Classical mechanics Books

Book SynopsisThis comprehensive volume presents a unified framework of continuum theories. It indicates that (i) microcontinuum theories (micromorphic and micropolar theories) are natural extension of classical continuum mechanics, and (ii) classical continuum mechanics is a special case of microcontinuum theories when the deformable material point is idealized as a single mathematical point. The kinematics and basic laws are rigorously derived. Based on axiomatic approach, constitutive theory is systematically derived for various kinds of materials, ranging from Stokesian fluid to thermo-visco-elastic-plastic solid. Material force and Thermomechanical-electromagnetic coupling are introduced and discussed. Moreover, general finite element methods for large-strain thermomechanical coupling physical phenomena are systematically formulated. Also, non-classical continuum theories (Nonlocal Theory, Mechanobiology, 4D printing, Poromechanics, and Non-Self-Similar Crack Propagation) are rigorously formulated with applications and demonstrated numerically.As an advanced monograph, this unique compendium can also be used as a textbook for several graduate courses, including continuum mechanics, finite element methods, and advanced engineering science theories. Extensive problems are provided to help students to better understand the topics covered.

Read more less

Book SynopsisThis book addresses the hydrostatics and stability of ships and other floating marine structures - a fundamental aspect of naval architecture and offshore engineering for naval architects and marine engineers. It starts from the most basic concepts, assuming that the reader has no prior knowledge of the subject. By presenting the topic in a methodical and step-by-step manner, the book helps students to enhance their understanding, while also providing valuable guidelines for lecturers teaching related courses.Table of ContentsBasic Ship Geometry.- Basic Hydrostatics.- Moments and Centroids.- Numerical Integration Methods.- Trim and Longitudinal Stability.- Statical Stability at Small Heels Angles.- Statical Stability at Large Heel Angles.- Dynamical Stability.- Intact Stability Criteria.- Damage Stability and Watertight Subdivision.

Read more less

Book Synopsis1. Mathematical Introduction.- 1.1. Linear Vector Spaces: Basics.- 1.2. Inner Product Spaces.- 1.3. Dual Spaces and the Dirac Notation.- 1.4. Subspaces.- 1.5. Linear Operators.- 1.6. Matrix Elements of Linear Operators.- 1.7. Active and Passive Transformations.- 1.8. The Eigenvalue Problem.- 1.9. Functions of Operators and Related Concepts.- 1.10. Generalization to Infinite Dimensions.- 2. Review of Classical Mechanics.- 2.1. The Principle of Least Action and Lagrangian Mechanics.- 2.2. The Electromagnetic Lagrangian.- 2.3. The Two-Body Problem.- 2.4. How Smart Is a Particle?.- 2.5. The Hamiltonian Formalism.- 2.6. The Electromagnetic Force in the Hamiltonian Scheme.- 2.7. Cyclic Coordinates, Poisson Brackets, and Canonical Transformations.- 2.8. Symmetries and Their Consequences.- 3. All Is Not Well with Classical Mechanics.- 3.1. Particles and Waves in Classical Physics.- 3.2. An Experiment with Waves and Particles (Classical).- 3.3. The Double-Slit Experiment with Light.- 3.4. Matter Waves (de Broglie Waves).- 3.5. Conclusions.- 4. The Postulatesa General Discussion.- 4.1. The Postulates.- 4.2. Discussion of Postulates I -III.- 4.3. The Schrödinger Equation (Dotting Your i's and Crossing your ?'s).- 5. Simple Problems in One Dimension.- 5.1. The Free Particle.- 5.2. The Particle in a Box.- 5.3. The Continuity Equation for Probability.- 5.4. The Single-Step Potential: a Problem in Scattering.- 5.5. The Double-Slit Experiment.- 5.6. Some Theorems.- 6. The Classical Limit.- 7. The Harmonic Oscillator.- 7.1. Why Study the Harmonic Oscillator?.- 7.2. Review of the Classical Oscillator.- 7.3. Quantization of the Oscillator (Coordinate Basis).- 7.4. The Oscillator in the Energy Basis.- 7.5. Passage from the Energy Basis to the X Basis.- 8. The Path Integral Formulation of Quantum Theory.- 8.1. The Path Integral Recipe.- 8.2. Analysis of the Recipe.- 8.3. An Approximation to U(t) for the Free Particle.- 8.4. Path Integral Evaluation of the Free-Particle Propagator.- 8.5. Equivalence to the Schrödinger Equation.- 8.6. Potentials of the Form V=a + bx + cx2 + d? + ex?.- 9. The Heisenberg Uncertainty Relations.- 9.1. Introduction.- 9.2. Derivation of the Uncertainty Relations.- 9.3. The Minimum Uncertainty Packet.- 9.4. Applications of the Uncertainty Principle.- 9.5. The Energy-Time Uncertainty Relation.- 10. Systems with N Degrees of Freedom.- 10.1. N Particles in One Dimension.- 10.2. More Particles in More Dimensions.- 10.3. Identical Particles.- 11. Symmetries and Their Consequences.- 11.1. Overview.- 11.2. Translational Invariance in Quantum Theory.- 11.3. Time Translational Invariance.- 11.4. Parity Invariance.- 11.5. Time-Reversal Symmetry.- 12. Rotational Invariance and Angular Momentum.- 12.1. Translations in Two Dimensions.- 12.2. Rotations in Two Dimensions.- 12.3. The Eigenvalue Problem of Lz.- 12.4. Angular Momentum in Three Dimensions.- 12.5. The Eigenvalue Problem of L2 and Lz.- 12.6. Solution of Rotationally Invariant Problems.- 13. TheHydrogen Atom.- 13.1. The Eigenvalue Problem.- 13.2. The Degeneracy of the Hydrogen Spectrum.- 13.3. Numerical Estimates and Comparison with Experiment.- 13.4. Multielectron Atoms and the Periodic Table.- 14. Spin.- 14.1. Introduction.- 14.2. What is the Nature of Spin?.- 14.3. Kinematics of Spin.- 14.4. Spin Dynamics.- 14.5. Return of Orbital Degrees of Freedom.- 15. Addition of Angular Momenta.- 15.1. A Simple Example.- 15.2. The General Problem.- 15.3. Irreducible Tensor Operators.- 15.4. Explanation of Some Accidental Degeneracies.- 16. Variational and WKB Methods.- 16.1. The Variational Method.- 16.2. The Wentzel-Kramers-Brillouin Method.- 17. Time-Independent Perturbation Theory.- 17.1. The Formalism.- 17.2. Some Examples.- 17.3. Degenerate Perturbation Theory.- 18. Time-Dependent Perturbation Theory.- 18.1. The Problem.- 18.2. First-Order Perturbation Theory.- 18.3. Higher Orders in Perturbation Theory.- 18.4. A General Discussion of Electromagnetic Interactions.- 18.5. Interaction of Atoms with Electromagnetic Radiation.- 19. Scattering Theory.- 19.1. Introduction.- 19.2. Recapitulation of One-Dimensional Scattering and Overview.- 19.3. The Born Approximation (Time-Dependent Description).- 19.4. Born Again (The Time-Independent Approximation).- 19.5. The Partial Wave Expansion.- 19.6. Two-Particle Scattering.- 20. The Dirac Equation.- 20.1. The Free-Particle Dirac Equation.- 20.2. Electromagnetic Interaction of the Dirac Particle.- 20.3. More on Relativistic Quantum Mechanics.- 21. Path IntegralsII.- 21.1. Derivation of the Path Integral.- 21.2. Imaginary Time Formalism.- 21.3. Spin and Fermion Path Integrals.- 21.4. Summary.- A.l. Matrix Inversion.- A.2. Gaussian Integrals.- A.3. Complex Numbers.Trade Review`An excellent text....The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succint manner.' - American Scientist, from a review of the First EditionTable of ContentsMathematical Introduction.- Review of Classical Mechanics.- All Is Not Well With Classical Mechanics. The Postulates-A General Discussion.- Simple Problems in One Dimension.- The Classical Limit.- The Harmonic Oscillator.- The Path Integral Formulation of Quantum Theory.- The Heisenberg Uncertainty Relations.- Systems with N Degrees of Freedom.- Symmetries and Their Consequences.- Rotational Invariance and Angular Momentum.- The Hydrogen Atom.- Spin.- Addition of Angular Momenta.- Variational and WKB Methods.- Time-Independent Perturbation Theory.- Time-Dependent Perturbation Theory.- Scattering Theory.- The Dirac Equation.- Path Integrals-II.- Appendix.- Answers to Selected Exercises.- Table of Constants.- Index

Read more less

Book SynopsisThe main theme of this highly successful book is that the transmission of energy by wave propogation is fundamental to almost every branch of physics. Therefore, besides giving students a thorough grounding in the theory of waves and vibrations, the book also demonstrates the pattern and unity of a large part of physics. This new edition has been thoroughly revised and has been redeisgned to meet the best contemporary standards. It includes new material on electron waves in solids using the Kronig-Penney model to show how their allowed energies are limited to Brillouin zones, The role of phonons is also discussed. An Optical Transform is used to demonstrate the modern method of lens testing. In the last two chapters the sections on chaos and solitons have been reduced but their essential contents remain. As with earlier editions, the book has a large number of problems together with hints on how to solve them. The Physics of Vibrations and Waves, 6th Edition will proveTrade Review"This is an excellent textbook, full of interesting material clearly explained, and fully worthy of being studied by future contributors ..." (Journal of Sound and Vibration: 293, July 2006)Table of ContentsIntroduction to First Edition. Introduction to Second Edition. Introduction to Third Edition. Introduction to Fourth Edition. Introduction to Fifth Edition. Introduction to Sixth Edition. 1. Simple Harmonic Motion. 2. Damped Simple Harmonic Motion. 3. The Forced Oscillator. 4. Coupled Oscillations. 5. Transverse Wave Motion. 6. Longitudinal Waves. 7. Waves on Transmission Lines. 8. Electromagnetic Waves. 9. Waves in More than One Dimension. 10. Fourier Methods. 11. Waves in Optical Systems. 12. Interference and Diffraction. 13. Wave Mechanics. 14 Non-linear Oscillations and Chaos. 15 Non-linear Waves, Shocks and Solitons. Appendix 1: Normal Modes, Phase Space and Statistical Physics. Appendix 2: Kirchhoff’s Integral Theorem. Appendix 3: Non-Linear Schrödinger Equation. Index.

Read more less

Book SynopsisThis unique volume introduces the reader to the mathematical language for complex systems and is ideal for students who are starting out in the study of stochastical dynamical systems. Unlike other books in the field, it covers a broad array of stochastic and statistical methods.Table of ContentsFrom the Contents: Stochastic Processes and Complex Systems/ Random Variables/ Analysis of Stationary Data/ Deduction of Models from Data/ Classification Methods/ Basic Equations for Stochastic Processes/ Master Equations/ Numerical Methods for the Solution of Master Equations/ Stochastic Differential Equations: Analytical Procedures/ Numerical Methods for Stochastic Differential Equations/ Functional Integrals in Stochastics/ Perturbation Theory and Approximations that Go Further/ Time Series/ Linear Models for Stochastic Processes

Read more less

Book SynopsisFriction and Wear of Materials Second Edition Written by one of the world''s foremost authorities on friction, this classic book offers a lucid presentation of the theory of mechanical surface interactions as it applies to friction, wear, adhesion, and boundary lubrication. To aid engineers in design decisions, Friction and Wear of Materials evaluates the properties of materials which, under specified conditions, cause one material to function better as a bearing material than another. Featured also are thorough treatments of lubricants and the sizes and shapes of wear particles. This updated Second Edition includes new material on erosive wear, impact wear, and friction. Professor Rabinowicz''s book will be especially welcomed by mechanical and design engineers, surface scientists, tribologists and others who design, produce and operate products, machines and equipment which involve friction and its effects.Table of ContentsMaterial Properties That Influence Surface Interactions. Surface Interactions. Friction. Types of Wear. Adhesive Wear. Abrasive and Other Types of Wear. Lubrication. Adhesion. Appendix. Sample Problems. Index.

