The Mathematical Foundations of Mixing the Linked Twist Maps as a Paradigm in Applications

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Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions. First book explaining new important ideas in our understanding of how fluids mix Authors are well-known book writers and leading researchers Starts with a broad, accessible and thought-provoking chapter, and ends with a collection of open problems

Quantum Mechanics A Paradigms Approach

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This popular undergraduate quantum mechanics textbook is now available in a more affordable printing from Cambridge University Press. Unlike many other books on quantum mechanics, this text begins by examining experimental quantum phenomena such as the Stern-Gerlach experiment and spin measurements, using them as the basis for developing the theoretical principles of quantum mechanics. Dirac notation is developed from the outset, offering an intuitive and powerful mathematical toolset for calculation, and familiarizing students with this important notational system. This non-traditional approach is designed to deepen students' conceptual understanding of the subject, and has been extensively class tested. Suitable for undergraduate physics students, worked examples are included throughout and end of chapter problems act to reinforce and extend important concepts. Additional activities for students are provided online, including interactive simulations of Stern-Gerlach experiments, and a fully worked solutions manual is available for instructors. Focuses on modern experimental quantum mechanics, immersing the reader in current research trends and developing an intuitive understanding of the subject Develops understanding and fluency of Dirac and matrix notation, giving students access to a powerful mathematical toolset Fully worked examples, homework problems, and interactive simulations enhance the book's pedagogical value Table of Contents Preface Prologue 1. Stern-Gerlach experiments 2. Operators and measurement 3. Schrödinger time evolution 4. Quantum spookiness 5. Quantized energies: particle in a box 6. Unbound states 7. Angular momentum 8. Hydrogen atom 9. Harmonic oscillator 10. Perturbation theory 11. Hyperfine structure and the addition of angular momenta 12. Perturbation of hydrogen 13. Identical particles 14. Time-dependent perturbation theory 15. Periodic systems 16. Modern applications of quantum mechanics Appendix A. Probability Appendix B. Complex numbers Appendix C. Matrices Appendix D. Waves and fourier analysis Appendix E. Separation of variables Appendix F. Integrals Appendix G. Physical constants Index