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準晶數(shù)學彈性理論及應用（第二版）（英文版） 
定 價：198 元 叢書名：Mathematics Monograph Series
9 7 4 8 7 7 4 0 2 3 9 0 2 讀者對象:準晶數(shù)學彈性理論實踐者、研究者，相關(guān)專業(yè)教師、研究生、高年級本科生 
本書介紹了固體準晶彈性和軟物質(zhì)準晶彈性-流體動力學理論的應用，內(nèi)容包括晶體，經(jīng)典彈性基礎，固體準晶及其性質(zhì)，固體準晶彈性的物理基礎，一維準晶彈性和化簡，二維準晶彈性與化簡，三維準晶彈性和應用，準晶彈性與缺陷動力學，準晶彈性和缺陷的復分析，準晶彈性的變分原理和數(shù)值解，準晶彈性解的若干數(shù)學原理，固體準晶的非線性，固體準晶的斷裂理論，準晶流體動力學，軟物質(zhì)準晶的彈性-流體動力學及其應用。
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The first edition of this book was pubLished by Scienec Press， Beijing/Springer-Verlag， Heidelberg， in 2010 mainly concerning a mathematical theory of elasticity of solid quasicrystals， in which the Landau symmetry breaking and elementary excitation principle plays a central role. Bak， Lubensky and other pioneering researchers introduced a new elementary excitation-phason drawn from theory of incommensurate phase apart from the phonon elemetary excitation well-known in condensed matter physics.
Since 2004， the soft-matter quasicrystals with 12-fold symmetry have been observed in liquid crystals， colloids and polymers; in particular， 18-fold symmetry quasicrystals were observed in 2011 in colloids; this symmetry in quasicrystals is discovered for the first time. These observations belong to an important event of chemistry in twenty-first century and have attracted a great deal of attention of researchers， Readers are interested in many topics of the new area of study. However， accumulated experimental data related with mechanical behaviour of the new phase are very limited， there is the lack offundamental data， the mechanism of deformation and motion of the matter has not sufficiently been exploared after the discovery over one decade， and it leads to fundamental difficultis to the study. Due to these difficulties， an introduction to soft-matter qusicrystals is given in very brief in Major Appendix of this book. Though the new edition increases some new contents， the title of the book has not been changed， because the main part of which is still concemed with elasticity of solid quasicrystals， and only new chapter-Chap. 16-on hydrodynamics of quasicrystals is added; the introduction on soft-matter quasicrystals is very limited and listed in the Major Appendix. The changes of the contents of the first 15 chapters are not too great; we add some examples with application significance and exclude ones ofless practical meaning; a part of contents of Appendix A is moved into the Appendix of Chap. 11， and add a new appendix， i. e. Appendix C in the Major Appendix， in which some additional derivations of hydrodynamic equations of solid quasicrystals based on the Poisson bracket method are included， which may be referred by readers. Some type and typesetting errors and mistakes contained in the first edition are removed， but some new errors and mistakes might appear in the new edition; any criticisms from readers are warmly welcome! The author sincerely thanks the National Natural Science Foundation of China and the Alexander von Humbold Foundation of Germany for their support over the years. Due to the support of AvH Foundation， the author could visit the Max-Planck Institute for Microstructure Physics in Halle and the Institute for Theoretical Physics in University of Stuttgart in Germany; the cooperative work and discussions with Ptofs. U. Messerschmidt， H. -R. Trebin and Dr， C. Walz were helpful， especially cordial thanks due to Prof. U. Messerschmidt for his outstanding monograph "Dislocation Dynamics During Plastic Deformation" which helped the work of the present edition of the book. Thanks also to Profs T. C. Lubensky in University of Pennsylvania， Z. D. Stepen Cheng in University of Akron in USA and Xian Fang Li of Central South University in China for beneficial discussions and Hnd helps. At last， the author thanks the readers， their downloading， view， review and citation are very active， and this encourages me to improve the work.