Read more less

Book Synopsis

Read more less

Book SynopsisA concise introductory course text on continuum mechanics Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours.Trade Review“Motivated students will benefit from this systematic, disciplined and concise treatment of the fundamentals of continuum mechanics. Many practitioners will also appreciate the logical organization, and the lucid descriptions of such matters as the distinctions between the various common stress and strain measures.” (Pure and Applied Geophysics, 1 November 2015) Table of ContentsPreface xiii Nomenclature xv Introduction 1 Part One Mathematical Preliminaries 3 1 Vectors 5 1.1 Examples 9 1.1.1 9 1.1.2 9 Exercises 9 Reference 11 2 Tensors 13 2.1 Inverse 15 2.2 Orthogonal Tensor 16 2.3 Principal Values 16 2.4 Nth-Order Tensors 18 2.5 Examples 18 2.5.1 18 2.5.2 18 Exercises 19 3 Cartesian Coordinates 21 3.1 Base Vectors 21 3.2 Summation Convention 23 3.3 Tensor Components 24 3.4 Dyads 25 3.5 Tensor and Scalar Products 27 3.6 Examples 29 3.6.1 29 3.6.2 29 3.6.3 29 Exercises 30 Reference 30 4 Vector (Cross) Product 31 4.1 Properties of the Cross Product 32 4.2 Triple Scalar Product 33 4.3 Triple Vector Product 33 4.4 Applications of the Cross Product 34 4.4.1 Velocity due to Rigid Body Rotation 34 4.4.2 Moment of a Force P about O 35 4.5 Non-orthonormal Basis 36 4.6 Example 37 Exercises 37 5 Determinants 41 5.1 Cofactor 42 5.2 Inverse 43 5.3 Example 44 Exercises 44 6 Change of Orthonormal Basis 47 6.1 Change of Vector Components 48 6.2 Definition of a Vector 50 6.3 Change of Tensor Components 50 6.4 Isotropic Tensors 51 6.5 Example 52 Exercises 53 Reference 56 7 Principal Values and Principal Directions 57 7.1 Example 59 Exercises 60 8 Gradient 63 8.1 Example: Cylindrical Coordinates 66 Exercises 67 Part Two Stress 69 9 Traction and Stress Tensor 71 9.1 Types of Forces 71 9.2 Traction on Different Surfaces 73 9.3 Traction on an Arbitrary Plane (Cauchy Tetrahedron) 75 9.4 Symmetry of the Stress Tensor 76 Exercise 77 Reference 77 10 Principal Values of Stress 79 10.1 Deviatoric Stress 80 10.2 Example 81 Exercises 82 11 Stationary Values of Shear Traction 83 11.1 Example: Mohr–Coulomb Failure Condition 86 Exercises 88 12 Mohr’s Circle 89 Exercises 93 Reference 93 Part Three Motion and Deformation 95 13 Current and Reference Configurations 97 13.1 Example 102 Exercises 103 14 Rate of Deformation 105 14.1 Velocity Gradients 105 14.2 Meaning of D 106 14.3 Meaning of W 108 Exercises 109 15 Geometric Measures of Deformation 111 15.1 Deformation Gradient 111 15.2 Change in Length of Lines 112 15.3 Change in Angles 113 15.4 Change in Area 114 15.5 Change in Volume 115 15.6 Polar Decomposition 116 15.7 Example 118 Exercises 118 References 120 16 Strain Tensors 121 16.1 Material Strain Tensors 121 16.2 Spatial Strain Measures 123 16.3 Relations Between D and Rates of EG and U 124 16.3.1 Relation Between Ė and D 124 16.3.2 Relation Between D and U 125 Exercises 126 References 128 17 Linearized Displacement Gradients 129 17.1 Linearized Geometric Measures 130 17.1.1 Stretch in Direction N 130 17.1.2 Angle Change 131 17.1.3 Volume Change 131 17.2 Linearized Polar Decomposition 132 17.3 Small-Strain Compatibility 133 Exercises 135 Reference 135 Part Four Balance of Mass, Momentum, and Energy 137 18 Transformation of Integrals 139 Exercises 142 References 143 19 Conservation of Mass 145 19.1 Reynolds’ Transport Theorem 148 19.2 Derivative of an Integral over a Time-Dependent Region 149 19.3 Example: Mass Conservation for a Mixture 150 Exercises 151 20 Conservation of Momentum 153 20.1 Momentum Balance in the Current State 153 20.1.1 Linear Momentum 153 20.1.2 Angular Momentum 154 20.2 Momentum Balance in the Reference State 155 20.2.1 Linear Momentum 156 20.2.2 Angular Momentum 157 20.3 Momentum Balance for a Mixture 158 Exercises 159 21 Conservation of Energy 161 21.1 Work-Conjugate Stresses 163 Exercises 165 Part Five Ideal Constitutive Relations 167 22 Fluids 169 22.1 Ideal Frictionless Fluid 169 22.2 Linearly Viscous Fluid 171 22.2.1 Non-steady Flow 173 Exercises 175 Reference 176 23 Elasticity 177 23.1 Nonlinear Elasticity 177 23.1.1 Cauchy Elasticity 177 23.1.2 Green Elasticity 178 23.1.3 Elasticity of Pre-stressed Bodies 179 23.2 Linearized Elasticity 182 23.2.1 Material Symmetry 183 23.2.2 Linear Isotropic Elastic Constitutive Relation 185 23.2.3 Restrictions on Elastic Constants 186 23.3 More Linearized Elasticity 187 23.3.1 Uniqueness of the Static Problem 188 23.3.2 Pressurized Hollow Sphere 189 Exercises 191 Reference 194 Index 195

Read more less

Book SynopsisPresents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-Table of ContentsPreface v 1 Geometric Setting 1 1.1 Vectors and Euclidean Point Space 2 1.1.1 Vectors 2 1.1.2 Euclidean Point Space 6 1.1.3 Summary 8 1.2 Tensors 8 1.2.1 First-Order Tensors and Vectors 8 1.2.2 Second-Order Tensors 11 1.2.3 Cross Products, Triple Products, and Determinants 15 1.2.4 Orthogonal Tensors 20 1.2.5 Invariants of a Tensor 21 1.2.6 Derivatives of Tensor-Valued Functions 24 1.2.7 Summary 27 2 Kinematics I: The Calculus of Motion 29 2.1 Bodies, Motions, and Deformations 29 2.1.1 Deformation 32 2.1.2 Examples of Motions 33 2.1.3 Summary 36 2.2 Derivatives of Motion 36 2.2.1 Time Derivatives 37 2.2.2 Derivatives with Respect to Position 38 2.2.3 The Deformation Gradient 40 2.2.4 Summary 42 2.3 Pathlines, Streamlines, and Streaklines 43 2.3.1 Three Types of Arc 43 2.3.2 An Example 45 2.3.3 Summary 49 2.4 Integrals Under Motion 49 2.4.1 Arc, Surface, and Volume Integrals 49 2.4.2 Reynolds Transport Theorem 55 2.4.3 Summary 57 3 Kinematics II: Strain and its Rates 59 3.1 Strain 59 3.1.1 Symmetric Tensors 60 3.1.2 Polar Decomposition and the Deformation Gradient 64 3.1.3 Examples 66 3.1.4 Cauchy–Green and Strain Tensors 68 3.1.5 Strain Invariants 70 3.1.6 Summary 71 3.2 Infinitesimal Strain 72 3.2.1 The Infinitesimal Strain Tensor 72 3.2.2 Summary 75 3.3 Strain Rates 75 3.3.1 Stretching and Spin Tensors 76 3.3.2 Skew Tensors, Spin, and Vorticity 79 3.3.3 Summary 84 3.4 Vorticity and Circulation 84 3.4.1 Circulation 84 3.4.2 Summary 88 3.5 Observer Transformations 89 3.5.1 Changes in Frame of Reference 89 3.5.2 Summary 95 4 Balance Laws 97 4.1 Mass Balance 98 4.1.1 Local Forms of Mass Balance 99 4.1.2 Summary 102 4.2 Momentum Balance 102 4.2.1 Analysis of Stress 104 4.2.2 Inertial Frames of Reference 110 4.2.3 Momentum Balance in Referential Coordinates 113 4.2.4 Summary 114 4.3 Angular Momentum Balance 115 4.3.1 Symmetry of the Stress Tensor 117 4.3.2 Summary 118 4.4 Energy Balance 119 4.4.1 Thermal Energy Balance 122 4.4.2 Summary 124 4.5 Entropy Inequality 124 4.5.1 Motivation 125 4.5.2 Clausius–Duhem Inequality 126 4.5.3 Summary 127 4.6 Jump Conditions 127 4.6.1 Singular Surfaces 129 4.6.2 Localization 132 4.6.3 Summary 135 5 Constitutive Relations: Examples of Mathematical Models 137 5.1 Heat Transfer 138 5.1.1 Properties of the Heat Equation 140 5.1.2 Summary 142 5.2 Potential Theory 143 5.2.1 Motivation 143 5.2.2 Boundary Conditions 144 5.2.3 Uniqueness of Solutions to the Poisson Equation 146 5.2.4 Maximum Principle 147 5.2.5 Mean Value Property 150 5.2.6 Summary 151 5.3 Fluid Mechanics 152 5.3.1 Ideal Fluids 152 5.3.2 An Ideal Fluid in a Rotating Frame of Reference 154 5.3.3 Acoustics 155 5.3.4 Incompressible Newtonian Fluids 158 5.3.5 Stokes Flow 159 5.3.6 Summary 163 5.4 Solid Mechanics 164 5.4.1 Static Displacements 164 5.4.2 Elastic Waves 167 5.4.3 Summary 170 6 Constitutive Theory 173 6.1 Conceptual Setting 174 6.1.1 The Need to Close the System 174 6.1.2 Summary 176 6.2 Determinism and Equipresence 177 6.2.1 Determinism 177 6.2.2 Equipresence 177 6.2.3 Summary 178 6.3 Objectivity 179 6.3.1 Reducing Functional Dependencies 180 6.3.2 Summary 182 6.4 SYMMETRY 183 6.4.1 Changes in Reference Configuration 183 6.4.2 Symmetry Groups 186 6.4.3 Classification of Materials 189 6.4.4 Implications for Thermoviscous Fluids 193 6.4.5 Summary 193 6.5 Admissibility 194 6.5.1 Implications of the Entropy Inequality 195 6.5.2 Analysis of Equilibrium 197 6.5.3 Linear, Isotropic, Thermoelastic Solids 199 6.5.4 Summary 202 7 Multiconstituent Continua 203 7.1 Constituents 204 7.1.1 Configurations and Motions 204 7.1.2 Volume Fractions and Densities 206 7.1.3 Summary 208 7.2 Multiconstituent Balance Laws 209 7.2.1 Multiconstituent Mass Balance 210 7.2.2 Multiconstituent Momentum Balance 212 7.2.3 Multiconstituent Angular Momentum Balance 214 7.2.4 Multiconstituent Energy Balance 215 7.2.5 Multiconstituent Entropy Inequality 216 7.2.6 Isothermal, Nonreacting Multiphase Mixtures 217 7.2.7 Summary 219 7.3 Fluid Flow in a Porous Solid 220 7.3.1 Modeling Assumptions for Porous Media 221 7.3.2 Balance Laws for the Fluid and Solid Phases 223 7.3.3 Equilibrium Constraints 225 7.3.4 Linear Extensions From Equilibrium 226 7.3.5 Commentary 228 7.3.6 Potential Formulation of Darcy’s Law 229 7.3.7 Summary 233 7.4 Diffusion in a Binary Fluid Mixture 234 7.4.1 Modeling Assumptions for Binary Diffusion 235 7.4.2 Balance Laws for the Two Species 235 7.4.3 Constitutive Relationships for Diffusion 236 7.4.4 Modeling Solute Transport 239 7.4.5 Summary 242 A Guide to Notation 243 A.1 General Conventions 243 A.2 Letters Reserved for Dedicated Uses 244 A.3 Special Symbols 245 B Vector Integral Theorems 247 B.1 Stokes’s Theorem 248 B.2 The Divergence Theorem 249 B.3 The Change-of-variables Theorem 252 C Hints and Solutions to Exercises 253 References 265 Index 269

