaries separatum it from closely related sciences.

Much attention is paid to disclosing the physical content of electrochemical phenomena and the essence of the related theoretical conceptions The mathematical apparatus is relatively simple, and only the general principles of electrochemical experiment are given. Experimental procedures are described in more detail only where it is necessary for the understanding of the nature of the process in question or the essence of the theoretical views concerned.

In writing this textbook I have tried to cover all the basic aspects of theoretical electrochemistry and to reflect as completely as possible the latest advances and trends in its development. I hope that this has been accomplished to some extent but though I have tried to be objective I have probably not avoided a certain preference what seemed to me more correct, and particularly more important and interesting. In this connection it would seem appropriate to recall Mendeleyev’s words in the preface to the fifth edition of his famous “Fundamentals of Chemistry”: – `in all objective expositions of science, there will always and inevitably be much that is subjective, bearing the stamp of the times and place… separate works, like a mirror, will reflect that which is near more clearly and strongly… although I have striven to make my book a true mirror—what is dear to me has involuntarily been reflected most sharply and illuminated more clearly, and presented, through the reflection, in all its pristine brightness’. The truth of these words has probably been felt by everyone who has tried to generalize the material of any science or branch of it.

The book was translated from the Russian by *Artavaz Beknararov*. And was published by Mir in 1972.

Many thanks to *Akbar Azimi* for original scans.

Some pages might have warping, but the book is readable.

**CONTENTS**

Principal Symbols

Introduction

**PART ONE EQUILIBRIUM IN ELECTROLYTE SOLUTIONS**

Chapter 1. Theory of Electrolytic Dissociation 33

Chapter 2. Theory of Ionic Interaction 45

Chapter 3. Solvation and Hydration of Ions 69

**PART TWO NONEQUILIBRIUM PHENOMENA IN ELECTROLYTIC SOLUTIONS**

Chapter 4. Electrical Conductance of Electrolytic Solutions 102

Chapter 5. Theoretical Interpretation of the Electrical Conductance of Electrolytes 123

Chapter 6. Diffusion in Electrolyte Solutions 142

**PART THREE ELECTRODE EQUILIBRIUM**

Chapter 7. Equilibrium Electrode Potential 155

Chapter 8. Electrochemical Systems 190

Chapter 9. The Mechanism of Buildup of Electromotive Force and the Nature of Electrode Potentials 209

**PART FOUR THE ELECTRICAL DOUBLE LAYER AT THE ELECTRODE-ELECTROLYTE INTERFACE**

Chapter 10. Electrokinetic and Electrocapillary Phenomena 243

Chapter 11. The Structure of the Electric Double Layer at the Electrode-Electrolyte Interface 282

**PART FIVE NONEQUILIBRIUM (IRREVERSIBLE) ELECTRODE PROCESSES**

Chapter 12. The Chemical Effect of Electric Current 297

Chapter 13. The Kinetics of Electrode Processes 308

Chapter 14. Concentration Polarization 317

Chapter 15. Phase Overpotential 343

Chapter 16. Electrochemical Overpotential 360

Chapter 17 Some Methods of Investigating Electrode Kinetics 388

Chapter 18 Polarography 395

**PART SIX THE KINETICS OF SOME ELECTRODE PROCESSES**

Chapter 19 The Hydrogen Evolution Reaction 411

Chapter 20 The Kinetics of the Oxygen Evolution Reaction 442

Chapter 21 The Kinetics of Electrochemical Reduction and Oxidation 452

Chapter 22 Electrodeposition of Metals from Solutions 477

Chapter 23 Electrochemical Dissolution and Passivity of Metals

Chapter 24 Electrochemical Corrosion of Metals 511

Chapter 25 Some Problems of Modern Electrochemistry 538

Bibliography 548

Name Index 551

Subject Index 555

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**About the book (From the Preface)**

The modern theory of nonlinear phenomena is going through a period of explosive growth. Each “invention” in the field is disseminated rapidly, generating general interest and unexpected applications. This was for instance the case with solitons, strange attractors, and stochasticity. That scientists from each of the different branches of the theory of nonlinear phenomena should cooperate needs no proof, and the value of this cooperation could be seen at a conference held in Kiev on nonlinear and turbulent processes in physics.* The same approach has been adopted for this collection, which includes articles on regular nonlinear phenomena (vortices, solitons, auto-waves) and some on stochasticity and turbulence. In addition, the collection includes two mathematical articles that develop the Kolmogorov-Amold-Moser theory, the importance of which for the theory of nonlinear dynamic systems is undoubted.

