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Turbulent Flows Stephen B. Pope Cornell University, New York This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up to date, comprehensive, and designed for teaching, it is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. The topics covered include: the Navier-Stokes equations; the statistical representation of turbulent fields; mean-flow equations; the energy cascade; turbulence spectra; and the Kolmogorov hypotheses. Part II is concerned with various approaches for modelling or simulating turbulent flows. The approaches described are: direct numerical simulation (DNS); turbulent viscosity models (e.g., the K-e model); Reynolds-stress models; probability-density-function (PDF) methods; and large-eddy simulation (LES). There are numerous appendices in which the necessary mathematical techniques are presented. This book is primarily intended as a graduate level text in turbulent flows for engineering students. It is also valuable to students in applied mathematics, physics, oceanography, atmospheric sciences, as well as researchers and practising engineers. Contents: List of tables; Preface; Nomenclature; Part I Fundamentals: 1. Introduction; 2. The equations of fluid motion; 3. The statistical description of turbulent flows; 4. Mean-flow equations; 5. Free shear flows; 6. The scales of turbulent motion; 7. Wall flows; Part II Modelling and Simulation: 8. An introduction to modelling and simulation; 9. Direct numerical simulation; 10. Turbulent-viscosity models; 11. Reynoldsstress and related models; 12. PDF methods; 13. Large-eddy simulation; Part III Appendices: Appendix A Cartesian tensors; Appendix B Properties of second-order tensors; Appendix C Dirac delta functions; Appendix D Fourier transforms; Appendix E Spectral representation of stationary random processes; Appendix F The discrete Fourier transform; Appendix G Power-law spectra; Appendix H Derivation of Eulerian PDF equations; Appendix I Characteristic functions; Appendix J Diffusion processes; Bibliography; Author Index; Subject index. Materials Science An Intermediate Text William F. Hosford Univesity of Michigan, Ann Arbor This exciting new textbook on the structure, property and applications of materials, is written for advanced undergraduate courses on the principles of Materials Science. It covers the main topics commonly encountered by students in materials science and engineering but explores them in greater depth than standard introductory textbooks, making it ideal for use on a secondlevel course and upwards. Major topics covered include crystallography, symmetry and bondingrelated properties, phase diagrams and transformations, ordering, diffusion, solidification, and dedicated chapters on amorphous, liquid crystal, magnetic and novel materials, including shape memory. Each chapter contains numerous illustrative examples, problem sets, references and notes of interest to aid student understanding, with a chapter of hints on engineering calculations to ensure mathematical competency. Contents: 1. Microstructural analysis; 2. Symmetry; 3. Miller-Bravais system; 4. Stereographic projection; 5. Crystal defects 6. Phase diagrams; 7. Free energy basis for phase diagrams; 8. Ordering of solid solutions; 9. Diffusion; 10. Freezing; 11. Phase transformations; 12. Surfaces; 13. Bonding; 14. Sintering; 15. Amorphous materials; 16. Liquid crystals; 17. Molecular morphology; 18. Magnetic materials; 19. Porous and novel materials 20. Shape memory and super-elasticity; 21. Calculations. ISBN: 9780521867054 252pp £ 55.00 ISBN: 9780521598866 806pp £ 53.00 76
Introduction to Lattices and Order 2nd Edition B. A. Davey La Trobe University, Victoria & H. A. Priestley University of Oxford Differential Equations A. C. King University of Birmingham J. Billingham University of Birmingham & S.R. Otto University of Birmingham APPLIED MATHEMATICS This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. Contents: Preface; Preface to the first edition; 1. Ordered sets; 2. Lattices and complete lattices; 3. Formal concept analysis; 4. Modular, distributive and Boolean lattices; 5. Representation theory: the finite case; 6. Congruences; 7. Complete lattices and Galois connections; 8. CPOs and fixpoint theorems; 9. Domains and information systems; 10. Maximality principles; 11. Representation: the general case; Appendix A. A topological toolkit; Appendix B. Further reading; Notation index; Index. ISBN: 9780521134514 310pp ` 395.00 Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject. The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed. MATLAB is used extensively to illustrate the material. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODES and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory. Contents: Preface; Part I. Linear Equations: 1. Variable coefficient, second-order, linear ordinary differential equations; 2. Legendre functions; 3. Bessel functions; 4. Boundary value problems, Green’s functions and Sturm-Liouville theory; 5. Fourier series and the Fourier transform; 6. Laplace transforms; 7. Classification Properties Modern Mathematical Methods for Physicists and Engineers C.D. Cantrell University of Texas, Dallas and Complex Variable Methods for Second Order Partial Differential equations; Part II. Nonlinear Equations and Advanced Techniques: 8. Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations; 9. Nonlinear ordinary differential equations; 10. Group theoretical methods; 11. Asymptotic methods: basic ideas; 12. Asymptotic methods: differential equations; 13. Stability, instability and bifurcations; 14. Timeoptimal control in the phase plane; 15. An introduction to chaotic systems; Appendix 1. Linear algebra; Appendix 2. Continuity and differentiability; Appendix 3. Power series; Appendix 4. Sequences of functions; Appendix 5. Ordinary differential equations; Appendix 6. Complex variables; Appendix 7. A short introduction to MATLAB; Bibliography; Index. ISBN: 9780521670456 552pp ` 545.00 Modern Mathematical Methods for Physicists and Engineers provides an up-to-date mathematical and computational education for students, researchers, and practising engineers. The author begins with a review of computation, and then deals with a range of key concepts including sets, fields, matrix theory, and vector spaces. He then goes on to cover more advanced subjects such as linear mappings, group theory, and special functions. In this way, he concentrates exclusively on the most important topics for the working physical scientist or engineer with the aim of helping them to make intelligent use of the latest computational and analytical methods. The book contains well over 400 homework problems and covers many topics not dealt with in other textbooks. It will be ideal for senior undergraduate and graduate students in the physical sciences and engineering, as well as a valuable reference for working engineers. Contents: Preface; 1. Foundations of computation; 2. Sets and mappings; 3. Evaluation of functions; 4. Groups, rings and fields; 5. Vector spaces; 6. Linear mappings I; 7. Linear functionals; 8. Inner products and norms; 9. Linear mappings II; 10. Convergence in normed vector spaces; 11. Group representations; 12. Special functions; Appendices. ISBN: 9780521670494 784pp ` 695.00 77
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