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Singularities: Formation, Structure, and Propagation


Part of Cambridge Texts in Applied Mathematics

  • Date Published: September 2015
  • availability: In stock
  • format: Paperback
  • isbn: 9781107485495

£ 42.99

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About the Authors
  • Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.

    • Discusses a wide range of singular phenomena from a unifying point of view
    • Makes current techniques for studying singularities available to a wider audience
    • Contains 70 examples to reinforce the reader's understanding of important concepts and 180 exercises ranging in difficulty
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    Reviews & endorsements

    'The book will serve as an excellent introduction to the field of singularities in continuum mechanics, and a valuable resource for researchers … In short, a wonderful achievement!' H. K. Moffatt, Journal of Fluid Mechanics

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    Product details

    • Date Published: September 2015
    • format: Paperback
    • isbn: 9781107485495
    • length: 470 pages
    • dimensions: 227 x 152 x 20 mm
    • weight: 0.74kg
    • contains: 125 b/w illus. 8 colour illus. 180 exercises
    • availability: In stock
  • Table of Contents

    Part I. Setting the Scene:
    1. What are singularities all about?
    2. Blow-up
    3. Similarity profile
    4. Continuum equations
    5. Local singular expansions
    6. Asymptotic expansions of PDEs
    Part II. Formation of Singularities:
    7. Drop break-up
    8. A numerical example: drop pinch-off
    9. Slow convergence
    10. Continuation
    Part III. Persistent Singularities – Propagation:
    11. Shock waves
    12. The dynamical system
    13. Vortices
    14. Cusps and caustics
    15. Contact lines and cracks
    Appendix A. Vector calculus
    Appendix B. Index notation and the summation convention
    Appendix C. Dimensional analysis

  • Authors

    J. Eggers, University of Bristol
    J. Eggers is Professor of Applied Mathematics at the University of Bristol. His career has been devoted to the understanding of self-similar phenomena, and he has more than fifteen years of experience in teaching non-linear and scaling phenomena to undergraduate and postgraduate students. Eggers has made fundamental contributions to our mathematical understanding of free-surface flows, in particular the break-up and coalescence of drops. His work was instrumental in establishing the study of singularities as a research field in applied mathematics and in fluid mechanics. He is a member of the Academy of Arts and Sciences in Erfurt, Germany, a fellow of the American Physical Society, and has recently been made a Euromech Fellow.

    M. A. Fontelos, Universidad Autónoma de Madrid
    M. A. Fontelos is a researcher in applied mathematics at the Spanish Research Council (CSIC). His scientific work has focused on partial differential equations and their applications to fluid mechanics, with special emphasis on the study of singularities and free-surface flows. His main results concern the formation of singularities (or not) combining the use of rigorous mathematical results with asymptotic and numerical methods.

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