Contents
1 Crystals1 1.1 Periodicity of Crystal Structure, Crystal Cell 1 1.2 Three-Dimensional LatticeTypes2 1.3 Symmetry and Point Groups 2 1.4 Reciprocal Lattice 5 1.5 Appendix of Chapter 1: Some Basic Concepts6 1.5.1 ConceptofPhonon6 1.5.2 Incommensurate Crystals 10 1.5.3 Glassy Structure 11 1.5.4 Mathematical Aspect of Group 11 References 12 2 Framework of Crystal Elasticity13 2.1 Review on Some Basic Concepts13 2.1.1 Vector13 2.1.2 Coordinate Frame 14 2.1.3 Coordinate Transformation 14 2.1.4 Tensor16 2.1.5 Algebraic Operation of Tensor 16 2.2 Basic Assumptions of Theory of Elasticity17 2.3 Displacement and Deformation17 2.4 Stress Analysis 19 2.5 Generalized Hooke’sLaw20 2.6 Elastodynamics, Wave Motion 24 2.7 Summary25 References 26 3 Quasicrystal and Its Properties27 3.1 Discovery of Quasicrystal 27 3.2 Structure and Symmetry of Quasicrystals 29 3.3 A Brief Introduction on Physical Properties of Quasicrystals 31 3.4 One-, Two-and Three-Dimensional Quasicrystals 32 3.5 Two-Dimensional Quasicrystals and Planar Quasicrystals 32 References 33 4 The Physical Basis of Elasticity of Solid Quasicrystals37 4.1 Physical Basis of Elasticity of Quasicrystals 37 4.2 Deformation Tensors38 4.3 Stress Tensors and Equations of Motion 40 4.4 Free Energy Density and Elastic Constants 42 4.5 Generalized Hooke’sLaw44 4.6 Boundary Conditions and Initial Conditions 44 4.7 A Brief Introduction on Relevant Material Constants of Solid Quasicrystals 46 4.8 Summary and Mathematical Solvability of Boundary Value or Initial-Boundary Value Problem47 4.9 Appendix of Chapter 4: Description on Physical Basis of Elasticity of Quasicrystals Based on the Landau Density WaveTheory48 References 53 5 Elasticity Theory of One-Dimensional Quasicrystals and Simplification 55 5.1 Elasticity of Hexagonal Quasicrystals55 5.2 Decomposition of the Elasticity into a Superposition of Plane and Anti-plane Elasticity58 5.3 Elasticity of Monoclinic Quasicrystals61 5.4 Elasticity of Orthorhombic Quasicrystals64 5.5 Tetragonal Quasicrystals 65 5.6 The Space Elasticity of Hexagonal Quasicrystals 66 5.7 Other Results of Elasticity of One-Dimensional Quasicrystals 68 References 68 6 Elasticity of Two-Dimensional Quasicrystals and Simplification 71 6.1 Basic Equations of Plane Elasticity of Two-Dimensional Quasicrystals: Point Groups 5m and 10mm in Five-and TenfoldSymmetries75 6.2 Simplification of the Basic Equation Set: Displacement Potential Function Method81 6.3 Simplification of Basic Equations Set: Stress Potential Function Method 83 6.4 Plane Elasticity of Point Group 5, 5 and 10, 10 Pentagonal and Decagonal Quasicrystals85 6.5 Plane Elasticity of Point Group 12mm of Dodecagonal Quasicrystals 89 6.6 Plane Elasticity of Point Group8mm of Octagonal Quasicrystals, Displacement Potential93 6.7 Stress Potential of Point Group5;5 Pentagonal and Point Group 10;10 Decagonal Quasicrystals98 6.8 Stress Potential ofPointGroup8mm Octagonal Quasicrystals 100 6.9 Engineering and Mathematical Elasticity of Quasicrystals 103 References 106 7 Application I—Some Dislocation and Interface Problems and Solutions in One-and Two-Dimensional Quasicrystals109 7.1 Dislocations in One-Dimensional Hexagonal Quasicrystals 110 7.2 Dislocations in