Classical mechanics Books

Book SynopsisThis book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This approach allows students to solve more advanced and applied problems at an earlier stage and equips them to deal with real-world examples well beyond the typical special cases treated in standard textbooks.Another advantage of this approach is that students are brought closer to the way physics is actually discovered and applied, as they are introduced right from the start to a more exploratory way of understanding phenomena and of developing their physical concepts.While not a requirement, it is advantageous for the reader to have some prior knowledge of scientific programming with a scripting-type language. This edition of the book uses Matlab, and a chapter devoted to the basics of scientific programming with Matlab is included. A parallel edition using Python instead of Matlab is also available.Last but not least, each chapter is accompanied by an extensive set of course-tested exercises and solutions.Table of Contents Introduction.- Getting started with programming.- Units and measurement.- Motion in one dimension.- Forces in one dimension.- Motion in two and three dimensions.- Forces in two and three dimensions.- Constrained motion.- Forces and constrained motion.- Work.- Energy.- Momentum, impulse, and collisions.- Multiparticle systems.- Rotational motion.- Rotation of rigid bodies.- Dynamics of rigid bodies.- Proofs.- Solutions.- Index.

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Book SynopsisThis is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero­ dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.Table of Contents1. Introduction.- 1.1. Historical Background.- 1.2. Some Examples of Spectral Methods.- 1.2.1. A Fourier Galerkin Method for the Wave Equation.- 1.2.2. A Chebyshev Collocation Method for the Heat Equation.- 1.2.3. A Legendre Tau Method for the Poisson Equation.- 1.2.4. Basic Aspects of Galerkin, Tau and Collocation Methods.- 1.3. The Equations of Fluid Dynamics.- 1.3.1. Compressible Navier-Stokes.- 1.3.2. Compressible Euler.- 1.3.3. Compressible Potential.- 1.3.4. Incompressible Flow.- 1.3.5. Boundary Layer.- 1.4. Spectral Accuracy for a Two-Dimensional Fluid Calculation.- 1.5. Three-Dimensional Applications in Fluids.- 2. Spectral Approximation.- 2.1. The Fourier System.- 2.1.1. The Continuous Fourier Expansion.- 2.1.2. The Discrete Fourier Expansion.- 2.1.3. Differentiation.- 2.1.4. The Gibbs Phenomenon.- 2.2. Orthogonal Polynomials in ( — 1, 1).- 2.2.1. Sturm—Liouville Problems.- 2.2.2. Orthogonal Systems of Polynomials.- 2.2.3. Gauss-Type Quadratures and Discrete Polynomial Transforms.- 2.3. Legendre Polynomials.- 2.3.1. Basic Formulas.- 2.3.2. Differentiation.- 2.4. Chebyshev Polynomials.- 2.4.1. Basic Formulas.- 2.4.2. Differentiation.- 2.5. Generalizations.- 2.5.1. Jacobi Polynomials.- 2.5.2. Mapping.- 2.5.3. Semi-Infinite Intervals.- 2.5.4. Infinite Intervals.- 3. Fundamentals of Spectral Methods for PDEs.- 3.1. Spectral Projection of the Burgers Equation.- 3.1.1. Fourier Galerkin.- 3.1.2. Fourier Collocation.- 3.1.3. Chebyshev Tau.- 3.1.4. Chebyshev Collocation.- 3.2. Convolution Sums.- 3.2.1. Pseudospectral Transform Methods.- 3 2 2 Aliasing Removal by Padding or Truncation.- 3.2.3. Aliasing Removal by Phase Shifts.- 3.2.4. Convolution Sums in Chebyshev Methods.- 3.2.5. Relation Between Collocation and Pseudospectral Methods.- 3.3. Boundary Conditions.- 3.4. Coordinate Singularities.- 3.4.1. Polar Coordinates.- 3.4.2. Spherical Polar Coordinates.- 3.5. Two-Dimensional Mapping.- 4. Temporal Discretization.- 4.1. Introduction.- 4.2. The Eigenvalues of Basic Spectral Operators.- 4.2.1. The First-Derivative Operator.- 4.2.2. The Second-Derivative Operator.- 4.3. Some Standard Schemes.- 4.3.1. Multistep Schemes.- 4.3.2. Runge—Kutta Methods.- 4.4. Special Purpose Schemes.- 4.4.1. High Resolution Temporal Schemes.- 4.4.2. Special Integration Techniques.- 4.4.3. Lerat Schemes.- 4.5. Conservation Forms.- 4.6. Aliasing.- 5. Solution Techniques for Implicit Spectral Equations.- 5.1. Direct Methods.- 5.1.1. Fourier Approximations.- 5.1.2. Chebyshev Tau Approximations.- 5.1.3. Schur-Decomposition and Matrix-Diagonalization.- 5.2. Fundamentals of Iterative Methods.- 5.2.1. Richardson Iteration.- 5.2.2. Preconditioning.- 5.2.3. Non-Periodic Problems.- 5.2.4. Finite-Element Preconditioning.- 5.3. Conventional Iterative Methods.- 5.3.1. Descent Methods for Symmetric, Positive-Definite Systems.- 5.3.2. Descent Methods for Non-Symmetric Problems.- 5.3.3. Chebyshev Acceleration.- 5.4. Multidimensional Preconditioning.- 5.4.1. Finite-Difference Solvers.- 5.4.2. Modified Finite-Difference Preconditioners.- 5.5. Spectral Multigrid Methods.- 5.5.1. Model Problem Discussion.- 5.5.2. Two-Dimensional Problems.- 5.5.3. Interpolation Operators.- 5.5.4. Coarse-Grid Operators.- 5.5.5. Relaxation Schemes.- 5.6. A Semi-Implicit Method for the Navier—Stokes Equations.