Read more less

Book SynopsisA revised edition to applied gas dynamics with exclusive coverage on jets and additional sets of problems and examples The revised and updated second edition of Applied Gas Dynamics offers an authoritative guide to the science of gas dynamics. Written by a noted expert on the topic, the text contains a comprehensive review of the topic; from a definition of the subject, to the three essential processes of this science: the isentropic process, shock and expansion process, and Fanno and Rayleigh flows. In this revised edition, there are additional worked examples that highlight many concepts, including moving shocks, and a section on critical Mach number is included that helps to illuminate the concept. The second edition also contains new exercise problems with the answers added. In addition, the information on ram jets is expanded with helpful worked examples. It explores the entire spectrum of the ram jet theory and includes a set of exercise problems to aid in the understanding ofTable of ContentsPreface xv Author Biography xvii About the Companion Website xix 1 Basic Facts 1 1.1 Definition of Gas Dynamics 1 1.2 Introduction 1 1.3 Compressibility 2 1.3.1 Limiting Conditions for Compressibility 3 1.4 Supersonic Flow – What is it? 4 1.5 Speed of Sound 5 1.6 Temperature Rise 7 1.7 Mach Angle 8 1.7.1 Small Disturbance 10 1.7.2 Finite Disturbance 10 1.8 Thermodynamics of Fluid Flow 11 1.9 First Law of Thermodynamics (Energy Equation) 11 1.9.1 Energy Equation for an Open System 12 1.9.2 Adiabatic Flow Process 14 1.10 The Second Law of Thermodynamics (Entropy Equation) 15 1.11 Thermal and Calorical Properties 16 1.11.1 Thermally Perfect Gas 16 1.12 The Perfect Gas 17 1.12.1 Entropy Calculation 18 1.12.2 Isentropic Relations 20 1.12.3 Limitations on Air as a Perfect Gas 25 1.13 Wave Propagation 26 1.14 Velocity of Sound 26 1.15 Subsonic and Supersonic Flows 27 1.16 Similarity Parameters 28 1.17 Continuum Hypothesis 28 1.18 Compressible Flow Regimes 30 1.19 Summary 31 Exercise Problems 34 2 Steady One-Dimensional Flow 43 2.1 Introduction 43 2.2 Fundamental Equations 43 2.3 Discharge from a Reservoir 45 2.3.1 Mass Flow Rate per Unit Area 47 2.3.2 Critical Values 51 2.4 Streamtube Area–Velocity Relation 54 2.5 de Laval Nozzle 57 2.5.1 Mass Flow Relation in Terms of Mach Number 65 2.5.2 Maximum Mass Flow Rate per Unit Area 65 2.6 Supersonic Flow Generation 66 2.6.1 Nozzles 68 2.6.2 Physics of the Nozzle Flow Process 69 2.7 Performance of Actual Nozzles 71 2.7.1 Nozzle Efficiency 71 2.7.2 Nozzle Discharge Coefficient 73 2.8 Diffusers 75 2.8.1 Special Features of Supersonic Diffusers 77 2.8.2 Supersonic Wind Tunnel Diffusers 78 2.8.3 Supersonic Inlets 81 2.8.4 Fixed-Geometry Inlet 82 2.8.5 Variable-Geometry Inlet 83 2.8.6 Diffuser Efficiency 84 2.9 Dynamic Head Measurement in Compressible Flow 88 2.9.1 Compressibility Correction to Dynamic Pressure 91 2.10 Pressure Coefficient 95 2.11 Summary 97 Exercise Problems 99 3 Normal Shock Waves 113 3.1 Introduction 113 3.2 Equations of Motion for a Normal Shock Wave 113 3.3 The Normal Shock Relations for a Perfect Gas 115 3.4 Change of Stagnation or Total Pressure Across a Shock 118 3.5 Hugoniot Equation 121 3.5.1 Moving Shocks 123 3.6 The Propagating Shock Wave 123 3.6.1 Weak Shock 128 3.6.2 Strong Shock 130 3.7 Reflected Shock Wave 133 3.8 Centered Expansion Wave 138 3.9 Shock Tube 139 3.9.1 Shock Tube Applications 142 3.10 Summary 145 Exercise Problems 148 4 Oblique Shock and Expansion Waves 155 4.1 Introduction 155 4.2 Oblique Shock Relations 156 4.3 Relation Between 𝛽 and 𝜃 158 4.4 Shock Polar 160 4.5 Supersonic Flow Over a Wedge 162 4.6 Weak Oblique Shocks 165 4.7 Supersonic Compression 167 4.8 Supersonic Expansion by Turning 169 4.9 The Prandtl–Meyer Expansion 170 4.9.1 Velocity Components Vr and V𝜙 172 4.9.2 The Prandtl–Meyer Function 175 4.9.3 Compression 177 4.10 Simple and Nonsimple Regions 178 4.11 Reflection and Intersection of Shocks and Expansion Waves 178 4.11.1 Intersection of Shocks of the Same Family 181 4.11.2 Wave Reflection from a Free Boundary 183 4.12 Detached Shocks 189 4.13 Mach Reflection 191 4.14 Shock-Expansion Theory 197 4.15 Thin Airfoil Theory 202 4.15.1 Application of Thin Aerofoil Theory 203 4.16 Summary 210 Exercise Problems 212 5 Compressible Flow Equations 221 5.1 Introduction 221 5.2 Crocco’s Theorem 221 5.2.1 Basic Solutions of Laplace’s Equation 224 5.3 General Potential Equation for Three-Dimensional Flow 225 5.4 Linearization of the Potential Equation 226 5.4.1 Small Perturbation Theory 227 5.5 Potential Equation for Bodies of Revolution 229 5.5.1 Conclusions 230 5.5.2 Solution of Nonlinear Potential Equation 231 5.6 Boundary Conditions 231 5.6.1 Bodies of Revolution 232 5.7 Pressure Coefficient 233 5.7.1 Bodies of Revolution 234 5.8 Summary 234 Exercise Problems 237 6 Similarity Rule 239 6.1 Introduction 239 6.2 Two-Dimensional Flow: The Prandtl–Glauert Rule for Subsonic Flow 239 6.2.1 Prandtl–Glauert Transformations 239 6.2.2 The Direct Problem (Version I) 241 6.2.3 The Indirect Problem (Case of Equal Potentials): P–G Transformation (Version II) 243 6.2.4 Streamline Analogy (Version III): Gothert’s Rule 244 6.3 Prandtl–Glauert Rule for Supersonic Flow: Versions I and II 245 6.3.1 Subsonic Flow 246 6.3.2 Supersonic Flow 246 6.4 The von Karman Rule for Transonic Flow 248 6.4.1 Use of the von Karman Rule 249 6.5 Hypersonic Similarity 250 6.6 Three-Dimensional Flow: Gothert’s Rule 252 6.6.1 General Similarity Rule 252 6.6.2 Gothert’s Rule 254 6.6.3 Application toWings of Finite Span 255 6.6.4 Application to Bodies of Revolution and Fuselages 255 6.6.5 The Prandtl–Glauert Rule 257 6.6.6 The von Karman Rule for Transonic Flow 261 6.7 Critical Mach Number 261 6.7.1 Calculation of M∗∞ 264 6.8 Summary 266 Exercise Problems 269 7 Two-Dimensional Compressible Flows 271 7.1 Introduction 271 7.2 General Linear Solution for Supersonic Flow 271 7.2.1 Existence of Characteristics in a Physical Problem 273 7.2.2 Equation for the Streamlines from Kinematic Flow Condition 274 7.3 Flow over a Wave-Shaped Wall 276 7.3.1 Incompressible Flow 276 7.3.2 Compressible Subsonic Flow 277 7.3.3 Supersonic Flow 278 7.3.4 Pressure Coefficient 278 7.4 Summary 280 Exercise Problems 280 8 Flow with Friction and Heat Transfer 283 8.1 Introduction 283 8.2 Flow in Constant Area Duct with Friction 283 8.2.1 The Fanno Line 284 8.3 Adiabatic, Constant-Area Flow of a Perfect Gas 285 8.3.1 Definition of Friction Coefficient 286 8.3.2 Effects of Wall Friction on Fluid Properties 287 8.3.3 Second Law of Thermodynamics 288 8.3.4 Working Relations 289 8.4 Flow with Heating or Cooling in Ducts 294 8.4.1 Governing Equations 294 8.4.2 Simple-Heating Relations for a Perfect Gas 295 8.5 Summary 300 Exercise Problems 303 9 Method of Characteristics 309 9.1 Introduction 309 9.2 The Concepts of Characteristics 309 9.3 The Compatibility Relation 310 9.4 The Numerical Computational Method 312 9.4.1 Solid and Free Boundary Points 313 9.4.2 Sources of Error 316 9.4.3 Axisymmetric Flow 316 9.4.4 Nonisentropic Flow 317 9.5 Theorems for Two-Dimensional Flow 318 9.6 Numerical Computation with Weak Finite Waves 320 9.6.1 Reflection of Waves 320 9.7 Design of Supersonic Nozzle 323 9.7.1 Contour Design Details 324 9.8 Summary 328 10 Measurements in Compressible Flow 329 10.1 Introduction 329 10.2 Pressure Measurements 329 10.2.1 Liquid Manometers 329 10.2.2 Measuring Principle of Manometers 330 10.2.3 Dial-Type Pressure Gauges 332 10.2.4 Pressure Transducers 333 10.3 Temperature Measurements 335 10.4 Velocity and Direction 338 10.5 Density Problems 339 10.6 Compressible Flow Visualization 339 10.6.1 Supersonic Flows 340 10.7 Interferometer 341 10.7.1 Formation of Interference Patterns 341 10.7.2 Quantitative Evaluation 342 10.7.3 Fringe-Displacement Method 344 10.8 Schlieren System 344 10.8.1 Range and Sensitivity of the Schlieren System 347 10.8.2 Optical Components Quality Requirements 347 10.8.3 Sensitivity of the Schlieren Method for Shock and Expansion Studies 350 10.9 Shadowgraph 352 10.9.1 Comparison of the Schlieren and Shadowgraph Methods 353 10.10 Wind Tunnels 354 10.10.1 High-SpeedWind Tunnels 354 10.10.2 Blowdown TypeWind Tunnels 354 10.10.3 Induction Type Tunnels 355 10.10.4 Continuous Supersonic Wind Tunnels 356 10.10.5 Losses in Supersonic Tunnels 357 10.10.6 Supersonic Wind Tunnel Diffusers 358 10.10.7 Effects of Second Throat 360 10.10.8 Compressor Tunnel Matching 362 10.10.9 The Mass Flow Rate 365 10.10.10 Blowdown Tunnel Operation 369 10.10.11 Optimum Conditions 372 10.10.12 Running Time of Blowdown Wind Tunnels 373 10.11 Hypersonic Tunnels 375 10.11.1 Hypersonic Nozzle 377 10.12 Instrumentation and Calibration ofWind Tunnels 380 10.12.1 Calibration of SupersonicWind Tunnels 380 10.12.2 Calibration 381 10.12.3 Mach Number Determination 381 10.12.4 Pitot Pressure Measurement 382 10.12.5 Static Pressure Measurement 382 10.12.6 Determination of Flow Angularity 383 10.12.7 Determination of Turbulence Level 383 10.12.8 Determination of Test-Section Noise 384 10.12.9 Use of Calibration Results 384 10.12.10 Starting of Supersonic Tunnels 384 10.12.11 Starting Loads 385 10.12.12 Reynolds Number Effects 385 10.12.13 Model Mounting-Sting Effects 385 10.13 Calibration and Use of Hypersonic Tunnels 386 10.13.1 Calibration of Hypersonic Tunnels 386 10.13.2 Mach Number Determination 386 10.13.3 Determination of Flow Angularity 388 10.13.4 Determination of Turbulence Level 388 10.13.5 Reynolds Number Effects 389 10.13.6 Force Measurements 389 10.14 Flow Visualization 390 10.15 Summary 390 Exercise Problems 393 11 Ramjet 395 11.1 Introduction 395 11.2 The Ideal Ramjet 396 11.3 Aerodynamic Losses 401 11.4 Aerothermodynamics of Engine Components 404 11.4.1 Engine Inlets 404 11.5 Flow Through Inlets 405 11.5.1 Inlet Flow Process 406 11.5.2 Boundary Layer Separation 406 11.5.3 Flow Over the Inlet 406 11.6 Performance of Actual Intakes 410 11.6.1 Isentropic Efficiency 410 11.6.2 Stagnation Pressure Ratio 411 11.6.3 Supersonic Inlets 411 11.6.4 Supersonic Diffusers 412 11.6.5 Starting Problem 413 11.7 Shock–Boundary Layer Interaction 418 11.8 Oblique Shock Wave Incident on Flat Plate 419 11.9 Normal Shocks in Ducts 420 11.10 External Supersonic Compression 422 11.11 Two-Shock Intakes 423 11.12 Multi-Shock Intakes 427 11.13 Isentropic Compression 429 11.14 Limits of External Compression 431 11.15 External Shock Attachment 433 11.16 Internal Shock Attachment 433 11.17 Pressure Loss 434 11.18 Supersonic Combustion 442 11.19 Summary 444 Exercise Problems 447 12 Jets 451 12.1 Introduction 451 12.1.1 Subsonic Jets 453 12.2 Mathematical Treatment of Jet Profiles 454 12.3 Theory of Turbulent Jets 455 12.3.1 Mean Velocity and Mean Temperature 456 12.3.2 Turbulence Characteristics of Free Jets 457 12.3.3 Mixing Length 458 12.4 Experimental Methods for Studying Jets and the Techniques Used for Analysis 461 12.4.1 Pressure Measurement 462 12.5 Expansion Levels of Jets 464 12.5.1 Overexpanded Jets 464 12.5.2 Correctly Expanded Jets 467 12.5.3 Underexpanded Jets 469 12.6 Control of Jets 471 12.6.1 Classification of Control Methods 473 12.6.2 Role of Shear Layer in Flow Control 474 12.6.3 Supersonic Shear Layers 475 12.6.4 Use of Tabs for Jet Control 477 12.6.5 Evaluation of the Effectiveness of Some Specific Passive Controls 481 12.6.6 Grooves and Cutouts 519 12.7 Noncircular Jets and Shifted Tabs 519 12.7.1 Jet Control with Tabs 523 12.7.2 Shifted Tabs 527 12.7.3 Ventilated Triangular Tabs 532 12.7.4 Tab Edge Effect 535 12.8 Summary 541 Appendix A 547 References 619 Index 625

Read more less

Book SynopsisThe formalism processing of unbuckled solids mechanics involves several mathematical tools which are to be mastered at the same time. This volume collects the main points which take place in the course of the formalism, so that the user immediately finds what he needs without looking for it. Furthermore, the book contains a methodological formulary to guide the user in his approach.Table of ContentsIntroduction xi Table of Notations xiii Chapter 1. Vector Calculus 1 1.1. Vector space 1 1.1.1. Definition 1 1.1.2. Vector space – dimension – basis 2 1.1.3. Affine space 3 1.2. Affine space of dimension 3 – free vector 4 1.3. Scalar product a⋅b 5 1.3.1. Properties of the scalar product 6 1.3.2. Scalar square – unit vector 6 1.3.3. Geometric interpretation of the scalar product 7 1.3.4. Solving the equation a�� ⋅ x�� = 0 9 1.4. Vector product a ∧ b 9 1.4.1. Definition 9 1.4.2. Geometric interpretation of the vector product 10 1.4.3. Properties of vector product 11 1.4.4. Solving the equation a ∧ x = b 11 1.5. Mixed product (a ,b, c ) 12 1.5.1. Definition 12 1.5.2. Geometric interpretation of the mixed product 12 1.5.3. Properties of the mixed product 13 1.6. Vector calculus in the affine space of dimension 3 15 1.6.1. Orthonormal basis 15 1.6.2. Analytical expression of the scalar product 16 1.6.3. Analytical expression of the vector product 16 1.6.4. Analytical expression of the mixed product 17 1.7. Applications of vector calculus 18 1.7.1. Double vector product 18 1.7.2. Resolving the equation a�� ⋅ x�� = b 22 1.7.3. Resolving the equation a ∧ x = b 23 1.7.4. Equality of Lagrange 25 1.7.5. Equations of planes 25 1.7.6. Relations within the triangle 27 1.8. Vectors and basis changes 28 1.8.1. Einstein’s convention 28 1.8.2. Transition table from basis (e) to basis (E) 30 1.8.3. Characterization of the transition table 32 Chatper 2. Torsors and Torsor Calculus 35 2.1. Vector sets 35 2.1.1. Discrete set of vectors 35 2.1.2. Set of vectors defined on a continuum 36 2.2. Introduction to torsors 37 2.2.1. Definition 37 2.2.2. Equivalence of vector families 38 2.3. Algebra torsors 38 2.3.1. Equality of two torsors 38 2.3.2. Linear combination of torsors 39 2.3.3. Null torsors 39 2.3.4. Opposing torsor 40 2.3.5. Product of two torsors 40 2.3.6. Scalar moment of a torsor – equiprojectivity 41 2.3.7. Invariant scalar of a torsor 43 2.4. Characterization and classification of torsors 43 2.4.1. Torsors with a null resultant 43 2.4.2. Torsors with a no-null resultant 45 2.5. Derivation torsors 48 2.5.1. Torsor dependent on a single parameter q 49 2.5.2. Torsor dependent of n parameters qi functions of p 51 2.5.3. Explicitly dependent torsor of n + 1 parameters 52 Chapter 3. Derivation of Vector Functions 55 3.1. Derivative vector: definition and properties 55 3.2. Derivative of a function in a basis 56 3.3. Deriving a vector function of a variable 57 3.3.1. Relations between derivatives of a function in different bases 57 3.3.2. Differential form associated with two bases 63 3.4. Deriving a vector function of two variables 65 3.5. Deriving a vector function of n variables 68 3.6. Explicit intervention of the variable p 70 3.7. Relative rotation rate of a basis relative to another 71 Chapter 4. Vector Functions of One Variable Skew Curves 73 4.1. Vector function of one variable 73 4.2. Tangent at a point M 74 4.3. Unit tangent vector τ ( q) 76 4.4. Main normal vector ( ) q ν 77 4.5. Unit binormal vector ( ) q β 79 4.6. Frenet’s basis 80 4.7. Curvilinear abscissa 81 4.8. Curvature, curvature center and curvature radius 83 4.9. Torsion and torsion radius 84 4.10. Orientation in (λ) of the Frenet basis 87 Chapter 5. Vector Functions of Two Variables Surfaces 91 5.1. Representation of a vector function of two variables 91 5.1.1. Coordinate curves 91 5.1.2. Regular or singular point – tangent plane – unit normal vector 93 5.1.3. Distinctive surfaces 95 5.1.4. Ruled surfaces 101 5.1.5. Area element 110 5.2. General properties of surfaces 111 5.2.1. First quadratic form 111 5.2.2. Darboux–Ribaucour’s trihedral 114 5.2.3. Second quadratic form 119 5.2.4. Meusnier’s theorems 121 5.2.5. Geodesic torsion 123 5.2.6. Prominent curves traced on a surface 125 5.2.7. Directions and principal curvatures of a surface 127 Chapter 6. Vector Function of Three Variables: Volumes 135 6.1. Vector functions of three variables 135 6.1.1. Coordinate surfaces 135 6.1.2. Coordinate curves 136 6.1.3. Orthogonal curvilinear coordinates 136 6.2. Volume element 137 6.2.1. Definition 137 6.2.2. Applications to traditional coordinate systems 138 6.3. Rotation rate of the local basis 139 6.3.1. Calculation of the partial rotation rate 1δ (λ ,e) 140 6.3.2. Calculation of the rotation rate 143 Chapter 7. Linear Operators 145 7.1. Definition 145 7.2. Intrinsic properties 145 7.3. Algebra of linear operators 147 7.3.1. Unit operator 147 7.3.2. Equality of two linear operators 147 7.3.3. Product of a linear operator by a scalar 147 7.3.4. Sum of two linear operators 148 7.3.5. Multiplying two linear operators 148 7.4. Bilinear form 149 7.5. Quadratic form 150 7.6. Linear operator and basis change 150 7.7. Examples of linear operators 152 7.7.1. Operation f = a ^ F 152 7.7.2. Operation f = a ^ (a ^ F) 152 7.7.3. Operation f = a(b ⋅ F) 153 7.7.4. Operation f = a ^ (F ^ a) 155 7.8. Vector rotation Ru��,a 156 7.8.1. Expression of the vector rotation 156 7.8.2. Quaternion associated with the vector rotation Ru��,a 159 7.8.3. Matrix representation of the vector rotation 160 7.8.4. Basis change and rotation vector 162 Chapter 8. Homogeneity and Dimension 165 8.1. Notion of homogeneity 165 8.2. Dimension 165 8.3. Standard mechanical dimensions 166 8.4. Using dimensional equations 168 Bibliography 171 Index 173