Quasicrystals with Point Groups 5m and 10 mm Symmetries112 7.3 Dislocations in Quasicrystals with Point Groups 5; 5 Fivefold and 10, 10 Tenfold Symmetries 119 7.4 Dislocations in Quasicrystals with Eightfold Symmetry124 7.4.1 Fourier Transform Method 125 7.4.2 Complex Variable Function Method 127 7.5 Dislocations in Dodecagonal Quasicrystals 128 7.6 Interface Between Quasicrystal and Crystal 129 7.7 Dislocation Pile up, Dislocation Group and Plastic Zone133 7.8 Discussions and Conclusions134 References 134 8Application II—Solutions of Notch and Crack Problems of One-and Two-Dimensional Quasicrystals137 8.1 Crack Problem and Solution of One-Dimensional Quasicrystals 138 8.1.1 GriffithCrack138 8.1.2 Brittle Fracture Theory 143 8.2 Crack Problem in Finite-Sized One-Dimensional Quasicrystals 145 8.2.1 Cracked Quasicrystal Strip with Finite Height 145 8.2.2 Finite Strip with Two Cracks 149 8.3 Griffith Crack Problems in Point Groups5m and 10mm Quasicrystal Based on Displacement Potential Function Method150 8.4 Stress Potential Function Formulation and Complex Analysis Method for Solving Notch/Crack Problem of Quasicrystals of Point Groups5,5and10;10155 8.4.1 Complex Analysis Method 156 8.4.2 The Complex Representation of Stresses and Displacements 156 8.4.3 Elliptic Notch Problem158 8.4.4 Elastic Field Caused by a Griffith Crack 162 8.5 Solutions of Crack/Notch Problems of Two-Dimensional Octagonal Quasicrystals 163 8.6 Approximate Analytic Solutions of Notch/Crack of Two-Dimensional Quasicrystals with5-and 10-Fold Symmetries165 8.7 Cracked Strip with Finite Height of Two-Dimensional Quasicrystals with 5-and 10-Fold Symmetries and Exact Analytic Solution 168 8.8 Exact Analytic Solution of Single Edge Crack in a Finite Width Specimen of a Two-Dimensional Quasicrystal of 10-FoldSymmetry 172 8.9 Perturbation Solution of Three-Dimensional Elliptic Disk Crack in One-Dimensional Hexagonal Quasicrystals 175 8.10 Other Crack Problems in One-and Two-Dimensional Quasicrystals 179 8.11 Plastic Zone Around Crack Tip 179 8.12 Appendix1 ofChapter8: Some Derivations in Sect.8.1179 8.13 Appendix2 of Chapter8: Some Further Derivation of Solution in Sect.8.9 181 References 186 9 Theory of Elasticity of Three-Dimensional Quasicrystals and Its Applications189 9.1 Basic Equations of Elasticity of Icosahedral Quasicrystals190 9.2 Anti-plane Elasticity of Icosahedral Quasicrystals and Problem of Interface of Quasicrystal–Crystal194 9.3 Phonon-Phason Decoupled Plane Elasticity of Icosahedral Quasicrystals 200 9.4 Phonon-Phason Coupled Plane Elasticity of Icosahedral Quasicrystals—Displacement Potential Formulation 202 9.5 Phonon-Phason Coupled Plane Elasticity of Icosahedral Quasicrystals—Stress Potential Formulation 205 9.6 A Straight Dislocation in an Icosahedral Quasicrystal 207 9.7 Application of Displacement Potential to Crack Problem of Icosahedral Quasicrystal212 9.8 An Elliptic Notch/Griffith Crack in an Icosahedral Quasicrystal220 9.8.1 The Complex Representation of Stresses and Displacements 220 9.8.2 Elliptic Notch Problem222 9.8.3 BriefSummary226 9.9 Elasticity of Cubic Quasicrystals—The Anti-plane and AxisymmetricDeformation226 References 231 10 Phonon-Phason Dynamics and Defect Dynamics of Solid