- 6. Simple Incompressible Flows.- 6.1. Burgers Equation.- 6.2. Shear Flow Past a Circle.- 6.3. Boundary-Layer Flows.- 6.4. Linear Stability.- 7. Some Algorithms for Unsteady Navier—Stokes Equations.- 7.1. Introduction.- 7.2. Homogeneous Flows.- 7.2.1. A Spectral Galerkin Solution Technique.- 7.2.2. Treatment of the Nonlinear Terms.- 7.2.3. Refinements.- 7.2.4. Pseudospectral and Collocation Methods.- 7.3. Inhomogeneous Flows.- 7.3.1. Coupled Methods.- 7.3.2. Splitting Methods.- 7.3.3. Galerkin Methods.- 7.3.4. Other Confined Flows.- 7.3.5. Unbounded Flows.- 7.3.6. Aliasing in Transition Calculations.- 7.4. Flows with Multiple Inhomogeneous Directions.- 7.4.1. Choice of Mesh.- 7.4.2. Coupled Methods.- 7.4.3. Splitting Methods.- 7.4.4. Other Methods.- 7.5. Mixed Spectral/Finite-Difference Methods.- 8. Compressible Flow.- 8.1. Introduction.- 8.2. Boundary Conditions for Hyperbolic Problems.- 8.3. Basic Results for Scalar Nonsmooth Problems.- 8.4. Homogeneous Turbulence.- 8.5. Shock-Capturing.- 8.5.1. Potential Flow.- 8.5.2. Ringleb Flow.- 8.5.3. Astrophysical Nozzle.- 8.6. Shock-Fitting.- 8.7. Reacting Flows.- 9. Global Approximation Results.- 9.1. Fourier Approximation.- 9.1.1. Inverse Inequalities for Trigonometric Polynomials.- 9.1.2. Estimates for the Truncation and Best Approximation Errors.- 9.1.3. Estimates for the Interpolation Error.- 9.2. Sturm—Liouville Expansions.- 9.2.1. Regular Sturm—Liouville Problems.- 9.2.2. Singular Sturm—Liouville Problems.- 9.3. Discrete Norms.- 9.4. Legendre Approximations.- 9.4.1. Inverse Inequalities for Algebraic Polynomials.- 9.4.2. Estimates for the Truncation and Best Approximation Errors.- 9.4.3. Estimates for the Interpolation Error.- 9.5. Chebyshev Approximations.- 9.5.1. Inverse Inequalities for Polynomials.- 9.5.2. Estimates for the Truncation and Best Approximation Errors.- 9.5.3. Estimates for the Interpolation Error.- 9.5.4. Proofs of Some Approximation Results.- 9.6. Other Polynomial Approximations.- 9.6.1. Jacobi Polynomials.- 9.6.2. Laguerre and Hermite Polynomials.- 9.7. Approximation Results in Several Dimensions.- 9.7.1. Fourier Approximations.- 9.7.2. Legendre Approximations.- 9.7.3. Chebyshev Approximations.- 9.7.4. Blended Fourier and Chebyshev Approximations.- 10. Theory of Stability and Convergence for Spectral Methods.- 10.1. The Three Examples Revisited.- 10.1.1. A Fourier Galerkin Method for the Wave Equation.- 10.1.2. A Chebyshev Collocation Method for the Heat Equation.- 10.1.3. A Legendre Tau Method for the Poisson Equation.- 10.2. Towards a General Theory.- 10.3. General Formulation of Spectral Approximations to Linear Steady Problems.- 10.4. Galerkin, Collocation and Tau Methods.- 10.4.1. Galerkin Methods.- 10.4.2. Tau Methods.- 10.4.3. Collocation Methods.- 10.5. General Formulation of Spectral Approximations to Linear Evolution Equations.- 10.5.1. Conditions for Stability and Convergence: The Parabolic Case.- 10.5.2. Conditions for Stability and Convergence: The Hyperbolic Case.- 10.6. The Error Equation.- 11. Steady, Smooth Problems.- 11.1. The Poisson Equation.- 11.1.1. Legendre Methods.- 11.1.2. Chebyshev Methods.- 11.1.3. Other Boundary Value Problems.- 11.2. Advection-Diffusion Equation.- 11.2.1. Linear Advection-Diffusion Equation.- 11.2.2. Steady Burgers Equation.- 11.3. Navier—Stokes Equations.- 11.3.1. Compatibility Conditions Between Velocity and Pressure.- 11.3.2. Direct Discretization of the Continuity Equation: The “inf-sup” Condition.- 11.3.3. Discretizations of the Continuity Equation by an Influence-Matrix Technique: The Kleiser—Schumann Method.- 11.3.4. Navier—Stokes Equations in Streamfunction Formulation.- 11.4. The Eigenvalues of Some Spectral Operators.- 11.4.1. The Discrete Eigenvalues for Lu = ? uxx.- 11.4.2. The Discrete Eigenvalues for Lu = ? vuxx + bux.- 11.4.3. The Discrete Eigenvalues for Lu = ux.- 12. Transient, Smooth Problems.- 12.1. Linear Hyperbolic Equations.- 12.1.1. Periodic Boundary Conditions.- 12.1.2. Non-Periodic Boundary Conditions.- 12.1.3. Hyperbolic Systems.- 12.1.4. Spectral Accuracy for Non-Smooth Solutions.- 12.2. Heat Equation.- 12.2.1. Semi-Discrete Approximation.- 12.2.2. Fully Discrete Approximation.- 12.3. Advection-Diffusion Equation.- 12.3.1. Semi-Discrete Approximation.- 12.3.2. Fully Discrete Approximation.- 13. Domain Decomposition Methods.- 13.1. Introduction.- 13.2. Patching Methods.- 13.2.1. Notation.- 13.2.2. Discretization.- 13.2.3. Solution Techniques.- 13.2.4. Examples.- 13.3. Variational Methods.- 13.3.1. Formulation.- 13.3.2. The Spectral-Element Method.- 13.4. The Alternating Schwarz Method.- 13.5. Mathematical Aspects of Domain Decomposition Methods.- 13.5.1. Patching Methods.- 13.5.2. Equivalence Between Patching and Variational Methods.- 13.6. Some Stability and Convergence Results.- 13.6.1. Patching Methods.- 13.6.2. Variational Methods.- Appendices.- A. Basic Mathematical Concepts.- B. Fast Fourier Transforms.- C. Jacobi—Gauss—Lobatto Roots.- References.