Read more less

Book SynopsisFluid mechanics is an important scientific field with various industrial applications for flows or energy consumption and efficiency issues. This book has as main aim to be a textbook of applied knowledge in real fluids as well as to the Hydraulic systems components and operation, with emphasis to the industrial or real life problems for piping and aerodynamic design geometries. Various problems will be presented and analyzed through this book. Table of ContentsPreface ix Chapter 1. Pipe Networks 1 1.1. Introduction 1 1.2. Calculation of pipe networks 3 1.3. Problem-solving methodology for pipe networks 10 1.4. Overall approach for the network calculation 12 1.5. The Hazen–Williams equation for network analysis 13 1.6. Hazen–Williams and Darcy–Weisbach identity 15 1.7. Hardy–Cross method 18 1.8. Formulae 21 1.9. Questions 23 1.10. Problems with solutions 23 1.11. Problems to be solved 53 Chapter 2. Open Channel Flow 57 2.1. Introduction 57 2.2. Non-dimensional parameters in open channels 58 2.3. Open channel types of flow 59 2.4. Open channels’ geometrical shapes 61 2.4.1. Channels of rectangular cross-sectional area 61 2.4.2. Channels of trapezoidal cross-sectional area 62 2.4.3. Channels of circular cross-sectional area 63 2.5. The hydraulic jump 65 2.6. Calculation of the depth flow after the hydraulic jump 65 2.7. Velocity distribution 68 2.8. Velocity distribution at the vertical level 68 2.9. Uniform flow in open channel equations – Chezy type 70 2.10. Best hydraulic cross-sectional area 75 2.11. Specific flow energy 79 2.12. Channels of rectangular cross-sectional area 80 2.13. Open channels’ more adequate cross-sectional areas 83 2.13.1. Rectangular cross-sectional area 83 2.13.2. Trapezoidal cross-sectional area 85 2.14. Non-uniform flow in open channels 88 2.15. Channels of non-rectangular cross-section area 90 2.16. Formulae 92 2.16.1. Channels of rectangular cross-sectional area formulae 93 2.16.2. Channels of trapezoidal cross-section formulae 93 2.16.3. Channels of circular cross-sectional area formulae 94 2.16.4. Channels of rectangular cross-sectional area formulae 99 2.16.5. Channels of non-rectangular cross-sectional area formulae 100 2.17. Questions 101 2.18. Problems with solutions 103 2.19. Problems to be solved 116 Chapter 3. Boundary Layer 119 3.1. Introduction 119 3.2. Laminar incompressible boundary layer 120 3.3. Characteristic values of the boundary layer 125 3.3.1. Thickness δ of the boundary layer 125 3.3.2. The thickness displacement 1 δ1’.126 3.4. Flow types in the boundary layer 127 3.5. Formulae 131 3.6. Questions 133 3.7. Problems with solutions 133 3.8. Problems to be solved 145 Chapter 4. Flow Around Solid Bodies 147 4.1. Introduction 147 4.2. Geometrical characteristics of an airfoil 148δ 4.3. Kutta–Joukowski equation 150 4.4. Aerodynamic paradox 152 4.5. Pressure distribution in an airfoil 153 4.6. Lift curve 156 4.7. Drag force and drag coefficient curve 158 4.7.1. Drag of skin friction 158 4.7.2. Form drag 159 4.7.3. Induced drag 161 4.8. Parameters that influence the drag coefficient CD 163 4.8.1. Dependence of CD on the body’s shape 163 4.8.2. Dependence of CD on relative roughness 165 4.8.3. Dependence of CD on the Reynolds number 170 4.9. External flow around industrial solid bodies 177 4.9.1. Car’s motion 177 4.9.2. Surface vessel’s motion 178 4.9.3. Wind flow in ground constructions 179 4.9.4. Airplane’s motion 181 4.10. Drag in fluid drops and gas bubbles in creeping flow 190 4.11. Formulae 191 4.12. Questions 193 4.13. Problems with solutions 196 4.14. Problems to be solved 209 Appendices 211 Appendix 1. Symbols and Units 213 Appendix 2. Tables and Diagrams of Natural Values 219 Appendix 3. Symbols and Basic Conversion Factors 237 Appendix 4. International Standard Atmosphere, SI Units 239 Appendix 5. International Standard Atmosphere, in BS 251 Appendix 6. NACA Airfoils’ Diagrams 259 Bibliography 287 Index 289

Read more less

Book Synopsis Mechanical behaviors of materials are highly influenced by their architectures and/or microstructures. Hence, progress in material science involves understanding and modeling the link between the microstructure and the material behavior at different scales. This book gathers contributions from eminent researchers in the field of computational and experimental material modeling. It presents advanced experimental techniques to acquire the microstructure features together with dedicated numerical and analytical tools to take into account the randomness of the micro-structure. Table of ContentsPreface xi Chapter 1. Synchrotron Imaging and Diffraction for In Situ 3D Characterization of Polycrystalline Materials 1Henry PROUDHON 1.1. Introduction 1 1.2. 3D X-ray characterization of structural materials 3 1.2.1. Early days of X-ray computed tomography 3 1.2.2. X-ray absorption and Beer Lambert’s law 4 1.2.3. X-ray detection 6 1.2.4. Radon’s transform and reconstruction 8 1.2.5. Synchrotron X-ray microtomography 10 1.2.6. Phase contrast tomography 13 1.2.7. Diffraction contrast tomography 14 1.3. Nanox: a miniature mechanical stress rig designed for near-field X-ray diffraction imaging techniques 16 1.4. Coupling diffraction contrast tomography with the finite-element method. 19 1.4.1. Motivation for image-based mechanical computations 19 1.4.2. 3D mesh generation from tomographic images 20 1.4.3. Toward a fatigue model at the scale of the polycrystal 28 1.5. Conclusion and outlook 29 1.6. Bibliography 31 Chapter 2. Determining the Probability of Occurrence of Rarely Occurring Microstructural Configurations for Titanium Dwell Fatigue 41Adam L. PILCHAK, Joseph C. TUCKER and Tyler J. WEIHING 2.1. Introduction 42 2.2. Experimental methods 44 2.2.1. MTR quantification metrics 44 2.2.2. Synthetic microstructure generation 46 2.2.3. Crystallographic analysis for titanium dwell fatigue 48 2.2.4. Block maxima 50 2.3. Results and discussion 51 2.3.1. Probability of occurrence 53 2.3.2. “Hard” MTR size distributions 57 2.3.3. Block maxima 58 2.4. Summary and outlook 63 2.5. Bibliography 64 Chapter 3. Wave Propagation Analysis in 2D Nonlinear Periodic Structures Prone to Mechanical Instabilities 67Hilal REDA, Yosra RAHALI, Jean-François GANGHOFFER and Hassan LAKISS 3.1. Introduction 68 3.2. Extensible energy of pantograph for dynamic analysis 70 3.2.1. Expression of the pantographic network energy 70 3.2.2. Dynamic equilibrium equation 73 3.3. Wave propagation in a nonlinear elastic beam 75 3.3.1. Legendre–Hadamard ellipticity condition and loss of stability 77 3.3.2. Supersonic and subsonic modes for 1D wave propagation 78 3.3.3. Wave dispersion relation in 2D nonlinear periodic structures 81 3.3.4. Anisotropic behavior of 2D pantographic networks versus the degree of nonlinearity 84 3.4. Conclusion 85 3.5. Appendix 86 3.6. Bibliography 94 Chapter 4. Multiscale Model of Concrete Failure 99Emir KARAVELIĆ, Mijo NIKOLIĆ and Adnan IBRAHIMBEGOVIĆ 4.1. Introduction 99 4.2. Meso-scale model 102 4.3. Macroscopic model response 106 4.3.1. Uniaxial tests 106 4.3.2. Failure surface 111 4.4. Conclusions 117 4.5. Acknowledgments 119 4.6. Bibliography 120 Chapter 5. Discrete Numerical Simulations of the Strength and Microstructure Evolution During Compaction of Layered Granular Solids 123Bereket YOHANNES, Marcial GONZALEZ and Alberto M. CUITIÑO 5.1. Introduction 123 5.2. Numerical simulation 127 5.2.1. Discrete particle simulations of powder compaction 127 5.2.2. Discrete particle simulation of layered compacts 129 5.3. Discussion 131 5.4. Conclusion 137 5.5. Acknowledgements 137 5.6. Bibliography 137 Chapter 6. Microstructural Views of Stresses in Three-Phase Granular Materials 143Jérôme DURIEZ, Richard WAN and Félix DARVE 6.1. Microstructural expression of triphasic total stresses 145 6.1.1. Stress description within micro-scale volumes and interfaces of triphasic materials 145 6.1.2. Total stress derivation 146 6.2. Numerical modeling of wet ideal granular materials 149 6.2.1. DEM description of fluid microstructure 149 6.2.2. DEM description of stress and strains 152 6.3. Anisotropy of the capillary stress contribution 154 6.3.1. Mechanical loading 155 6.3.2. Hydraulic loading 157 6.4. Effective stress 160 6.5. Conclusion 162 6.6. Bibliography 163 Chapter 7. Effect of the Third Invariant of the Stress Deviator on the Response of Porous Solids with Pressure-Insensitive Matrix 167José Luis ALVES and Oana CAZACU 7.1. Introduction 168 7.2. Problem statement and method of analysis 171 7.2.1. Drucker yield criterion for isotropic materials 171 7.2.2. Unit cell model 173 7.3. Results 179 7.3.1. Yield surfaces and porosity evolution 179 7.4. Conclusions 190 7.5. Bibliography 194 Chapter 8. High Performance Data-Driven Multiscale Inverse Constitutive Characterization of Composites 197John MICHOPOULOS, Athanasios ILIOPOULOS, John HERMANSON, John STEUBEN and Foteini KOMNINELI 8.1. Introduction 198 8.2. Automated multi-axial testing 202 8.2.1. Loading space 204 8.2.2. Experimental campaign 206 8.3. Constitutive formalisms 207 8.3.1. Small strain formulation 208 8.3.2. Finite strain formulation 209 8.4. Meshless random grid method for experimental evaluation of strain fields 209 8.5. Inverse determination of HDM via design optimization 211 8.5.1. Numerical results of design optimization 214 8.6. Surrogate models for characterization 216 8.6.1. Definition and construction of the surrogate model 218 8.6.2. Characterization by optimization 219 8.6.3. Validation with physical experiments 221 8.7. Multi-scale inversion 221 8.7.1. Forward problem: mathematical homogenization 222 8.7.2. Inverse problem 224 8.8. Computational framework and synthetic experiments 226 8.9. Conclusions and plans 230 8.10. Acknowledgments 232 8.11. Bibliography 232 Chapter 9. New Trends in Computational Mechanics: Model Order Reduction, Manifold Learning and Data-Driven 239Jose Vicente AGUADO, Domenico BORZACCHIELLO, Elena LOPEZ, Emmanuelle ABISSET-CHAVANNE, David GONZALEZ, Elias CUETO and Francisco CHINESTA 9.1. Introduction 240 9.1.1. The big picture 240 9.1.2. The PGD at a glance 242 9.2. Constructing slow manifolds 245 9.2.1. From principal component analysis (PCA) to kernel principal component analysis (kPCA) 245 9.2.2. Kernel principal component analysis (kPCA) 249 9.2.3. Locally linear embedding (LLE) 250 9.2.4. Discussion 251 9.3. Manifold-learning-based computational mechanics 252 9.4. Data-driven simulations 253 9.4.1. Data-based weak form 254 9.4.2. Constructing the constitutive manifold 254 9.5. Data-driven upscaling of viscous flows in porous media 257 9.5.1. Upscaling Newtonian and generalized Newtonian fluids flowing in porous media 258 9.6. Conclusions 260 9.7. Bibliography 261 List of Authors 267 Index 271