Quasicrystals 233 10.1 Elastodynamics of Quasicrystals Followed Bak’s Argument 234 10.2 Elastodynamics of Anti-plane Elasticity for Some Quasicrystals 235 10.3 Moving Screw Dislocation in Anti-plane Elasticity236 10.4 Mode III Moving Griffith Crack in Anti-plane Elasticity 240 10.5 Two-Dimensional Phonon-Phason Dynamics, Fundamental Solution 243 10.6 Phonon-Phason Dynamics and Solutions of Two-Dimensional Decagonal Quasicrystals 249 10.6.1 The Mathematical Formalism of Dynamic Crack Problems of Decagonal Quasicrystals 249 10.6.2 Examination on the Physical Model 252 10.6.3 Testing the Scheme and the Computer Programme254 10.6.4 Results of Dynamic Initiation of Crack Growth 256 10.6.5 Results of the Fast Crack Propagation257 10.7 Phonon-Phason Dynamics and Applications to Fracture Dynamics of Icosahedral Quasicrystals259 10.7.1 Basic Equations, Boundary and Initial Conditions259 10.7.2 Some Results 261 10.7.3 Conclusion and Discussion 263 10.8 Appendix of Chapter 10: The Detail of Finite Difference Scheme264 References 268 11 Complex Analysis Method for Elasticity of Quasicrystals271 11.1 Harmonic and Biharmonic in Anti-Plane Elasticity of One-Dimensional Quasicrystals272 11.2 Biharmonic Equations in Plane Elasticity of Point Group 12mm Two-Dimensional Quasicrystals 272 11.3 The Complex Analysis of Quadruple Harmonic Equations and Applications in Two-Dimensional Quasicrystals273 11.3.1 Complex Representation of Solution of the Governing Equation 273 11.3.2 Complex Representation of the Stresses and Displacements 274 11.3.3 The Complex Representation of Boundary Conditions275 11.3.4 Structure of Complex Potentials276 11.3.5 Conformal Mapping 281 11.3.6 Reduction in the Boundary Value Problem to Function Equations 282 11.3.7 Solution of the Function Equations283 11.3.8 Example1 Elliptic Notch/Crack Problem and Solution284 11.3.9 Example2 Infinite Plane with an Elliptic Hole Subjected to a Tension at Infinity 286 11.3.10 Example3 Infinite Plane with an Elliptic Hole Subjected to a Distributed Pressure at a Part of Surface of the Hole 286 11.4 Complex Analysis for Sextuple Harmonic Equation and Applications to Three-Dimensional Icosahedral Quasicrystals 287 11.4.1 The Complex Representation of Stresses and Displacements288 11.4.2 The Complex Representation of Boundary Conditions290 11.4.3 Structure of Complex Potentials291 11.4.4 Case of InfiniteRegions294 11.4.5 Conformal Mapping and Function Equations at f-Plane295 11.4.6 Example: Elliptic Notch Problem and Solution297 11.5 Complex Analysis of Generalized Quadruple Harmonic Equation 300 11.6 Conclusion and Discussion 301 11.7 Appendix of Chapter 11: Basic Formulas of Complex Analysis302 11.7.1 Complex Functions, Analytic Functions 302 11.7.2 Cauchy’s formula 303 11.7.3 Poles 306 11.7.4 Residual Theorem 306 11.7.5 Analytic Extension309 11.7.6 Conformal Mapping 309 References 311 12 Variational Principle of Elasticity of Quasicrystals, Numerical Analysis and Applications 313 12.1 Review of Basic Relations of Elasticity of Icosahedral Quasicrystals 314 12.2 General Variational Principle for Static Elasticity of Quasicrystals 315 12.3 Finite Element Method for Elasticity of Icosahedral Quasicrystals 319 12.4 Numerical Results 323 12.5 