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Book SynopsisThin shells are three-dimensional structures with a dimension (the thickness) small with respect to the two others.Such thin structures are widely used in automobileandaviation industries,or in civil engineering, because they provide animportantsti?ness, due to theircurvature,with a small weight. Fig. 0.1. Airbus A380 Fig. 0.2. Hemispherical roof (Marseille, France) One ofthechallenges is often to reduce the weight (andconsequently the thickness)oftheshells, preservingtheirsti?ness.So that it is essential to have 1 accuratemodelsforthinandevenverythinshells ,andtobeabletocomputethe displacements resultingfromagivenloading.In particular, singularities leading to fractures in some cases must be absolutely predicted a priori and ofcourse avoided (see Fig.0.3 forexample). Since the pioneeringmodels of Novozhilov-Donnell [81] and Koiter [65][66], numerous works havebeen devoted to establish linear and non linear elastic shell model usingdirect orsurfacic approaches [18][25][100]. More recently, the asymptoticmethods [87] havebeen used, to try tojustify rigorously, fromthe three-dimensional equations, the shell models obtained by direct approaches - lying onapriori assumption, andto construct new models [54][55]. This way, 1 Very thin shells are present in certain domains of industry, as plastic ?lms for pa- aging or for electronics, streched sails, or even very thin metal sheets obtained by drawing. E. Sanchez-Palencia et al.: Singular Problems in Shell Theory, LNACM 54, pp. 1-11.Trade ReviewFrom the reviews:“The book under review is devoted to a mathematically rigorous study of singularities in linear elastic shell theory which appear for very small thickness. … This well-written book is a reader-friendly and good organized research work in the field of mathematical theory of shells. It can be recommended to highly-qualified experts in this field.” (Igor Andrianov, Zentralblatt MATH, Vol. 1208, 2011)Table of ContentsGeometric Formalism of Shell Theory.- Singularities and Boundary Layers in Thin Elastic Shell Theory.- Anisotropic Error Estimates in the Layers.- Numerical Simulation with Anisotropic Adaptive Mesh.- Singularities of Parabolic Inhibited Shells.- Singularities of Hyperbolic Inhibited Shells.- Singularities of Elliptic Well-Inhibited Shells.- Generalities on Boundary Conditions for Equations and Systems: Introduction to Sensitive Problems.- Numerical Simulations for Sensitive Shells.- Examples of Non-inhibited Shell Problems (Non-geometrically Rigid Problems).

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Book SynopsisThis book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.Table of ContentsErgodicity – A Basic Concept.- Large Deviations in Statistical Mechanics: Rigorous and Non-Rigorous.- Large Deviation Techniques for Long-Range Interactions.- Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium Phenomena and Back.- Stochastic Fluctuations in Deterministic Systems.- Large Deviation and Disordered Systems.- Large Deviations in Turbulence.- Ergodicity Breaking Challenges Monte Carlo Methods.- Anomalous Diffusion: Deterministic and Stochastic Perspectives.- The Use of Fluctuation Relations for the Analysis of Free-Energy Landscapes.

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Book SynopsisOne studying the motion of fluids relative to particulate systems is soon impressed by the dichotomy which exists between books covering theoretical and practical aspects. Classical hydrodynamics is largely concerned with perfect fluids which unfortunately exert no forces on the particles past which they move. Practical approaches to subjects like fluidization, sedimentation, and flow through porous media abound in much useful but uncorrelated empirical information. The present book represents an attempt to bridge this gap by providing at least the beginnings of a rational approach to fluid­ particle dynamics, based on first principles. From the pedagogic viewpoint it seems worthwhile to show that the Navier-Stokes equations, which form the basis of all systematic texts, can be employed for useful practical applications beyond the elementary problems of laminar flow in pipes and Stokes law for the motion of a single particle. Although a suspension may often be viewed as a continuum for practical purposes, it really consists of a discrete collection of particles immersed in an essentially continuous fluid. Consideration of the actual detailed boundary­ value problems posed by this viewpoint may serve to call attention to the limitation of idealizations which apply to the overall transport properties of a mixture of fluid and solid particles.Table of Contents1. Introduction.- 1–1 Definition and purpose, 1. 1–2 Historical review, 8. 1–3 Application in science and technology, 13..- 2. The Behavior of Fluids in Slow Motion.- 2–1 The equations of change for a viscous fluid, 23. 2–2 Mechanical energy dissipation in a viscous fluid, 29. 2–3 Force and couple acting on a body moving in a viscous fluid, 30. 2–4 Exact solutions of the equations of motion for a viscous fluid, 31. 2–5 Laminar flow in ducts, 33. 2–6 Simplifications of the Navier-Stokes equations, especially for slow motion, 40. 2–7 Paradoxes in the solution of the creeping motion equations, 47. 2–8 Molecular effects in fluid dynamics, 49. 2–9 Non-newtonian flow, 51. 2–10 Unsteady creeping flows, 52..- 3. Some General Solutions and Theorems Pertaining to the Creeping Motion Equations.- 3–1 Introduction, 58. 3–2 Spherical coordinates, 62. 3–3 Cylindrical coordinates, 71. 3–4 Integral representations, 79. 3–5 Generalized reciprocal theorem, 85. 3–6 Energy dissipation, 88..- 4. Axisymmetrical Flow.- 4–1 Introduction, 96. 4–2 Stream function, 96. 4–3 Relation between stream function and local velocity, 98. 4–4 Stream function in various coordinate systems, 99. 4–5 Intrinsic coordinates, 100. 4–6 Properties of the stream function, 102. 4–7 Dynamic equation satisfied by the stream function, 103. 4–8 Uniform flow, 106. 4–9 Point source or sink, 106. 4–10 Source and sink of equal strength, 107. 4–11 Finite line source, 108. 4–12 Point force, 110. 4–13 Boundary conditions satisfied by the stream function, 111. 4–14 Drag on a body, 113. 4–15 Pressure, 116. 4–16 Separable coordinate systems, 117. 4–17 Translation of a sphere, 119. 4–18 Flow past a sphere, 123. 4–19 Terminal settling velocity, 124. 4–20 Slip at the surface of a sphere, 125. 4–21 Fluid sphere, 127. 4–22 Concentric spheres, 130. 4–23 General solution in spherical coordinates, 133. 4–24 Flow through a conical diffuser, 138. 4–25 Flow past an approximate sphere, 141. 4–26 Oblate spheroid, 145. 4–27 Circular disk, 149. 4–28 Flow in a venturi tube, 150. 4–29 Flow through a circular aperture, 153. 4–30 Prolate spheroid, 154. 4–31 Elongated rod, 156. 4–32 Axisymmetric flow past a spherical cap, 157..- 5. The Motion of a Rigid Particle of Arbitrary Shape in an Unbounded Fluid.- 5–1. Introduction, 159. 5–2 Translational motions, 163. 5–3 Rotational motions, 169. 5–4 Combined translation and rotation, 173. 5–5 Symmetrical particles, 183. 5–6 Nonskew bodies, 192. 5–7 Terminal settling velocity of an arbitrary particle, 197. 5–8 Average resistance to translation, 205. 5–9 The resistance of a slightly deformed sphere, 207. 5–10 The settling of spherically isotropic bodies, 219. 5–11 The settling of orthotopic bodies, 220..- 6. Interaction between Two or More Particles.- 6–1 Introduction, 235. 6–2 Two widely spaced spherically isotropic particles, 240: 6–3 Two spheres by the method of reflections and similar techniques, 249. 6–4 Exact solution for two spheres falling along their line of centers, 270. 6–5 Comparison of theories with experimental data for two spheres, 273. 6–6 More than two spheres, 276. 6–7 Two spheroids in a viscous liquid, 278. 6–8 Limitations of creeping motion equations, 281..- 7. Wall Effects on the Motion of a Single Particle.- 7–1 Introduction, 286. 7–2 The translation of a particle in proximity to container walls, 288. 7–3 Sphere moving in an axial direction in a circular cylindrical tube, 298. 7–4 Sphere moving relative to plane walls, 322. 7–5 Spheroid moving relative to cylindrical and plane walls, 331. 7–6 k-coefficients for typical boundaries, 340. 7–7 One- and two-dimensional problems, 341. 7–8 Solid of revolution rotating symmetrically in a bounded fluid, 346. 7–9 Unsteady motion of a sphere in the presence of a plane wall, 354..- 8. Flow Relative to Assemblages of Particles.- 8–1 Introduction, 358. 8–2 Dilute systems—no interaction effects, 360. 8–3 Dilute systems—first-order interaction effects, 371. 8–4 Concentrated systems, 387. 8–5 Systems with complex geometry, 400. 8–6 Particulate suspensions, 410. 8–7 Packed beds, 417. 8–8 Fluidization, 422..- 9. The Viscosity of Particulate Systems.- 9–1 Introduction, 431. 9–2 Dilute systems of spheres—no interaction effects, 438. 9–3 Dilute systems—first-order interaction effects, 443. 9–4 Concentrated systems, 448. 9–5 Nonspherical and nonrigid particles, 456. 9–6 Comparison with data, 462. 9–7 Non-newtonian behavior, 469..- Appendix A. Orthogonal Curvilinear Coordinate Systems.- A-l Curvilinear coordinates, 474. A-2 Orthogonal curvilinear coordinates, 477. A-3 Geometrical properties, 480. A-4 Differentiation of unit vectors, 481. A-5 Vector differential invariants, 483. A-6 Relations between cartesian and orthogonal curvilinear coordinates, 486. A-7 Dyadics in orthogonal curvilinear coordinates, 488. A-8 Cylindrical coordinate systems, 490. A-9 Circular cylindrical coordinates, 490. A-10 Conjugate cylindrical coordinate systems, 494. A-ll Elliptic cylinder coordinates, 495. A-12 Bipolar cylinder coordinates, 497. A-l3 Parabolic cylinder coordinates, 500. A-14 Coordinate systems of revolution, 501. A-l5 Spherical Coordinates, 504. A-l6 Conjugate coordinate systems of revolution, 508. A-17 Prolate spheroidal coordinates, 509. A-18 Oblate spheroidal coordinates, 512. A-19 Bipolar coordinates, 516. A-20 Toroidal coordinates, 519. A-21 Paraboloidal Coordinates, 521..- Appendix B. Summary of Notation and Brief Review of Polyadic Algebra.- Name Index.