The articles are to some degree grouped around the nonlinear problems of plasma physics and hydrodynamics, in their broadest sense.

Hydrodynamics and plasma physics are traditional sources of exciting problems and ideas for the physics of nonlinear phenomena. We need only recall the classical examples of the discovery of solitons in shallow water, the exact integrability of the Korteweg-de Vries equation, and the discoveries of a strange attractor in the Lorcntz system and stochasticity in Hamiltonian systems with small numbers of degrees of freedom.

These ideas and results, all stimulated by problems in hydrodynamics and plasma physics, quickly gained more general significance for physics as a whole. In turn, many new and efficient techniques are tested on such traditionally difficult subjects as turbulence. For instance, there is the recent application to turbulence of the renormalization group methods, which were successfully employed first in field theory and the physics of phase transitions.

Finally, all this culminates in general fund of knowledge in the

physics of nonlinear phenomena. I hope that the publication of

this collection will advance the progress of physics.

The book was translated from the Russian by Valerii Ilyushchenko, and was first published by Mir in 1986.

Many thanks to *Akbar Azimi* for providing the raw 2-in-1 scans. We cleaned and OCRed the scans.

This book has an essay by A. Zhabotinsky of the Belousov–Zhabotinsky reaction

**Contents**

Preface 7

**Vortices In Plasma and Hydrodynamics by A.B. Mikhailovskii**

Introduction 8

Nonlinear Equations for Rossby Waves 12

The Simplest Nonlinear Equations for Drift Waves 14

Vector Vortical Structures 16

Scalar Vortical Structures 18

Further Development of Concepts Concerning Electrostatic Vortices in Plasma 19

Electromagnetic Vortices 22

Conclusion 24

References 28

**Oscillations and Bifurcations in Reversible Systems by V. I. Arnol’d and M. B. Sevryuk 31 **

Introduction 31

Reversible Mappings 32

Reversible Flows 33

Integrable Reversible Mappings and Vector Fields 34

Kolmogorov’s Tori 35

Weak Reversibility 37

The Local Theory 37

Weak Reversibility in a Local Situation 42

Periodic Solutions 42

Kolmogorov’s Tori for Additional “Even” Coordinates 44

The Local Theory for Additional “Even” Coordinates 45

Application to Reversible Equations 48

Kon-Autonomour Reversible Systems 49

The Lyapunov-Devaney Theorem 51

The Resonance 1:1 52

Further Resonances l:N (N > 2) 54

References 83

**Regular and Chaotic Dynamics of Particles In a Magnetic Field by R. Z. Sagdeev and C. U. Zaslavskii 85 **

Introduction 65

Equations of Motion 67

The Resonances of Longitudinal Motion 69

The Overlapping of the Resonances of Longitudinal Motion 72

A Kinetic Description 75

Equations of Transverse Motion 78

The Resonances of High-Energy Particles 83

Resonances in a Weak Magnetic Field 84

Generalization to a Wave Packet 85

A Kinetic Description of Transverse Motion 86

Quasi-Resonance Particles 88

References 92

**The Renormalization Group Method and Kolmogorov-Arnold-Moser Theory by K. M. Khanin and Ya. G. Sinai 93**

Introduction 93

Rectification of the Nonlinear Rotation of a Circle 97

Construction of Invariant KAM Curves by the Renormalization

Group Method 110

References 118

**Nonlinear Problems of Turbulent Dynamo by Ya B, Zel’dovich and A. A. Rukmalkin 119**

Introduction 119

Nonlinear Mean Field Dynamo 121

MHD Turbulence 130

References 135

Problems of the Theory of Strong Turbulence and Topological Solitons by R. Z. Sagdeev, S. S. Molseev, A. V. Tur, and V. V. Yanovskii 137