Conclusion332 References 332 13 Some Mathematical Principles on Solutions of Elasticity of Quasicrystals333 13.1 Uniqueness of Solution of Elasticity of Quasicrystals 333 13.2 Generalized Lax–Milgram Theorem 335 13.3 Matrix Expression of Elasticity of Three-Dimensional Quasicrystals 339 13.4 The Weak Solution of Boundary Value Problem of Elasticity of Quasicrystals 343 13.5 The Uniqueness of Weak Solution 344 13.6 Conclusion and Discussion 347 References 347 14 Nonlinear Behaviour of Quasicrystals349 14.1 Macroscopic Behaviour of Plastic Deformation of Quasicrystals 350 14.2 Possible Scheme of Plastic Constitutive Equations 352 14.3 Nonlinear Elasticity and Its Formulation 355 14.4 Nonlinear Solutions Based on Some Simple Models356 14.4.1 Generalized Dugdale–Barenblatt Model for Anti-plane Elasticity for Some Quasicrystals 356 14.4.2 Generalized Dugdale–Barenblatt Model for Plane Elasticity of Two-Dimensional Point Groups 5 m, 10 mm and 5;5, 10;10 Quasicrystals 359 14.4.3 Generalized Dugdale–Barenblatt Model for Plane Elasticity of Three-Dimensional Icosahedral Quasicrystals 361 14.5 Nonlinear Analysis Based on the Generalized Eshelby Theory 362 14.5.1 Generalized Eshelby Energy-Momentum Tensor and Generalized Eshelby Integral 362 14.5.2 Relation Between Crack Tip Opening Displacement and the Generalized Eshelby Integral 364 14.5.3 Some Further Interpretation on Application of E-Integral to the Nonlinear Fracture Analysis of Quasicrystals 365 14.6 Nonlinear Analysis Based on the Dislocation Model366 14.6.1 Screw Dislocation Pile-Up for Hexagonal or Icosahedral or Cubic Quasicrystals 366 14.6.2 Edge Dislocation Pile-Up for Pentagonal or Decagonal Two-Dimensional Quasicrystals 369 14.6.3 Edge Dislocation Pile-Up for Three-Dimensional Icosahedral Quasicrystals 370 14.7 Conclusion and Discussion 371 14.8 Appendix of Chapter 14: Some Mathematical Details 371 14.8.1 Proof on Path-Independency of E-Integral 371 14.8.2 Proof on the Equivalency of E-Integral to Energy Release Rate Under Linear Elastic Case for Quasicrystals373 14.8.3 On the Evaluation of the Critic Value ofE-Integral376 References 377 15 Fracture Theory of Solid Quasicrystals379 15.1 Linear Fracture Theory of Quasicrystals 379 15.2 Crack Extension Force Expressions of Standard Quasicrystal Samples and Related Testing Strategy for Determining Critical Value GIC383 15.2.1 Characterization of GI and GIC of Three-Point Bending Quasicrystal Samples 383 15.2.2 Characterization of GI and GIC of Compact Tension Quasicrystal Sample 384 15.3 Nonlinear Fracture Mechanics 385 15.4 Dynamic Fracture387 15.5 Measurement of Fracture Toughness and Relevant Mechanical Parameters of Quasicrystalline Material 388 15.5.1 FractureToughness389 15.5.2 Tension Strength389 References 391 16 Hydrodynamics of Solid Quasicrystals393 16.1 ViscosityofSolid393 16.2 Generalized Hydrodynamics of Solid Quasicrystals 394 16.3 Simplification of Plane Field Equations in Two-Dimensional 5-and 10-Fold Symmetrical Solid Quasicrystals 396 16.4 Numerical Solution 396 16.5 Conclusion and Discussion 405 References 405 17 Remarkable Conclusion 407 References 408 Major Appendix: On Some Mathematical Additional Materials411
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