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Book SynopsisThis book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and re­ searchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materi­ als: plasticity, fracture and fatigue, constitutive equations, composite materi­ als, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method. ' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.Trade Review`Professor Mura's book may be heartily recommended to those interested in either applying or learning to apply the methods of continuum mechanics to treat defects in the solid state. This monograph could serve as the perfect text for a second-level graduate course with the same title as that of the book.' Journal of Applied Mechanics Table of Contents1. General theory of eigenstrains.- 1. Definition of eigenstrains.- 2. Fundamental equations of elasticity.- Hooke’s law.- Equilibrium conditions.- Compatibility conditions.- 3. General expressions of elastic fields for given eigenstrain distributions.- Periodic solutions.- Method of Fourier series and Fourier integrals.- Method of Green’s functions.- Isotropic materials.- Cubic crystals.- Hexagonal crystals (transversely isotropic).- 4. Exercises of general formulae.- A straight screw dislocation.- A straight edge dislocation.- Periodic distribution of cuboidal precipitates.- 5. Static Green’s functions.- Isotropic materials.- Anisotropic materials.- Transversely isotropic materials.- Kröner’s formula.- Derivatives of Green’s functions.- Two-dimensional Green’s function.- 6. Inclusions and inhomogeneities.- Inclusions.- Inhomogeneities.- Effect of isotropic elastic moduli on stress.- 7. Dislocations.- Volterra and Mura formulas.- The Indenbom and Orlov formula.- Disclinations.- 8. Dynamic solutions.- Uniformly moving edge dislocation.- Uniformly moving screw dislocation.- 9. Dynamic Green’s functions.- Isotropic materials.- Steady State.- 10. Incompatibility.- Riemann-Christoffel curvature tensor.- 2. Isotropic inclusions.- 11. Eshelby’s solution.- Interior points.- Sphere.- Elliptic cylinder.- Penny-shape.- Flat ellipsoid.- Oblate spheroid.- Prolate spheroid.- Exterior points.- Thermal expansion with central symmetry.- 12. Ellipsoidal inclusions with polynomial eigenstrains.- The I-integrals.- Sphere.- Elliptic cylinder.- Oblate spheroid.- Prolate spheroid.- Elliptical plate.- The Ferrers and Dyson formula.- 13. Energies of inclusions.- Elastic strain energy.- Interaction energy.- Strain energy due to a spherical inclusion.- Elliptic cylinder.- Penny-shaped flat ellipsoid.- Spheroid.- 14. Cuboidal inclusions.- 15. Inclusions in a half space.- Green’s functions.- Ellipsoidal inclusion with a uniform dilatational eigenstrain.- Cuboidal inclusion with uniform eigenstrains.- Periodic distribution of eigenstrains.- Joined half-spaces.- 3. Anisotropic inclusions.- 16. Elastic field of an ellipsoidal inclusion.- 17. Formulae for interior points.- Uniform eigenstrains.- Spheroid.- Cylinder (elliptic inclusion).- Flat ellipsoid.- Eigenstrains with polynomial variation.- Eigenstrains with a periodic form.- 18. Formulae for exterior points.- Examples.- 19. Ellipsoidal inclusions with polynomial eigenstrains in anisotropic media.- Special cases.- 20. Harmonic eigenstrains.- 21. Periodic distribution of spherical inclusions.- 4. Ellipsoidal inhomogeneities.- 22. Equivalent inclusion method.- Isotropic materials.- Sphere.- Penny shape.- Rod.- Anisotropic inhomogeneities in isotropic matrices.- Stress field for exterior points.- 23. Numerical calculations.- Two ellipsoidal inhomogeneities.- 24. Impotent eigenstrains.- 25. Energies of inhomogeneities.- Elastic strain energy.- Interaction energy.- Colunneti’s theorem.- Uniform plastic deformation in a matrix.- Energy balance.- 26. Precipitates and martensites.- Isotropic precipitates.- Anistropic precipitates.- Incoherent precipitates.- Martensitic transformation.- Stress orienting precipitation.- 5. Cracks.- 27. Critical stresses of crakes in isotropic media.- Penny-shaped cracks.- Slit-like cracks.- Flat ellipsoidal cracks.- Crack opening displacement.- 28. Critical stresses of cracks in anisotropic media.- Uniform applied stress.- Non-uniform applied stress.- II integrals for a penny-shaped crack.- II integrals for cubic crystals.- II integrals for transversely isotropic materials.- 29. Stress intensity factor for a flat ellipsoidal crack.- Uniform applied stresses.- Non-uniform applied stresses.- 30. Stress intensity factor for a slit-like crack.- Uniform applied stresses.- Non-uniform applied stresses.- Isotropic materials.- 31. Stress concentration factors.- Simple tension.- Pure shear.- 32. Dugdale-Barenblatt cracks.- BCS model.- Penny shaped crack.- 33. Stress intensity factor for an arbitrarily shaped plane crack.- Numerical examples.- 34. Crack growth.- Energy release rate.- The J-integral.- Fatigue.- Dynamic crack growth.- 6. Dislocations.- 35. Displacement fields.- Parallel dislocations.- A straight dislocation.- 36. Stress fields.- Dislocation segments.- Willis’ formula.- The Asaro et al. formula.- Dislocation loops.- 37. Dislocation density tensor.- Surface dislocation density.- Impotent distribution of dislocations.- 38. Dislocation flux tensor.- Line integral expression of displacement and plastic distortion fields.- The elastic field of moving dislocationswave equations of tensor potentials.- Wave equations of tensor potentials.- 39. Energies and forces.- Dynamic consideration.- 40. Plasticity.- Mathematical theory of plasticity.- Dislocation theory.- Plane strain problems.- Beams and cylinders.- 41. Dislocation model for fatigue crack initiation.- 7. Material properties and related topics.- 42. Macroscopic average.- Average of internal stresses.- Macroscopic strains.- Tanaka-Mori’s theorem.- Image stress.- Random distribution of inclusions-Mori and Tanaka’s theory.- 43. Work-hardening of dispersion hardened alloys.- Work-hardening in simple shear.- Dislocations around an inclusion.- Uniformity of plastic deformation.- 44. Diffusional relaxation of internal and external stresses.- Relaxation of the internal stress in a plastically deformed dispersion strenthened alloy.- Diffusional relaxation process, climb rate of an Orowan loop.- Recovery creep of a dispersion strengthened alloy.- Interfacial diffusional relaxation.- 45. Average elastic moduli of composite materials.- The Voigt approximation.- The Reuss approximation.- Hill’s theory.- Eshelby’s method.- Self-consistent method.- Upper and lower bounds.- Other related works.- 46. Plastic behavior of polycrystalline metals and composites.- Taylor’s analysis.- Self-consistent method.- Embedded weakened zone.- 47. Viscoelasticity of composite materials.- Homogeneous inclusions.- Inhomogeneous inclusions.- Waves in an infinite medium.- 48. Elastic wave scattering.- Dynamic equivalent inclusion method.- Green’s formula.- 49. Interaction between dislocations and inclusions.- Inclusions and dislocations.- Cracks in two-phase materials.- 50. Eigenstrains in lattice theory.- A uniformly moving screw dislocation.- 51. Sliding inclusions.- Shearing Eigenstrains.- Spheroidol inhomogeneous inclusions.- 52. Recent developments.- Inclusions, precipitates, and composites.- Half-spaces.- Non-elastic matrices.- Cracks and inclusions.- Sliding and debonding inclusions.- Dynamic cases.- Miscellaneous.- Appendix 1.- Einstein summation convention.- Kronecker delta.- Permutation tensor.- Appendix 2.- The elastic moduli for isotropic materials.- Appendix 3.- Fourier series and integrals.- Dirac’s delta function and Heaviside’s step function.- Laplace transform.- Appendix 4.- Dislocations pile-up.- References.- Author index.