Read more less

Book SynopsisLagrangian Mechanics explains the subtleties of analytical mechanics and its applications in rigid body mechanics. The authors demonstrate the primordial role of parameterization, which conditions the equations and thus the information obtained; the essential notions of virtual kinematics, such as the virtual derivative and the dependence of the virtual quantities with respect to a reference frame; and the key concept of perfect joints and their intrinsic character, namely the invariance of the fields of compatible virtual velocities with respect to the parameterization. Throughout the book, any demonstrated results are stated with the respective hypotheses, clearly indicating the applicability conditions for the results to be ready for use. Numerous examples accompany the text, facilitating the understanding of the calculation mechanisms. The book is mainly intended for Bachelor's, Master's or engineering students who are interested in an in-depth study of analytical mechanics and its applications. Table of ContentsPreface xi 1 Kinematics 1 1.1 Observer – Reference frame 1 1.2 Time 2 1.2.1 Date postulate 2 1.2.2 Date change postulate 2 1.3 Space 3 1.3.1 Physical space 3 1.3.2 Mathematical space 4 1.3.3 Position postulate 4 1.3.4 Typical operations on the mathematical space E 6 1.3.5 Position change postulate 7 1.3.6 The common reference frame R0 9 1.3.7 Coordinate system of a reference frame 12 1.3.8 Fixed point and fixed vector in a reference frame 14 1.4 Derivative of a vector with respect to a reference frame 15 1.5 Velocity of a particle 17 1.6 Angular velocity 17 1.7 Reference frame defined by a rigid body: Rigid body defined by a reference frame 19 1.8 Point attached to a rigid body: Vector attached to a rigid body 19 1.9 Velocities in a rigid body 20 1.10 Velocities in a mechanical system 22 1.11 Acceleration 24 1.11.1 Acceleration of a particle 24 1.11.2 Accelerations in a mechanical system 24 1.12 Composition of velocities and accelerations 24 1.12.1 Composition of velocities 24 1.12.2 Composition of accelerations 25 1.13 Angular momentum: Dynamic moment 25 2 Parameterization and Parameterized Kinematics 27 2.1 Position parameters 27 2.1.1 Position parameters of a particle 27 2.1.2 Position parameters for a rigid body 28 2.1.3 Position parameters for a system of rigid bodies 32 2.2 Mechanical joints 33 2.3 Constraint equations 33 2.4 Parameterization 37 2.5 Dependence of the rotation tensor of the reference frame on the retained parameters 39 2.6 Velocity of a particle 41 2.7 Angular velocity 44 2.8 Velocities in a rigid body 45 2.9 Velocities in a mechanical system 47 2.10 Parameterized velocity of a particle 48 2.10.1 Definition 48 2.10.2 Practical calculation of the parameterized velocity 49 2.11 Parameterized velocities in a rigid body 50 2.12 Parameterized velocities in a mechanical system 51 2.13 Lagrange’s kinematic formula 52 2.14 Parameterized kinetic energy 54 3 Efforts 57 3.1 Forces 57 3.2 Torque 59 3.3 Efforts 60 3.4 External and internal efforts 61 3.4.1 External effort 61 3.4.2 Internal effort 62 3.5 Given efforts and constraint efforts 62 3.6 Moment field 64 4 Virtual Kinematics 67 4.1 Virtual derivative of a vector with respect to a reference frame 67 4.2 Virtual velocity of a particle 70 4.3 Virtual angular velocity 75 4.4 Virtual velocities in a rigid body 81 4.4.1 The virtual velocity field (VVF) associated with a parameterization 81 4.4.2 Virtual velocity field (VVF) in a rigid body 82 4.5 Virtual velocities in a system 83 4.5.1 VVF associated with a parameterization 83 4.5.2 VVF on each rigid body of a system 84 4.5.3 Virtual velocity of the center of mass 84 4.6 Composition of virtual velocities 85 4.6.1 Composition of virtual velocities of a particle 85 4.6.2 Composition of virtual angular velocities 86 4.6.3 Composition of VVFs in rigid bodies 87 4.7 Method of calculating the virtual velocity at a point 88 5 Virtual Powers 91 5.1 Principle of virtual powers 91 5.2 VP of efforts internal to each rigid body 92 5.3 VP of efforts 92 5.4 VP of efforts exerted on a rigid body 94 5.4.1 General expression 94 5.4.2 VP of zero moment field efforts exerted upon a rigid body 94 5.4.3 Dependence of the VP of efforts on the reference frame 94 5.5 VP of efforts exerted on a system of rigid bodies 95 5.5.1 General expression 95 5.5.2 Dependence of the VP of the efforts on the reference frame 96 5.5.3 VP of zero moment field efforts exerted on a system of rigid bodies 96 5.5.4 VP of inter-efforts between the rigid bodies of a system 96 5.5.5 The specific case of the inter-efforts between two rigid bodies 97 5.6 Summary of the cases where the VV and VP are independent of the reference frame 98 5.7 VP of efforts expressed as a linear form of the qi∗99 5.8 Potential 101 5.8.1 Definition 101 5.8.2 Examples of potential 101 5.9 VP of the quantities of acceleration 108 6 Lagrange’s Equations 111 6.1 Choice of the common reference frame R0 111 6.2 Lagrange’s equations 112 6.3 Review and the need to model joints 115 6.4 Existence and uniqueness of the solution 116 6.5 Equations of motion 118 6.6 Example 1 118 6.7 Example 2 120 6.7.1 Reduced parameterization 120 6.7.2 Total parameterization 121 6.7.3 Comparing the two parameterizations 122 6.8 Example 3 123 6.8.1 Independent parameterization 124 6.8.2 Total parameterization 126 6.8.3 Comparing the two parameterizations 127 6.9 Working in a non-Galilean reference frame 127 7 Perfect Joints 131 7.1 VFs compatible with a mechanical joint 132 7.1.1 Definition 132 7.1.2 Generalizing the definition of a compatible VVF 134 7.1.3 Example 1 for VVFs compatible with a mechanical joint 135 7.1.4 Example 2 136 7.1.5 Example 3: particle moving along a hoop rotating around a fixed axis 137 7.2 Invariance of the compatible VVFs with respect to the choice of the primitive parameters 139 7.2.1 Context 139 7.2.2 Relationships between the real quantities resulting from the two parameterizations 140 7.2.3 Relationships between the virtual quantities resulting from the two parameterizations 141 7.2.4 Identity between the VVFs associated with the two parameterizations and compatible with a mechanical joint 143 7.2.5 Example 145 7.3 Invariance of the compatible VVFs with respect to the choice of the retained parameters 148 7.3.1 Context 148 7.3.2 Relationships between the real quantities resulting from the two parameterizations 150 7.3.3 Relationships between the virtual quantities resulting from the two parameterizations 151 7.3.4 Identity between the VVFs associated with the two paramaterizations and compatible with a mechanical joint 153 7.3.5 Example 1 155 7.3.6 Example 2 156 7.3.7 Example 3: particle moving along a hoop rotating around a fixed axis 156 7.4 Invariance of the compatible VVFs with respect to the choice of the parameterization 157 7.5 Perfect joints 158 7.5.1 Definition of a perfect joint 158 7.5.2 Example 1 160 7.5.3 Example 2 161 7.5.4 Example 3 162 7.5.5 Example 4 165 7.6 Example: a perfect compound joint 167 7.6.1 Perfect combined joint 168 7.6.2 Superimposition of two perfect elementary joints 169 8 Lagrange’s Equations in the Case of Perfect Joints 173 8.1 Lagrange’s equations in the case of perfect joints and an independent parameterization 174 8.1.1 Lagrange’s equations 174 8.1.2 Review 174 8.1.3 Particular case 175 8.2 Lagrange’s equations in the case of perfect joints and in the presence of complementary constraint equations 175 8.2.1 Lagrange’s equations with multipliers 176 8.2.2 Practical calculation using Lagrange’s multipliers 178 8.2.3 Review 180 8.2.4 Remarks 180 8.3 Example: particle on a rotating hoop 181 8.3.1 Independent parameterization 182 8.3.2 Reduced parameterization no. 1 183 8.3.3 Reduced parameterization no. 2 184 8.3.4 Calculation of the engine torque 185 8.4 Example: rigid body connected to a rotating rod by a spherical joint (no. 1) 187 8.5 Example: rigid body connected to a rotating rod by a spherical (joint no. 2) 189 8.5.1 Total parameterization 189 8.5.2 Independent parameterization 191 8.6 Example: rigid body subjected to a double contact 191 8.6.1 Preliminary analysis 192 8.6.2 Independent parameterization 194 8.6.3 Reduced parameterization 196 9 First Integrals 199 9.1 Painlevé’s first integral 199 9.1.1 Painlevé’s lemma 199 9.1.2 Painlevé’s first integral 201 9.2 The energy integral: conservative systems 203 9.2.1 Energy considerations in addition to the energy integral 204 9.3 Example: disk rolling on a suspended rod 205 9.4 Example: particle on a rotating hoop 208 9.5 Example: a rigid body connected to a rotating rod by a spherical joint (no. 1) 208 9.5.1 First integrals via Newtonian mechanics 209 9.6 Example: rigid body connected to a rotating rod by a spherical joint (no. 2) 209 9.7 Example: rigid body subjected to a double contact 210 9.7.1 Using Newtonian mechanics to find a first integral 211 10 Equilibrium 213 10.1 Definitions 213 10.1.1 Absolute equilibrium 213 10.1.2 Parametric equilibrium 214 10.2 Equilibrium equations 215 10.2.1 List of equations and unknowns 218 10.2.2 The explicit presence of time in equilibrium equations 218 10.3 Equilibrium equations in the case of perfect joints and independent parameterization 219 10.3.1 List of equations and unknowns 220 10.4 Equilibrium equations in the case of perfect joints and in the presence of complementary constraint equations 221 10.4.1 List of equations and unknowns 222 10.5 Stability of an equilibrium 223 10.6 Example: equilibrium of a jack 224 10.7 Example: equilibrium of a lifting platform 225 10.8 Example: equilibrium of a rod in a gutter 227 10.9 Example: existence of ranges of equilibrium positions 229 10.10 Example: relative equilibrium with respect to a rotating reference frame 230 10.11 Example: equilibrium in the presence of contact inequalities 232 10.12 Calculating internal efforts 236 10.13 Example: internal efforts in a truss 236 10.13.1 Tension force in bar A’A 236 10.13.2 Tension force in bar B’B 238 10.14 Example: internal efforts in a tripod 240 11 Revision Problems 243 11.1 Equilibrium of two rods 243 11.1.1 Analysis using Newton’s law 244 11.2 Equilibrium of an elastic chair 245 11.3 Equilibrium of a dump truck 246 11.4 Equilibrium of a set square 248 11.5 Motion of a metronome 250 11.5.1 Equation of motion 250 11.5.2 First integral 251 11.5.3 The case of small oscillations 251 11.5.4 Case where the base S may slide without friction on the table T 251 11.5.5 First integral 252 11.6 Analysis of a hemispherical envelope 252 11.6.1 Studying the static equilibrium 253 11.6.2 Studying the oscillatory motion 254 11.7 A block rolling on a cylinder 254 11.7.1 Studying the equilibrium 256 11.7.2 Dynamic analysis 257 11.7.3 Case of small oscillations 257 11.8 Disk welded to a rod 257 11.8.1 First parameterization 258 11.8.2 First integral 259 11.8.3 Second parameterization 259 11.8.4 Third parameterization 261 11.9 Motion of two rods 261 11.9.1 Equations of motion 262 11.9.2 Relative equilibrium 264 11.10 System with a perfect wire joint 264 11.10.1 Lagrange’s equations 265 11.10.2 First integral 267 11.11 Rotating disk–rod system 268 11.11.1 Independent parameterization 268 11.11.2 Total parameterization 269 11.11.3 Engine torque 271 11.12 Dumbbell 271 11.12.1 Equations set 272 11.12.2 First integrals 273 11.12.3 Analysis with specific initial conditions 275 11.12.4 Relative equilibrium 275 11.13 Dumbbell under engine torque 275 11.13.1 Independent parameterization 276 11.13.2 Painlevé’s first integral 277 11.13.3 Total parameterization 277 11.14 Rigid body with a non-perfect joint 278 11.14.1 Equations set 279 11.14.2 Solving the equations set 281 11.14.3 Power of the engine and work dissipated through friction 281 Appendix 1 283 Appendix 2 287 Bibliography 299 Index 301