Introduction 137

The Scaling Group and Functional Method 140

“Null-Modes” and the Self-Similar Spectrum 152

Invariant Properties of Hydrodynamic Models and Topological Solitons 163

References 180

Self-Oscillations and Auto-Waves in Chemical Systems by A. M. Zhabotinskii 183

Introduction 183

Experimental Studies 184

Theoretical Studies 195

Conclusion 207

References 208

Auto-Waves In Biologically Active Media by V. I. Krinskii 210

Introduction 210

Mathematical Description 211

Local Sources of Auto-Waves 213

Cardiac Disorders 215

Mathematical Simulation of Auto-Wave Sources 216

A Chemically Active Medium 216

New Auto-Wave Modes 217

Wave Sources in Three-Dimensional Active Media 217

The Effect of Medium Parameters on Auto-Wave Sources 218

An Anomalous Reverberator 219

Theoretical Studies of Reverberators 220

About the book

We may distinguish at least the following live sufficiently independent categories of vibratory processes differing in their nature:

free vibrations, i.e., vibrations which are performed by a mechanical system having no energy supply from outside if the system is disturbed from its position of equilibrium and then released;

critical states of rotating shafts and rotors which consist in a sudden increase in the deflections of their axes at definite speeds of rotation (or in definite ranges of speeds);

forced vibrations which result when the mechanical system is acted on by fluctuating external forces (driving forces);

parametric vibrations caused by periodic variations of the para meters of a system (for example, its stiffness);

self-excited vibrations, i.e., vibratory processes which are maintained by constant sources of energy of a non-vibratory nature.

Each of these categories of vibratory processes is discussed in the appropriate chapter.

The book was translated from the Russian by M. Konyaeva and was published by Mir in 1971.

Many thanks to *Akbar Azimi* for providing the raw scan 2-in-1 page scans. We cleaned the book with OCR.

**Contents**

Notation. 7

Introduction. 9

**CHAPTER I. FUNDAMENTALS. 11 **

1. Number of Degrees of Freedom of an Elastic System. 11

2. Classification of Forces. 15

3. Methods for Setting Up Equations of Motion in the General Case. 22

**CHAPTER II. Free vibrations . 24 **

4. Linear Systems of One Degree of Freedom Without Inelastic Resistances. 24

5. Effect of Inelastic Resisting Forces on Free Vibrations

of Linear Systems of One Degree of Freedom. 56

6. Undamped Systems of One Degree of Freedom with Non-Linear Restoring Forces. 68

7. Linear Systems of Several Degrees of Freedom. 87

8. Vibrations of Bars of Uniform Section (Exact Solution) 118

9. Vibrations of Ban of Variable Section. 138

10. Two-Dimensional Vibrations of Disks. 147

11. Flexural Vibrations of Disks. 153

12. Flexural Vibrations of Rectangular Plates. 157

**CHAPTER III. CRITICAL STATES OF ROTATING SHAFTS AND ROTORS 161 **

13. Shaft with One Disk. 161

14. Effect of Friction. 174

15. Automatic Balancing of Rotating Shafts. 185

16. Critical States of Helicopter Rotors. 187

17. Shalt with Several Disks. Rigid Rotor on Elastic Supports 190

**CHAPTER IV. FORCED VIBRATIONS. 193 **

18. Linear Systems of One Degree of Freedom without Inelastic Resistances. 193

19. Linear Systems of One Degree of Freedom with Inelastic Resisting Forces. 226

20. Systems with Non-Linear Restoring Forces (Single Degree of Freedom). 241

21. Linear Systems of Several Degrees of Freedom. 249

22. Linear Systems with Distributed Parameters. 269

**CHAPTER V. PARAMETRIC VIBRATIONS. 279 **

23. Basic Equation. 279

24. Cases of Periodic Variation of Stiffness. 283

25. Cases of Periodic Variation of Parametric Loads. 285

26. Pendulum with a Vibrating Point of Suspension. 288

27. Cases of Periodic Variation of the Inertia of a System. 289

**CHAPTER VI. SELF-EXCITED FRICTIONAL VIBRATIONS. 293**

28. Nature of Self-Excited Vibrations. 293

29. Self-Excited Vibrations of Quasi-Linear Systems. 298

30. Self-Excited Relaxation Vibrations. 304

Index. 314

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