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Book SynopsisThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.Trade ReviewFrom the reviews:“The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters … . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1172, 2009)Table of ContentsForeword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.

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Book SynopsisThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.Trade ReviewFrom the reviews:“The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters … . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1172, 2009)Table of ContentsForeword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.

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Book SynopsisMicro Electro Mechanical Systems (MEMS) is already about a billion dollars a year industry and is growing rapidly. So far major emphasis has been placed on the fabrication processes for various devices. There are serious issues related to tribology, mechanics, surfacechemistry and materials science in the operationand manufacturingof many MEMS devices and these issues are preventing an even faster commercialization. Very little is understood about tribology and mechanical properties on micro- to nanoscales of the materials used in the construction of MEMS devices. The MEMS community needs to be exposed to the state-of-the-artoftribology and vice versa. Fundamental understanding of friction/stiction, wear and the role of surface contamination and environmental debris in micro devices is required. There are significantadhesion, friction and wear issues in manufacturing and actual use, facing the MEMS industry. Very little is understood about the tribology of bulk silicon and polysilicon films used in the construction ofthese microdevices. These issues are based on surface phenomenaand cannotbe scaled down linearly and these become increasingly important with the small size of the devices. Continuum theory breaks down in the analyses, e. g. in fluid flow of micro-scale devices. Mechanical properties ofpolysilicon and other films are not well characterized. Roughness optimization can help in tribological improvements. Monolayers of lubricants and other materials need to be developed for ultra-low friction and near zero wear. Hard coatings and ion implantation techniques hold promise.Table of ContentsPreface. 1. MEMS Fabrication Techniques. 2. MEMS Applications and Tribology Issues. 3. State-of-the-Art of Tribology: Macroscale Processes. 4. State-of-the-Art of Tribology: Micro- to Nanoscale Processes. 5. Tribology of MEMS Components and Materials. 6. Mechanical Property Measurements. 7. Modification and Characterization of Surfaces. 8. Breakout Sessions Report. 9. Panel Discussion Report. List of Participants. Subject Index. Editor's Vita.