Read more less

Book SynopsisFlows with chemical reactions can occur in various fields such as combustion, process engineering, aeronautics, the atmospheric environment and aquatics.The examples of application chosen in this book mainly concern homogeneous reactive mixtures that can occur in propellers within the fields of process engineering and combustion:– propagation of sound and monodimensional flows in nozzles, which may include disequilibria of the internal modes of the energy of molecules;– ideal chemical reactors, stabilization of their steady operation points in the homogeneous case of a perfect mixture and classical instruments of experimental and theoretical analysis such as population balances, and the distribution of residence and passage times;– laminar and turbulent flames, separating those which are premixed from those which are not and which do not exhibit the same mechanisms, but which also occur in the case of triple flames.Flows and Chemical Reactions in Homogeneous Mixtures provides information on dimensional analysis, statistical thermodynamics with coupling between internal modes and chemical reactions, the apparition and damping of fluid turbulence as well as its statistical processing, bifurcations, flames in a confined medium and diffusion. Contents 1. Flows in Nozzles.2. Chemical Reactors.3. Laminar and Turbulent Flames.Appendix 1. Dimensionless Numbers, Similarity.Appendix 2. Thermodynamic Functions.Appendix 3. Concepts of Turbulence.Appendix 4. Thermodynamic functions for a mixture in disequilibrium.Appendix 5. Notion of bifurcation.Appendix 6. Confined flame.Appendix 7. Limits of Validity of the First-order Expansions for Diffusion Flames.Table of ContentsSymbols ix Preface xxiii Chapter 1. Flows in Nozzles 1 1.1. Sound propagation in the presence of chemical reactions 1 1.1.1. Thermodynamic considerations 2 1.1.2. Sound propagation in a mono-reactive medium 7 1.1.3. Sound propagation in a multi-reactive medium 12 1.2. Relaxed flows in nozzles 26 1.2.1. Calculation of a continuous flow with a recombination-dissociation reaction in a de Laval nozzle 27 1.2.2. Asymptotic study of the transonic zone of a continuous monodimensional flow in a de Laval nozzle 31 1.3. Flows in thermal and chemical non-equilibrium 35 1.3.1. Balance equations and closure relations in the presence of thermal and chemical non-equilibria 35 1.3.2. Application 37 1.4. Conclusion about flows in nozzles 45 Chapter 2. Chemical Reactors 47 2.1. Ideal reactors, real reactors, balance equations 48 2.1.1. Ideal chemical reactors 48 2.1.2. Balance equations for chemical reactors 50 2.2. Perfectly mixed homogeneous chemical reactors 55 2.2.1. Equations for a perfectly stirred homogeneous chemical reactor 55 2.2.2. Steady regimes in perfectly stirred homogeneous chemical reactors 59 2.2.3. Stability of operating points in the perfectly stirred homogeneous chemical reactor 61 2.3. Tubular reactor 67 2.3.1. Plug flow reactor 68 2.3.2. Reactor with axial mixing 70 2.3.3. Reactor with radial mixing 73 2.4. Residence time distribution 74 2.4.1. Balance equations 74 2.4.2. Perfectly stirred homogeneous reactors in a steady regime 76 2.4.3. Plug flow reactors 76 2.4.4. Poiseuille flow 76 2.4.5. Real reactors 78 Chapter 3. Laminar and Turbulent Flames 79 3.1. Laminar premixed combustion 79 3.1.1. Rankine-Hugoniot theory 80 3.1.2. Velocity and structure of the plane adiabatic laminar and steady premixed flame 87 3.1.3. Other examples of a steady laminar premixed flame 91 3.2. Laminar non-premixed combustion 95 3.2.1. Burke–Schumann problem 95 3.2.2. Other examples of diffusion flames 98 3.3. Turbulent combustion 104 3.3.1. Averaged balance equation for turbulent combustion 105 3.3.2. Premixed turbulent combustion regimes 107 3.3.3. Non-premixed turbulent combustion regimes 110 3.3.4. Models of turbulent combustion 112 3.3.5. LESs in combustion 119 3.3.6. Triple flames 121 APPENDICES 125 Appendix 1. Dimensionless Numbers, Similarity 127 A1.1. Fundamentals of dimensional analysis: groups 128 A1.1.1. Basic considerations 128 A1.1.2. Vaschy–Buckingham theorem (1890) or Π theorem 129 A1.1.3. Practical advantage to dimensional analysis 130 A1.1.4. Example of application: head loss in a cylindrical pipe 130 A1.2. Similarity 132 A1.2.1. Definition 132 A1.2.2. Application: condition of similarity in a soft balloon placed in a current of air with a given velocity 133 A1.3. Analytical searching for solutions to a heat transfer problem (self-similar solution) 135 A1.4. Some dimensionless numbers 137 Appendix 2. Thermodynamic Functions 141 A2.1. General points 141 A2.2. Translational motion 142 A2.3. Internal motions 143 A2.3.1. Monatomic species 143 A2.3.2. Diatomic species 145 A.2.3.3. Linear polyatomic species 146 A2.3.4. Nonlinear polyatomic species 147 Appendix 3. Concepts of Turbulence 149 A3.1. Experimental demonstration 151 A3.1.1. Reynolds’ experiment 151 A3.1.2. Viscous flow over a smooth plane plate 152 A3.1.3. Effect of roughness of the plate 153 A3.1.4. Effect of turbulence on chemical reactivity 153 A3.2. Apparition and damping of turbulence 154 A3.2.1. Instability between two superposed fluids 154 A3.2.2. Instability of a fluid between two rotating cylinders 158 A3.2.3. Instability of a premixed flame 165 A3.2.4. Damping of turbulence 169 A3.3. Classic turbulence (RANS model) 170 A3.3.1. Turbulent transfer and chemical kinetics coefficients 170 A3.3.2. Remarks about averages and scales 176 A3.3.3. models (closure for transfer terms) 178 A3.3.4. Spectral analysis and Kolmogorov’s theory 181 A3.4. Ideas about large eddy simulation 185 A3.4.1. Filtering 187 A3.4.2. Filtered balance equations for a non-reactive incompressible fluid 189 A3.4.3. Closure relations for the filtered balance equations 190 A3.5. Conclusion 193 Appendix 4. Thermodynamic functions for a mixture in disequilibrium 195 A4.1. Thermodynamics 195 A4.2. Chemistry 197 A4.3. Vibration 197 Appendix 5. Notion of bifurcation 199 Appendix 6. Confined flame 201 Appendix 7. Limits of Validity of the First-order Expansions for Diffusion Flames 203 A7.1. Burke–Schumann flame 203 A7.2. Juxtaposed oxidizer/fuel flows from rectangular burners 204 Bibliography 207 Index 219

Read more less

Book SynopsisThis book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the Helmholtz-Hodge decomposition plays an important role.Trade Review"This book develops a new and original approach to mechanics." (Zentralblatt MATH, 1 June 2015)Table of ContentsPREFACE ix LIST OF SYMBOLS xv INTRODUCTION xxi CHAPTER 1. FRAMEWORK OF DISCRETE MECHANICS 1 1.1. Frames of reference and uniform motions 1 1.2. Concept of a Discrete Medium 4 1.2.1. Vectors and components 6 1.2.2. Physical meaning of the differential operators 8 1.2.3. Use of the theorems of differential geometry 10 1.2.4. Two essential properties 12 1.2.5. Tensorial values 17 1.2.6. The scalar and vectorial potentials 19 1.3. The physical characteristics 20 1.4. Equilibrium stress state 22 1.4.1. Two examples of mechanical equilibrium 25 1.5. Thermodynamic non-equilibrium 26 1.5.1. Forces and fluxes 29 1.6. Conservation of mass 30 CHAPTER 2. MOMENTUM CONSERVATION 33 2.1. Classification of forces 33 2.2. Three fundamental experiments 35 2.2.1. Equilibrium in a glass of water 35 2.2.2. Couette flow 44 2.2.3. Poiseuille flow 47 2.3. Postulates 51 2.4. Modeling of the pressure forces 52 2.5. Modeling of the viscous forces 57 2.5.1. Modeling of the viscous effects of volume 57 2.5.2. Modeling of the viscous surface effects 59 2.5.3. Stress state 62 2.6. Objectivity 64 2.7. Discrete motion balance equation 67 2.7.1. Fundamental law of dynamics 67 2.7.2. Eulerian step 73 2.7.3. Mechanical equilibrium 74 2.8. Formulation in terms of density and temperature 78 2.9. Similitude parameters 81 2.9.1. Impact on the surface of a liquid 85 2.10. Hypercompressible media 88 CHAPTER 3. CONSERVATION OF HEAT FLUX AND ENERGY 91 3.1. Introduction 91 3.2. Conservation of flux 92 3.3. Conservation of energy 95 3.3.1. Conservation of total energy 95 3.3.2. Conservation of kinetic energy 97 3.3.3. Conservation of the internal energy 98 3.4. Discrete equations for the flux and the energy 99 3.5. A simple heat-conduction problem 100 3.5.1. Case of anisotropic materials 102 CHAPTER 4. PROPERTIES OF DISCRETE EQUATIONS 105 4.1. A system of equations and potentials 105 4.2. Physics represented 107 4.2.1. Poiseuille flow and potentials 110 4.2.2. Celerity and maximum velocity 112 4.2.3. Remarks about turbulence 113 4.3. Boundary conditions 114 4.3.1. Contact surface 114 4.3.2. Shockwaves 117 4.3.3. Edge conditions 118 4.3.4. Slip condition 119 4.3.5. Capillary effects 120 4.3.6. Thermal boundary conditions 124 4.4. Penalization of the potentials 125 4.5. Continua and discrete mediums 129 4.5.1. Differences with the Navier–Stokes equation 129 4.5.2. Dissipation 133 4.5.3. Case of rigidifying motions 135 4.5.4. An example of the dissipation of energy 137 4.6. Hodge–Helmholtz decomposition 139 4.7. Approximations 141 4.7.1. Bernoulli’s law 141 4.7.2. Irrotational flow 143 4.7.3. Inviscid fluid 144 4.7.4. Incompressible flow 145 4.8. Gravitational waves 147 4.9. Linear visco-elasticity 150 4.9.1. Viscous dissipation in a visco-elastic medium 153 4.9.2. Dissipation of longitudinal waves in a visco-elastic medium 155 4.9.3. Consistency with Continuum Mechanics 156 4.9.4. Pure compression 159 4.9.5. Pure shear stress 160 4.9.6. Bingham fluid 162 CHAPTER 5. MULTIPHYSICS 165 5.1. Extensions to other branches of physics 165 5.1.1. Coupling between a fluid and a porous medium 167 5.2. Flow around a cylinder in an infinite medium 169 5.2.1. Darcian model 170 5.2.2. Stokes model 174 5.2.3. Model of an ideal fluid 175 5.2.4. Brinkman model 176 5.3. Fluid statics 178 5.3.1. Perfect gas in isothermal evolution 179 5.3.2. Perfect gas in adiabatic evolution 181 5.4. Injection of a gas into a cavity 183 5.4.1. Isothermal injection 184 5.4.2. Adiabatic injection 185 5.5. Nonlinear wave propagation 188 5.5.1. Sod shock tube 190 5.6. Thermo-acoustics 192 5.6.1. Heating of a cavity filled with air 193 5.7. Natural convection in an enclosed cavity 198 5.8. Multi-component transport 200 5.9. Modeling of phase change 203 5.10. Critical opalescence 207 5.11. Conclusions regarding the multiphysics approach 209 APPENDIX 211 BIBLIOGRAPHY 215 INDEX 219

Read more less

Book SynopsisThis resource covers all areas of interest for the practicing engineer as well as for the student at various levels and educational institutions. It features the work of authors from all over the world who have contributed their expertise and support the globally working engineer in finding a solution for today‘s mechanical engineering problems. Each subject is discussed in detail and supported by numerous figures and tables.Table of ContentsPart A Fundamentals: .- Introduction to Mathematics.- Mechanics.- Thermodynamics.- Part B Materials: .- Atomic Structure and Microstructure Characterization.- Mechanical and Physical Properties.- Corrosion and Corrosion Resistance.- Nondestructive Inspection.- Engineering Materials and their Properties.- Tribology.- Part C Manufacturing: .- Casting.- Metal Forming.- Machining Processes.- Assembly, Disassembly, Joining Techniques.- Precision Machinery Using MEMS Technology.- Measuring and Quality Control.- Part D Machine and Systems Design: .- Machine Elements.- Engineering Design.- Piston Machines.- Pressure Vessels and Heat Exchangers.- Turbomachinery.- Conveying and Construction Machinery.- Part E Transportation – Mobility: .-Trends in mobility and transportation.- Automotive Engineering.- Railway Systems - Railway Engineering.- Aerospace Engineering.- Ships and Maritime Transportation.- Part F Related Engineering Fields: .- Electrical Engineering.- Power Generation.- Annex: General Tables.

Read more less

Book SynopsisThis research monograph presents a new dynamical framework for the study of secular morphological evolution of galaxies along the Hubble sequence. Classical approaches based on Boltzmann’s kinetic equation, as well as on its moment-equation descendants the Euler and Navier-Stokes fluid equations, are inadequate for treating the maintenance and long-term evolution of systems containing self-organized structures such as galactic density-wave modes. A global and synthetic approach, incorporating correlated fluctuations of the constituent particles during a nonequilibrium phase transition, is adopted to supplement the continuum treatment. The cutting-edge research combining analytical, N-body simulational, and observational aspects, as well as the fundamental-physics connections it provides, make this work a valuable reference for researchers and graduate students in astronomy, astrophysics, cosmology, many-body physics, complexity theory, and other related fields. Contents Dynamical Drivers of Galaxy Evolution N-Body Simulations of Galaxy Evolution Astrophysical Implications of the Dynamical Theory Putting It All Together Concluding Remarks Appendix: Relation to Kinetics and Fluid MechanicsTable of ContentsContent Preface page 1 Introduction 1.1 Observational Background 1.2 Theoretical Background 1.3 Organization of the Material 2 Drivers of Secular Morphological Evolution of Galaxies 2.1 Motivations for the Theoretical Approach 2.2 Density Wave Crest as the Site of Gravitational Instability 2.3 Potential-Density Phase Shifts for Density Wave Modes 2.4 Linear Regime and Quasi-Steady State of the Wave Modes 2.5 Torque Coupling and Angular Momentum Transport 2.6 Rates of Secular Evolution 2.7 Relation to “Broadening of Resonances” 2.8 In a Nutshell 3 Verification of Analytical Results through N-Body Simulations 3.1 Overview of the N-Body Simulations of Disk Galaxies 3.2 Simulation Codes and Basic State Specifications 3.3 Signature of Collisionless Shock in N-Body Spirals 3.4 Modal Nature of a Spontaneously-Formed Pattern 3.5 Qualitative Signature of Secular Mass Redistribution 3.6 Longevity of the Spiral Modes 3.7 Role of Gas 3.8 Implication on Orbits as “Building Blocks” 3.9 Second Generation Tests 4 Astrophysical Implications of the New Dynamical Theory 4.1 Motivations and General Outline 4.2 Potential-Density Phase Shift (PDPS) Method for CR Determination 4.3 Secular Mass Migration and Bulge Building 4.4 Secular Heating and The Age-Velocity-Dispersion Relation 4.5 Secular Heating and the Size-Linewidth Relation 4.6 Other Characteristics of the Milky Way Galaxy and External Galaxies 4.7 Universal Rotation Curve 4.8 Secular Evolution and the Maintenance of Galaxy Scaling Relations 4.9 Butcher-Oemler Effect and Evolution of Cluster Galaxies 4.10 Secular Evolution and the Origin of Color-Magnitude Relation 4.11 An Example of Secular Evolution in Interacting Galaxies 4.12 Black-Hole-Mass and Bulge-Mass Correlation 5 Putting in All Together: What We Have Learned So Far 5.1 Reexamine the Foundations 5.2 Role of Basic State Specification 5.3 Broader Implications 5.4 Implications on the Cosmological Evolution of Galaxies 6 Concluding Remarks 7 Appendix. Nonequilibrium Phase Transition and Classical Mechanics 7.1 Foundation of Kinetic Theory: the Boltzmann Equation 7.2 From Kinetic Theory to Fluid Mechanics 7.3 Nonequilibrium Phase Transition and Galaxy Evolution 7.4 The Proper Choice of Hierarchies 8 References

Read more less

Book SynopsisThis book focuses on the mechanical properties and performance of products made of fiber-based materials. It helps students to develop skills for solving problems of product performance and engineering challenges in product development. Organized with a problem-based approach - practical examples of product performance are presented and the relevant mechanics are analyzed to deduce which material properties control the performance. The new edition covers state-of-the-art and green technologies as modeling of fiber networks and applications of nanocellulose.