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Book SynopsisThis textbook covers all fundamental concepts of physics and describes how different theories are developed from physical observations and phenomena. After some essential calculus the author presents the complete classical mechanics giving numerous examples and with a clear focus on problem-solving techniques. Due to the high number of exercises at the end of each chapter and their solutions the work is valuable for self-study.

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Book SynopsisThe work shows, by means of examples coming from different corners of physics, how physical and mathematical questions can be answered using a computer. Starting with maps and neural networks, applications from Newton's mechanics described by ordinary differential equations come into the focus, like the computation of planetary orbits or classical molecular dynamics. A large part of the textbook is dedicated to deterministic chaos normally encountered in systems with sufficiently many degrees of freedom. Partial differential equations are studied considering (nonlinear) field theories like quantum mechanics, thermodynamics or fluid mechanics. In the second edition, a new chapter gives a detailed survey on delay or memory systems with a direct application to epidemic and road traffic models. Most of the algorithms are realized in FORTRAN, a language most suitable for effectively solving the discussed problems. On the other hand, the codes given and presented on the book’s homepage can be easily translated into other languages. Moreover, several MATLAB examples are presented, mainly for didactic reasons. The book is addressed to advanced Bachelor or Master students of physics, applied mathematics and mechanical engineering.

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Book SynopsisThis book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This approach allows students to solve more advanced and applied problems at an earlier stage and equips them to deal with real-world examples well beyond the typical special cases treated in standard textbooks.Another advantage of this approach is that students are brought closer to the way physics is actually discovered and applied, as they are introduced right from the start to a more exploratory way of understanding phenomena and of developing their physical concepts.While not a requirement, it is advantageous for the reader to have some prior knowledge of scientific programming with a scripting-type language. This edition of the book uses Python, and a chapter devoted to the basics of scientific programming with Python is included. A parallel edition using Matlab instead of Python is also available.Last but not least, each chapter is accompanied by an extensive set of course-tested exercises and solutions.Table of ContentsIntroduction.- Getting started with programming.- Units and measurement.- Motion in one dimension.- Forces in one dimension.- Motion in two and three dimensions.- Forces in two and three dimensions.- Constrained motion.- Forces and constrained motion.- Work.- Energy.- Momentum, impulse, and collisions.- Multiparticle systems.- Rotational motion.- Rotation of rigid bodies.- Dynamics of rigid bodies.- Proofs.- Solutions.- Index.

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Book SynopsisThis book addresses a range of basic and essential topics, selected from the author's teaching and research activities, offering a comprehensive guide in three parts: Statics, Kinematics and Kinetics. Chapter 1 briefly discusses the history of classical and modern mechanics, while Chapter 2, presents preliminary knowledge, preparing readers for the subsequent chapters. Chapters 3 to 7 introduce statics, force analysis, simplification of force groups, equilibrium of the general coplanar force group, and the center of the parallel force group. The Kinematics section (Chapters 8 to 10), covers the motion of a particle, basic motion and planar motion of a rigid body.Lastly, the Kinetics section (Chapters 11 to 14) explores Newton’s law of motion, theorem of momentum, theorem of angular momentum, and theorem of kinetic energy. With numerous examples from engineering, illustrations, and step-by-step tutorials, the book is suitable for both classroom use and self-study. After completing the course, students will be able to simplify complex engineering structures and perform force and motion analyses on particles and structures, preparing them for further study and research. The book can be used as a textbook for undergraduate courses on fundamental aspects of theoretical mechanics, such as aerospace, mechanical engineering, petroleum engineering, automotive and civil engineering, as well as material science and engineering.Table of ContentsPreface.- Preliminary knowledge.- Fundamentals of statics.- Force analysis.- Simplification of a force group.- Equilibrium of the general coplanar force gruop.- Center of the parallel force group.- Motion of a particle.- Basic motion of the rigid body.- Planar motion of the rigid body.- Newton’s laws of motion.- Theorem of momentum.- Theorem of angular momentum.- Theorem of kinetic energy.- Summary.

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Book Synopsis1. Einführung.- 2. Was ist Temperatur?- 3. Was ist Wärme?- 4. Die Entropie.- 5. Die Hauptsätze der Thermodynamik.- 6. Offene Systeme.- 7. Thermodynamische Potentiale.- 8. Erscheinungsformen der Materie, Phasen und Phasenübergänge.- 9. Suszeptibilität und Response.  Die Eigenschaften der Stoffe.- 10. Vom Gas zur Flüssigkeit. 11. Kristalline Festkörper.- 12. Reale Magnete.- 13. Strömung und Transport.- 14. Schwankungen.

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Book SynopsisFoundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.Table of ContentsPart I: Preliminaries 1. Differential Theory 2. Calculus on Manifolds Part II: Analytical Dynamics 3. HamiHonlan and Lagrangian Systems 4. Hamiltonian Systems with Symmetry 5. Hamilton-Jacobi Theory and Mathematical Physics Part III: An Outline of Qualitative Dynamics 6. Topological Dynamics 7. Differentiable Dynamics 8. Hamiltonian Dynamics Part IV: Celestial Mechanics 9. The Two-Body Problem 10. The Three-Body Problem

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Book SynopsisFoundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.Table of ContentsPart I: Preliminaries 1. Differential Theory 2. Calculus on Manifolds Part II: Analytical Dynamics 3. HamiHonlan and Lagrangian Systems 4. Hamiltonian Systems with Symmetry 5. Hamilton-Jacobi Theory and Mathematical Physics Part III: An Outline of Qualitative Dynamics 6. Topological Dynamics 7. Differentiable Dynamics 8. Hamiltonian Dynamics Part IV: Celestial Mechanics 9. The Two-Body Problem 10. The Three-Body Problem

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Book SynopsisEngineering Solid Mechanics bridges the gap between elementary approaches to strength of materials and more advanced, specialized versions on the subject.The book provides a basic understanding of the fundamentals of elasticity and plasticity, applies these fundamentals to solve analytically a spectrum of engineering problems, and introduces advanced topics of mechanics of materials - including fracture mechanics, creep, superplasticity, fiber reinforced composites, powder compacts, and porous solids.Text includes:stress and strain, equilibrium, and compatibility elastic stress-strain relations the elastic problem and the stress function approach to solving plane elastic problems applications of the stress function solution in Cartesian and polar coordinates Problems of elastic rods, plates, and shells through formulating a strain compatibility function as well as applying energy methods Elastic and elastic-plastic fracture mechanics Plastic and creep deformation Inelastic deformation and its applications This book presents the material in an instructive manner, suitable for individual self-study. It emphasizes analytical treatment of the subject, which is essential for handling modern numerical methods as well as assessing and creating software packages. The authors provide generous explanations, systematic derivations, and detailed discussions, supplemented by a vast variety of problems and solved examples.Primarily written for professionals and students in mechanical engineering, Engineering Solid Mechanics also serves persons in other fields of engineering, such as aerospace, civil, and material engineering.Trade Review"…an above average presentation of problems on thermoelasticity and plasticity… well written, with ample numbers of homework problems."-R. Solecki, emeritus, University of Connecticut in CHOICE, September 1999Table of ContentsAnalysis of Stress Analysis of Strain Elastic Stress-Strain Relations Solution of the Elastic Problem Elastic Plane Problems in Cartesian Coordinates Elastic Plane Problems in Polar Coordinates Elastic Rods Subjected to General Loading Some Problems of Elastic Plates and Shells Application to Fracture Mechanics Plastic Deformation Plastic Instability, Superplasticity and Creep Some Elastic-Plastic Problems

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Book SynopsisThis book presents to the design engineer the transducers and measurement techniques available, and evaluates their features and drawbacks. It is written for the instrument and systems designer, not the theoretician.Table of Contents1. Basics of Measurement Circuitry 2. Resistive Transducers 3. Magnetic Transducers 4. Capacitive Transducers 5. Self-Generating Transducers 6. Electrochemical Transducers 7. Semiconductor Transducers 8. Flow Measurement 9. Temperature Measurement 10. Pressure, Force, and Weight Measurement 11. Level Measurement 12. Interfacing to Computers

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Book SynopsisTo this point, the field of lubrication has been conceptualized using several noncontiguous modes of operation boundary, fluid-film, and dry and solid lubrication. Engineers and analysts have long had to deal with old evidence that many tribological devices, such as flat surface and centrally pivoted sliders, can act as viable bearings contradicting basic hydrodynamic theory. Tribology of Interface Layers introduces a new concept wherein disparate modes are shown to actually be particular phases of a tribological continuum spanning a wide array of material lubricants. The author details these phenomena and presents a novel definition of lubricants as intermediate layers. Explores the phenomenon of continuum spectrum as applied to new powder lubrication technology The book illustrates that contrary to previous understanding, the various lubrication modes from dry to hydrodynamic to powder lubrication alTable of ContentsHistorical Perspective. The Rheology of Interface Layers.The Phenomenology of Lubrication. Direct Contact–Hydrodynamic Continuum. Hydrodynamic–Solid Films Continuum. Experimental Performance of Powder Layers. Powder-Lubricated Devices. Theory of Powder Lubrication. Granular Films. The Tribological Continuum. Index.

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Book SynopsisPower Plant Synthesis provides an integrated approach to the operation, analysis, simulation, and dimensioning of power plants for electricity and thermal energy production. Fundamental concepts of energy and power, energy conversion, and power plant design are first presented, and integrated approaches for the operation and simulation of conventional electricity production systems are then examined. Hybrid power plants and cogeneration systems are covered, with operating algorithms, optimization, and dimensioning methods explained. The environmental impacts of energy sources are described and compared, with real-life case studies included to show the synthesis of the specific topics covered.

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Book SynopsisVolume 2 of Advances in Carbon Management Technologies has 21 chapters. It presents the introductory chapter again, for framing the challenges that confront the proposed solutions discussed in this volume. Section 4 presents various ways biomass and biomass wastes can be manipulated to provide a low-carbon footprint of the generation of power, heat and co-products, and of recovery and reuse of biomass wastes for beneficial purposes. Section 5 provides potential carbon management solutions in urban and manufacturing environments. This section also provides state-of the-art of battery technologies for the transportation sector. The chapters in section 6 deals with electricity and the grid, and how decarbonization can be practiced in the electricity sector.The overall topic of advances in carbon management is too broad to be covered in a book of this size. It was not intended to cover every possible aspect that is relevant to the topic. Attempts were made, however, to hTable of ContentsIntroductory Chapter. What key low-carbon technologies are needed to meet serious climate mitigation targets and what is their status. SECTION 1. BIOMASS SECTOR. Biomass as a source for heat, power, and coproducts. The Brazilian experience on the use of bioethanol. Biomass in regional and local context. Prioritizing uses for woody biowaste: a case study from British Columbia. Industrial oleochemicals from used cooking oils (UCOs)- sustainability benefits and challenges. Advances in carbon capture through thermochemical conversion of biomass waste. Phytowaste processing. Anaerobic digestion for energy recovery and carbon management. Critical aspects in developing sustainable biorefinery systems based on bioelectrochemical technology with carbon dioxide capture. Synthesis of regional bioproducts supply networks. Supply chain analysis for advancing carbon and nutrient recovery from organic waste. Efficient and low-carbon energy solution through polygeneration with biomass. SECTION II. MANUFACTURING AND CONSTRUCTION (BATTERIES, BUILT ENVIRONMENT, AUTOMOTIVE, AND OTHER INDUSTRIES). Urban carbon management strategies. Lean and green (L&G) manufacturing. Advances, challenges and opportunities of Li-ion batteries for electric vehicles. Charging strategies for electrified transport. SECTION III. ELECTRICITY AND THE GRID. Microgrids’ role in grid decarbonization. Storage of fluctuating energy. Lithium ion batteries – future technology development driven by environmental impact. Carbon constrained electricity sector planning with multiple objectives.