Read more less

Book SynopsisThis book is for engineers and students of aerospace, materials and mechanical engineering. It covers the transition from aluminum to composite materials for aerospace structures and includes advanced analyses used in industries. New in the 2nd Edition is material on morphing structures, large deflection plates, nondestructive methods, vibration correlation technique for shear loaded plates, vibrations to measure physical properties, and more.

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisDieses Lehrbuch bietet Studierenden der ersten Semester eine Einführung in die Theoretische Physik sowie die dazu erforderlichen mathematischen Werkzeuge. Parallel zu den Inhalten der Klassischen Mechanik lernen Sie die nötige Mathematik gleich mit – und auch die Denkweise in der Theoretischen Physik kennen. Unter sorgfältiger Berücksichtigung des Wissensstands von Studienanfängern wird eine ausführliche, schrittweise Darstellung von allen Herleitungen und Beispielen geboten. Dabei werden Ihnen nicht nur die analytischen Lösungsverfahren gezeigt, sondern Sie erhalten auch einen Einblick in die große Bedeutung von computergestützten, numerischen Verfahren. Das Buch beginnt mit den Leitbegriffen des Zustands und der Bewegungsgleichung, worauf aufbauend die Struktur der Newton‘schen Mechanik in leicht nachvollziehbarer Art und Weise vermittelt wird. Als dazugehörige mathematische Themen werden komplexe Zahlen, Vektoren und Matrizen, Taylor-Reihen, gewöhnliche Differenzialgleichungen, Fourier-Reihen, partielle Ableitungen und Elemente der Vektoranalysis behandelt. Ebenso finden Sie in diesem Buch eine Untersuchung elementarer Erhaltungssätze als auch deren Anwendung auf physikalische Fragestellungen wie z.B. die Begründung der Kepler‘schen Gesetze.Table of ContentsVorwort.- 1 Grundkonzepte.- 2 Beschreibung der Bewegung von Massenpunkten.- 3 Dynamische Gesetze für einen Massenpunkt.- 4 Gewöhnliche Differenzialgleichungen.- 5 Fourier-Reihen.- 6 Nichtlineare Dynamik.- 7 Systeme mit mehr als einem Teilchen.- 8 Partielle Ableitungen.- 9 Energie.- 10 Zweiteilchenproblem mit Gravitationskraft.- 11 Drehbewegungen.- 12 Spezielle Relativitätstheorie - 13 Anhänge: A Computerprogramm zu Kap. 1.- B Computerprogramm zu Kap. 6.- Index.

Read more less

Book SynopsisThis second volume on technology is mainly devoted to three prize-winning memoirs, answering questions related to ship-building which were proposed by the French Académie Royale des Sciences in the years 1737, 1755, and 1757. The volume hosts two further items: a popularizing text on astronomy from 1723, and the theory of the spiral pump, a technical item from 1772. In the introductory part of the volume every memoir is analysed and extensively summarized, so the reader should obtain a clear view of the content in modern terms.Table of ContentsGeneral Introduction.- Introductions to the contained original works.- Discours lû dans l'Assemblée.- Réfléxions sur la meilleure figure a donner aux Ancres....- Recherches sur la maniere la plus avantageuse....- Principes Hydrostatiques et Méchaniques....- Expositio theoretica singularis machinae hydraulicae tiguri Helvetiorum exstructae

Read more less

Book SynopsisIn his conversational style, Anthony Zee examines the nature of gravity and its role in our universe. Zee starts from a birthday gift that Albert Einstein received on his seventy-sixth birthday that worked on the main principle in his theory of gravity. From there Zee leads the reader through the implications of Einstein''s theory and its influence on modern physics. Einstein''s Universe in a witty and accessible style also examines how the theory of gravity has shaped our understanding of how the universe began, the development of stars and galaxies, and the nature of space itself. The new Oxford edition will include a new afterword by the author that will bring the subject matter up to date.Trade Review"An extraordinary writer: playful, inspired, and brilliant."--Publishers Weekly "Zee writes with wry, poetic humor.... It's as if he is conducting an easygoing conversation with his audience...a scientist who can clearly evoke the imagery hidden within a mathematical equation, treating some rather formidable material with enthusiasm and delight."--The New York Times "A brash, breezy, and authoritative discussion...a fascinating book."--The Washington Post "Through his engaging, conversational style, Zee...succeeds in informing while entertaining the reader with disarming stories."--The San Francisco Chronicle "Among the numerous authors who have written popularizations of contemporary physics, none is better than Zee at explaining things simply."--Library Journal "An extraordinary writer: playful, inspired, and brilliant."--Publishers Weekly "Zee writes with wry, poetic humor.... It's as if he is conducting an easygoing conversation with his audience...a scientist who can clearly evoke the imagery hidden within a mathematical equation, treating some rather formidable material with enthusiasm and delight."--The New York Times "A brash, breezy, and authoritative discussion...a fascinating book."--The Washington Post "Through his engaging, conversational style, Zee...succeeds in informing while entertaining the reader with disarming stories."--The San Francisco Chronicle "Among the numerous authors who have written popularizations of contemporary physics, none is better than Zee at explaining things simply."--Library Journal "How many times have you actually laughed out loud reading a book on physics? If your answer is 'Never!', then you should pick up a copy of An Old Man's Toy [Einstein's Universe].... Many books on physics can be very interesting, but it is rare to find one that is actually fun to read. I thoroughly enjoyed reading it and would recommend it to anyone. A. Zee has a style of writing that makes one keep turning the pages.... [The book] is interesting, playfully written, and very readable. Don't pass it up."--The Science Teacher "A. Zee is that rare creature: a physicist who knows how to tell a story. (His previous book) Fearful Symmetry was...lucid, entertaining. In this reprise, Zee is just as fascinating, and even funnier...with his prankish good humor and gifts for simplifying the complicated.... An Old Man's Toy [Einstein's Universe] is both a delightful read and a faithful yet accessible look at an avant-garde that is far more revolutionary than any downtown's club scene...it is too rare an opportunity to miss."--Life of New YorkTable of ContentsPROLOGUE: THE APPLE AND THE MOON ; I. THE RISE OF GRAVITY ; II. THE EXPANDING UNIVERSE ; III. STRUCTURES OUT OF THE VOID ; IV. THE MYSTERY OF GRAVITY

Read more less

Book SynopsisGives a physical treatment of the kinetic theory of gases and magnetoplasmas, using mean-free-path arguments when possible and identifying problem areas where received theory has either failed or fallen short of expectations. L.C. Woods has also written "The Thermodynamics of Fluid Systems".Trade Reviewthe book presents a treatment of the kinetic theory of gases and magnetoplasmas in such a way that it covers the standard material in a way as simple as possible .,.. The book seems to radiate a deep conviction - which is appreciated by the reviewer - that the development of the kinetic theory needs not only calculational skills and computational magic in evaluating the content of the theory in model arrangements, but equally, if not in excess, deep insight into the physical processes. * I. Abonyi, Besprechungsbelege, February 1994 *Table of Contents1. Basic concepts ; 2. The Maxwellian velocity distribution ; 3. Elementary kinetic theory ; 4. Particle diffusion ; 5. Intermediate kinetic theory ; 6. Advanced kinetic theory ; 7. Boltzmann's kinetic equation ; 8. Second-order kinetic theory ; 9. Dynamics of charged particles ; 10. Kinetic theory for magnetoplasmas ; 11. Transport across strong magnetic fields ; Appendix ; References ; Index

Read more less

Book SynopsisThis book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th- to 20th-Century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann''s influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion.Boltzmann was the centre of a scientific upheaval, and he has been proved right on many crucial issues. He anticipated Kuhn''s theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also Trade ReviewIt is valuable, not only for the wealth and scope of information it provides, but for offering an up-to-date view, accessible to all, of Boltzmann's scientific ideas. * Studies in History and Philosophy of Modern Physics *Carlo Cercignani has made an important contribution to our understanding of the man and his work in the context of his times... Much of the book will be interesting for the general reader. * George Fleck, The Chemical Intelligencer *I can warmly recommend the book to everybody who is interested in the history of science. * Dieter Flamm, Physics World *Table of ContentsForeword ; Preface ; Introduction ; 1. A short biography of Ludwig Boltzmann ; 2. Physics before Boltzmann ; 3. Kinetic theory before Boltzmann ; 4. The Boltzmann equation ; 5. Time irreversibility and the H-theorem ; 6. Boltzmann's relation and the statistical interpretation of entropy ; 7. Boltzmann, Gibbs and equilibrium statistical mechanics ; 8. The problem of polyatomic molecules ; 9. Boltzmann's contributions to other branches of physics ; 10. Boltzmann as a philosopher ; 11. Boltzmann and his contemporaries ; 12. The influence of Boltzmann's ideas on the science and technology of the twentieth century ; Epilogue ; Chronologys ; "A German professor's journey to Eldorado" ; Appendices

Read more less

Book SynopsisThe pendulum: a case study in physics is a unique book in several ways. Firstly, it is a comprehensive quantitative study of one physical system, the pendulum, from the viewpoint of elementary and more advanced classical physics, modern chaotic dynamics, and quantum mechanics. In addition, coupled pendulums and pendulum analogs of superconducting devices are also discussed. Secondly, this book treats the physics of the pendulum within a historical and cultural context, showing, for example, that the pendulum has been intimately connected with studies of the earth''s density, the earth''s motion, and timekeeping. While primarily a physics book, the work provides significant added interest through the use of relevant cultural and historical vignettes. This approach offers an alternative to the usual modern physics courses. The text is amply illustrated and augmented by exercises at the end of each chapter.Trade ReviewIn this well-illustrated treatment of the study of pendulum, Baker (Bryn Athyn College of the New Church) and Blackburn (Wilfrid Laurier U.) provide fascinating information about the history of the pendulum and what scientists thought it did, the revolution wrought by Foucault, the special cases of the torsion pendulum, the chaotic pendulum, the quantum pendulum, and coupled pendulums, the effects of superconductivity, and the most familiar to most of us, the pendulum clock. They include information on special interests in the appendices, such as the inverted pendulum and the longnow clock. * SciTech Book News *One of the delightful aspects of this book is its attention to historical detail. Not only does this add greatly to the enjoyment of reading it, it also gives a vivid impression of progress in our knowledge of the physical world, all too often absent in more focused and specialized works. * Contemporary Physics *The Pendulum presents insights and unusual approaches that will broaden the experience of undergraduate physics students. * Kenneth S. Krane, Physics Today *Table of Contents1. Introduction ; 2. Pendulums somewhat simple ; 3. Pendulums less simple ; 4. The Foucault pendulum ; 5. The torsion pendulum ; 6. The chaotic pendulum ; 7. Coupled pendulums ; 8. The quantum pendulum ; 9. Superconductivity and the pendulum ; 10. The pendulum clock ; A. Pendulum Q ; B. The inverted pendulum ; C. The double pendulum ; D. The cradle pendulum ; E. The long now clock ; F. The Blackburn pendulum

Read more less

Book SynopsisCombining solved standard and original physics problems from major American universities, this book equips graduate students with the knowledge necessary to pass the qualifying examination. It covers such topics as Mechanics; Relativity; Electrodynamics; Thermodynamics; Statistical Mechanics; and Quantum Mechanics.Table of ContentsMechanics: Falling Chain. Cat and Mouse Tug of War. Cube Bouncing off Wall. CueStruck Billiard Ball. Stability on Rotating Rollers. Swan and Crawfish. Mud from Tire. Car Down Ramp Up Loop. Pulling Strings. Thru Earth Train. String Oscillations. Hovering Helicopter. Astronaut Tether. Spiral Orbit. Relativity: Marking Sticks. Rockets in Collision. Photon Box. Cube's Apparent Rotation. Relativistic Rocket. Rapidity. Charge in Constant Electric Field. Charge in Electric Field and Flashing Satellites. Uniformly Accelerated Motion. Compton Scattering. Electrodynamics: Charge Distribution. Electrostatic Forces and Scaling. Dipole Energy. Charged Conducting Sphere in Constant Electric Field. Charge and Conducting Sphere. Charge and Conducting Sphere II. Conducting Cylinder and Line Charge. Spherical Void in Dielectric. Charge and Dielectric. Dielectric Cylinder in Uniform Electric Field. 125 additional problems. Index.