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Book SynopsisIn the dynamic digital age, the widespread use of computers has transformed engineering and science. A realistic and successful solution of an engineering problem usually begins with an accurate physical model of the problem and a proper understanding of the assumptions employed. With computers and appropriate software we can model and analyze complex physical systems and problems.However, efficient and accurate use of numerical results obtained from computer programs requires considerable background and advanced working knowledge to avoid blunders and the blind acceptance of computer results. This book provides the background and knowledge necessary to avoid these pitfalls, especially the most commonly used numerical methods employed in the solution of physical problems. It offers an in-depth presentation of the numerical methods for scales from nano to macro in nine self-contained chapters with extensive problems and up-to-date references, covering:<Trade Review"The book includes detailed descriptions of trending materials modeling methods such as concurrent multiscale methods and molecular dynamics methods. The authors explain well how these methods can be used to model materials at very fine scales and improve predictions compared to conventional approaches. The description contains enough numerical implementation details to allow students, engineers and researchers interested in high fidelity materials modeling to try the methods presented in the book."-- Wing Kam Liu, Northwestern University, USA"This is a one-of-a-kind book and good for numerical methods to solve problems in mechanics of materials, from the nanoscale to the macroscale."-- Shaofan Li, University of California, Berkeley, USA"The book would be of greatest use for practicing engineers or graduate students in mechanical engineering, applied mechanics, applied physics, materials science, and related fields."--J. Lambropoulos, University of Rochester in Choice ConnectTable of ContentsThe Role of Numerical Methods in Engineering. Numerical Analysis and Weighted Residuals. Finite Difference Methods. The Finite Element Method. Specialized Methods. The Boundary Element Method. Meshless Methods of Analysis. Multiphysics in Molecular Dynamics Simulation. Multiscale Modeling from Atoms to Genuine Continuum.

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Book SynopsisIn this Element, the authors investigate the philosophical and foundational issues that arise in statistical mechanics . They introduce the theoretical approaches in SM, Boltzmannian SM and Gibbsian SM, and discuss how they conceptualise equilibrium and explain the approach to it. This title is also available as Open Access on Cambridge Core.Table of Contents1. Introduction; 2. Mechanics and probability; 3. Boltzmannian statistical mechanics; 4. Gibbsian statistical mechanics; Bibliography.

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Book SynopsisThis book is a self-contained discussion of the major subjects in magnetostatics, the mathematical theory that describes the forces and fields resulting from the steady flow of electrical currents. This 2016 title has been reissued as an Open Access publication on Cambridge Core.Trade Review'[Principles of Magnetostatics] is a well-written combination of physics theory, application, and magnet design. The work will be of interest to physicists, engineers, and (of course) magnet designers. Also, an undergraduate that has completed the typical introductory physics and mathematics sequence should be adequately prepared to handle the presented material. … based on the examples given and the interesting design challenges, the reviewer believes this text can work well as a supplement to an upper-division physics course in electricity and magnetism. It will certainly be an excellent starting point for any individual interested in pursuing studies in magnet design and field analysis.' E. Kincanon, ChoiceTable of ContentsPreface; 1. Basic concepts; 2. Magnetic materials; 3. Potential theory; 4. Conductor-dominant transverse fields; 5. Complex analysis of transverse fields; 6. Iron-dominant transverse fields; 7. Axial field configurations; 8. Periodic magnetic channels; 9. Permanent magnets; 10. Time-varying fields; 11. Numerical methods; Appendices: A. Symbols and SI units; B. Vector analysis; C. Bessel functions; D. Legendre functions; E. Complex variable analysis; F. Complete elliptic integrals; Index.

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Book SynopsisThis book is a self-contained discussion of the major subjects in magnetostatics, the mathematical theory that describes the forces and fields resulting from the steady flow of electrical currents. This 2016 title has been reissued as an Open Access publication on Cambridge Core.Trade Review'[Principles of Magnetostatics] is a well-written combination of physics theory, application, and magnet design. The work will be of interest to physicists, engineers, and (of course) magnet designers. Also, an undergraduate that has completed the typical introductory physics and mathematics sequence should be adequately prepared to handle the presented material. … based on the examples given and the interesting design challenges, the reviewer believes this text can work well as a supplement to an upper-division physics course in electricity and magnetism. It will certainly be an excellent starting point for any individual interested in pursuing studies in magnet design and field analysis.' E. Kincanon, ChoiceTable of ContentsPreface; 1. Basic concepts; 2. Magnetic materials; 3. Potential theory; 4. Conductor-dominant transverse fields; 5. Complex analysis of transverse fields; 6. Iron-dominant transverse fields; 7. Axial field configurations; 8. Periodic magnetic channels; 9. Permanent magnets; 10. Time-varying fields; 11. Numerical methods; Appendices: A. Symbols and SI units; B. Vector analysis; C. Bessel functions; D. Legendre functions; E. Complex variable analysis; F. Complete elliptic integrals; Index.

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Book SynopsisThis hands-on text demystifies numerical modelling for early-stage physics and engineering students, with each chapter focusing on an intriguing physics problem. Developed over many years of teaching a computational modelling course, this stand-alone book gives students an essential numerical modelling toolkit for today's data-driven landscape.Table of ContentsPreface; How to use this book; First steps; 1. Rectangular finite quantum well – Stationary Schrödinger Equation in 1D; 2. Diffraction of light on a slit; 3. Pendulum as a standard unit of time; 4. Planetary system; 5. Gravitation inside a star; 6. Normal modes in a cylindrical waveguide; 7. Thermal insulation properties of a wall; 8. Cylindrical capacitor; 9. Coupled harmonic oscillators; 10. The Fermi-Pasta-Ulam problem; 11. Cold hydrogen star; 12. Rectangular quantum well filled with electrons – The idea of self-consistent calculations; 13. Time dependent Schrödinger Equation Dawid Dworzański; 14. Poisson equation in 2D; Appendices; Further Reading; Index.

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Book SynopsisIn this Element, the authors investigate the philosophical and foundational issues that arise in statistical mechanics . They introduce the theoretical approaches in SM, Boltzmannian SM and Gibbsian SM, and discuss how they conceptualise equilibrium and explain the approach to it. This title is also available as Open Access on Cambridge Core.Table of Contents1. Introduction; 2. Mechanics and probability; 3. Boltzmannian statistical mechanics; 4. Gibbsian statistical mechanics; Bibliography.

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

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

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

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

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

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

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

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

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

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

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

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