Read more less

Book SynopsisPulsed Systems: Design Principles.- Lumped Parameter Pulse Systems.- Pulse Generation Using Long Lines.- Physics of Pulsed Electrical Discharges.- The Vacuum Discharge.- The Pulsed Discharge in Gas.- Electrical Discharges in Liquids.- Properties of Coaxial Lines.- Solid-Insulated Coaxial Lines.- Liquid-Insulated Lines.- Vacuum Lines with Magnetic Self-Insulation.- Spark Gap Switches.- High-Pressure Gas Gaps.- Low-Pressure Spark Gaps.- Solid-State and Liquid Spark Gaps.- Generators with Plasma Closing Switches.- Generators with Gas-Discharge Switches.- Marx Generators.- Pulse Transformers.- Generators with Plasma Opening Switches.- Pulse Generators with Electrically Exploded Conductors.- Pulse Generators with Plasma Opening Switches.- Electron-Triggered Gas-Discharge Switches.- Pulse Power Generators with Solid-State Switches.- Semiconductor Closing Switches.- Semiconductor Opening Switches.- Pulse Power Generators in Circuits with Magnetic Elements.- Long Lines with Nonlinear ParameterTable of ContentsPreface Part 1: Pulsed Systems: Design Principles 1. Lumped Parameter Pulse Systems 2. Pulse Generation Using Long Lines Part 2: Physics of Pulsed Electrical Discharges 3. The Vacuum Discharge 4. The Pulsed Discharge in Gas 5. Electrical Discharges in Liquids Part 3: Properties of Coaxial Lines 6. Solid-Insulated Coaxial Lines 7. Liquid-Insulated Lines 8. Vacuum Lines with Magnetic Self-Insulation Part 4: Spark Gap Switches 9. High-Pressure Gas Gaps 10. Low-Pressure Spark Gaps 11. Solid-State and Liquid Spark Gaps Part 5: Generators with Plasma Closing Switches 12. Generators with Gas-Discharge Switches 13. Marx Generators 14. Pulse Transformers Part 6: Generators with Plasma Opening Switches 15. Pulse Generators with Electrically Exploded Conductors 16. Pulse Generators with Plasma Opening Switches 17. Electron-Triggered Gas-Discharge Switches Part 7: Pulse Power Generators with Solid-State Switches 18. Semiconductor Closing Switches 19 Semiconductor Opening Switches 20. Pulse Power Generators in Circuits with Magnetic Elements 21. Long Lines with Nonlinear Parameters Part 8: Electron Diodes and Electron-Diode-Based Accelerators 22. Large-Cross-Section Electron Beams 23. Annular Electron Beams 24. Dense Electron Beams and Their Focusing Part 9: High-Power Pulse Sources of Electromagnetic Radiation 25. High-Power X-Ray Pulses 26. High-Power Pulsed Gas Lasers 27. Generation of High-Power Pulsed Microwaves 28. Generation of Ultrawideband Radiation Pulses Index

Read more less

Book SynopsisI Introductory.- 1 Material constitution of rocks.- 2 Mechanical state.- 3 Change in mechanical state.- 4 Mechanical significance of structure.- II Forces in Rocks.- 5 Classes of forces.- 6 Stress on a plane.- 7 The stress ellipsoid, I.- 8 The stress ellipsoid, II.- 9 Mohr circle for stress.- 10 Tensor components of stress.- 11 Cauchy's formula, transformation of tensor components.- 12 Stress fields.- 13 Stress history.- III Deformation of Rocks.- 14 Distortion and deformation, measures of distortion.- 15 The strain ellipsoid.- 16 Mohr circle for infinitesimal strain.- 17 Mohr circle for finite strain.- 18 Displacement and deformation gradients.- 19 Tensor components of infinitesimal strain, I.- 20 Tensor components of infinitesimal strain, II.- 21 Tensor components of finite strain, I.- 22 Tensor components of finite strain, II.- 23 Strain fields.- 24 Strain history.- IV Topics Involving Forces and Deformation.- 25 Hookean behavior.- 26 Newtonian behavior.- 27 Energy consumed in deforTable of ContentsI Introductory.- 1 Material constitution of rocks.- 2 Mechanical state.- 3 Change in mechanical state.- 4 Mechanical significance of structure.- II Forces in Rocks.- 5 Classes of forces.- 6 Stress on a plane.- 7 The stress ellipsoid, I.- 8 The stress ellipsoid, II.- 9 Mohr circle for stress.- 10 Tensor components of stress.- 11 Cauchy’s formula, transformation of tensor components.- 12 Stress fields.- 13 Stress history.- III Deformation of Rocks.- 14 Distortion and deformation, measures of distortion.- 15 The strain ellipsoid.- 16 Mohr circle for infinitesimal strain.- 17 Mohr circle for finite strain.- 18 Displacement and deformation gradients.- 19 Tensor components of infinitesimal strain, I.- 20 Tensor components of infinitesimal strain, II.- 21 Tensor components of finite strain, I.- 22 Tensor components of finite strain, II.- 23 Strain fields.- 24 Strain history.- IV Topics Involving Forces and Deformation.- 25 Hookean behavior.- 26 Newtonian behavior.- 27 Energy consumed in deformation.

Read more less

Book SynopsisClearly written in a conceptual language, it provides readers with an understanding of the dynamic behavior of the instrument, including structural and component dynamics, and various analytical models, such as discrete, finite element, and boundary element models.Trade ReviewFrom the reviews: „…[This is the only book] that deals with the engineering aspects of guitars. Thus it serves a real need for scientifically-oriented guitar makers and aficionados as well as those interested in a broad overview of the world of guitars… The overall broad view of the book makes good reading for those interested in the myriad details involve in constructing a string instrument and then evaluating it scientifically, as the author’s personal building experience and knowledge of a wide variety of guitar construction techniques are put to good use… a significant, commendable addition to the guitar literature in a very broad-ranging book on a very important string instrument."George Bissinger, East Carolina University, EXPERIMENTAL TECHNIQUES (May-June 2009)“French discusses whether the math models are … sufficient to capture the features of acoustic responses that are highly correlated with good sound quality. In conclusion … this book will help luthiers at all levels think more clearly about how to successfully manufacture guitars of high sound quality. The book … particularly valuable to students of guitar construction and repair. For the rest of us, this book makes interesting reading.” (Leo Beranek, International Journal of Acoustics and Vibration, Vol. 14 (2), 2009)“Why do guitars sound like they do, and how do you set about making one? These are central questions addressed … in this attractive new book. … The book is well written, and generously illustrated with interesting … graphs. … a unique and special addition to the literature, and it deserves to be widely read. For anyone contemplating construction of a guitar it will surely be indispensible. Physicists and engineers with musical inclinations, as well as guitar players … are likely to be fascinated.” (Peter V. E. McClintock, Contemporary Physics, Vol. 51 (6), 2010)Table of ContentsHistory of the Guitar.- Acoustics and Musical Theory.- Structure of the Guitar.- Dynamic Behavior.- Analytical Models.- Manufacturing Processes.- Sound Quality.- Guitar Electronics.- Unique Characteristics.

Read more less

Book SynopsisSeries Preface.- Preface to the Third Edition.- Linear Systems.- Nonlinear Systems: Local Theory.- Nonlinear Systems: Global Theory.- Nonlinear Systems: Bifurcation Theory.- References.- Additional References.- Index.Trade ReviewReviews from the first edition: “...The text succeeds admiraby ... Examples abound, figures are used to advantage, and a reasonable balance is maintained between what is proved in detail and what is asserted with supporting references ... Each section closes with a set of problems, many of which are quite interesting and round out the text material ... this book is to be highly recommended both for use as a text, and for professionals in other fields wanting to gain insight into modern aspects of the geometric theory of continuous (i.e., not discrete) dynamical systems.” MATHEMATICAL REVIEWSTable of ContentsSeries Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

Read more less

Book SynopsisRevised and updated, it includes expanded discussions of * the fundamentals of geostrophic turbulence * the theory of wave-mean flow interaction * thermocline theory * finite amplitude barocline instability.Trade ReviewFrom the reviews"The author has done a masterful job in presenting the theory with the necessary mathematical foundation, while keeping the physical aspects in clear view ... it is an outstanding introduction to a complex and important subject." (GEOPHYSICS)Table of ContentsPreliminaries * Fundamentals * Inviscid Shallow-Water Theory * Friction and Viscous Flow * Homogeneous Models of the Wind-Driven Oceanic Circulation * Quasigeostrophic Motion of a Stratified Fluid on a Sphere * Instability Theory * Ageostrophic Motion

Read more less

Book Synopsis1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- 1.4. The DoobMeyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- 2.5. The Markov Property.- 2.6. The Strong Markov Property and the Reflection Principle.- 2.7. Brownian Filtrations.- 2.8. Computations Based on Passage Times.- 2.9. The Brownian Sample Paths.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- 3.3. The Change-of-Variable Formula.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- 3.5. The Girsanov Theorem.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- 4.3. The One-Dimensional Heat Equation.- 4.4. The Formulas of Feynman and Kac.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- 5.3. Weak Solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- 5.5. A Study of the One-Dimensional Case.- 5.6. Linear Equations.- 5.7. Connections with Partial Differential Equations.- 5.8. Applications to Economics.- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy's Theory of Brownian Local Time.-6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- 6.3. Two Independent Reflected Brownian Motions.- 6.4. Elastic Brownian Motion.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.Trade ReviewSecond Edition I. Karatzas and S.E. Shreve Brownian Motion and Stochastic Calculus "A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."—MATHEMATICAL REVIEWSTable of Contents1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- A. Fundamental inequalities.- B. Convergence results.- C. The optional sampling theorem.- 1.4. The Doob—Meyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- A. The consistency theorem.- B. The Kolmogorov—?entsov theorem.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- A. Weak convergence.- B. Tightness.- C. Convergence of finite-dimensional distributions.- D. The invariance principle and the Wiener measure.- 2.5. The Markov Property.- A. Brownian motion in several dimensions.- B. Markov processes and Markov families.- C. Equivalent formulations of the Markov property.- 2.6. The Strong Markov Property and the Reflection Principle.- A. The reflection principle.- B. Strong Markov processes and families.- C. The strong Markov property for Brownian motion.- 2.7. Brownian Filtrations.- A. Right-continuity of the augmented filtration for a strong Markov process.- B. A “universal” filtration.- C. The Blumenthal zero-one law.- 2.8. Computations Based on Passage Times.- A. Brownian motion and its running maximum.- B. Brownian motion on a half-line.- C. Brownian motion on a finite interval.- D. Distributions involving last exit times.- 2.9. The Brownian Sample Paths.- A. Elementary properties.- B. The zero set and the quadratic variation.- C. Local maxima and points of increase.- D. Nowhere differentiability.- E. Law of the iterated logarithm.- F. Modulus of continuity.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- A. Simple processes and approximations.- B. Construction and elementary properties of the integral.- C. A characterization of the integral.- D. Integration with respect to continuous, local martingales.- 3.3. The Change-of-Variable Formula.- A. The Itô rule.- B. Martingale characterization of Brownian motion.- C. Bessel processes, questions of recurrence.- D. Martingale moment inequalities.- E. Supplementary exercises.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- A. Continuous local martingales as stochastic integrals with respect to Brownian motion.- B. Continuous local martingales as time-changed Brownian motions.- C. A theorem of F. B. Knight.- D. Brownian martingales as stochastic integrals.- E. Brownian functionals as stochastic integrals.- 3.5. The Girsanov Theorem.- A. The basic result.- B. Proof and ramifications.- C. Brownian motion with drift.- D. The Novikov condition.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- A. Definition of local time and the Tanaka formula.- B. The Trotter existence theorem.- C. Reflected Brownian motion and the Skorohod equation.- D. A generalized Itô rule for convex functions.- E. The Engelbert—Schmidt zero-one law.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- A. The mean-value property.- B. The Dirichlet problem.- C. Conditions for regularity.- D. Integral formulas of Poisson.- E. Supplementary exercises.- 4.3. The One-Dimensional Heat Equation.- A. The Tychonoff uniqueness theorem.- B. Nonnegative solutions of the heat equation.- C. Boundary crossing probabilities for Brownian motion.- D. Mixed initial/boundary value problems.- 4.4. The Formulas of Feynman and Kac.- A. The multidimensional formula.- B. The one-dimensional formula.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- A. Definitions.- B. The Itô theory.- C. Comparison results and other refinements.- D. Approximations of stochastic differential equations.- E. Supplementary exercises.- 5.3. Weak Solutions.- A. Two notions of uniqueness.- B. Weak solutions by means of the Girsanov theorem.- C. A digression on regular conditional probabilities.- D. Results of Yamada and Watanabe on weak and strong solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- A. Some fundamental martingales.- B. Weak solutions and martingale problems.- C. Well-posedness and the strong Markov property.- D. Questions of existence.- E. Questions of uniqueness.- F. Supplementary exercises.- 5.5. A Study of the One-Dimensional Case.- A. The method of time change.- B. The method of removal of drift.- C. Feller’s test for explosions.- D. Supplementary exercises.- 5.6. Linear Equations.- A. Gauss—Markov processes.- B. Brownian bridge.- C. The general, one-dimensional, linear equation.- D. Supplementary exercises.- 5.7. Connections with Partial Differential Equations.- A. The Dirichlet problem.- B. The Cauchy problem and a Feynman—Kac representation.- C. Supplementary exercises.- 5.8. Applications to Economics.- A. Portfolio and consumption processes.- B. Option pricing.- C. Optimal consumption and investment (general theory).- D. Optimal consumption and investment (constant coefficients).- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy’s Theory of Brownian Local Time.- 6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- A. The process of passage times.- B. Poisson random measures.- C. Subordinators.- D. The process of passage times revisited.- E. The excursion and downcrossing representations of local time.- 6.3. Two Independent Reflected Brownian Motions.- A. The positive and negative parts of a Brownian motion.- B. The first formula of D. Williams.- C. The joint density of (W(t), L(t), ? +(t)).- 6.4. Elastic Brownian Motion.- A. The Feynman—Kac formulas for elastic Brownian motion.- B. The Ray—Knight description of local time.- C. The second formula of D. Williams.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.

Read more less

Book SynopsisThe text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject.Trade Review From the reviews: "… The book contains some of the basic ideas of fluid mechanics in a mathematically attractive manner...has the very advantage of providing the solution of the differential equations using the new and modern techniques...the material is very well presented both the mathematical arguments as well as the physical input." PhysicaliaTable of ContentsPreface.- 1. The Equations of Motion: 1.1. Euler's Equations. 1.2. Rotation and Vorticity. 1.3. The Navier-Stokes Equations.- 2. Potential Flow and Slightly Viscous Flow: 2.1. Potential Flow. 2.2. Boundary Layers. 2.3. Vortex Sheets. 2.4. Remarks on Stability and Bifurcation.- 3. Gas Flow in One Dimension: 3.1. Characteristics. 3.2. Shocks. 3.3. The Riemann Problem. 3.4. Combustion Waves.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book SynopsisThis 2006 book is intended for undergraduate courses in dynamics. The work is a unique blend of conceptual, theoretical, and practical aspects of dynamics generally not found in dynamics books at the undergraduate level. In particular, in this book the concepts are developed in a highly rigorous manner and are applied to examples using a step-by-step approach that is completely consistent with the theory. In addition, for clarity, the notation used to develop the theory is identical to that used to solve example problems. The result of this approach is that a student is able to see clearly the connection between the theory and the application of theory to example problems. While the material is not new, instructors and their students will appreciate the highly pedagogical approach that aids in the mastery and retention of concepts. The approach used in this book teaches a student to develop a systematic approach to problem-solving.Trade Review“The book leads students from first principles through problem solving. It includes lots of detailed solutions to example problems, a wide range of possible homework problems, and beautiful figures and diagrams. The prose flows smoothly and is written with clarity.” Choice"All examples are worked in detail, are tied in well with the text, and are accompanied by excellent illustrations. These examples are a great aid to learning the material and will leave the student in good shape for solving the complex problems that will come up in the 'real world'." Mark D. Ardema, Santa Clara University, SIAM ReviewTable of Contents1. Introductory concepts; 2. Kinematics; 3. Kinetics of particles; 4. Kinetics of a system of particles; 5. Kinetics of rigid bodies; A. Principal-axis moments of inertia of homogeneous bodies; B. Identities, derivatives, integrals and gradient; C. Answers to selected problems; Bibliography.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less