Singularities: Formation, Structure and Propagation

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Opis: Singularities: Formation, Structure and Propagation - M. A. Fontelos, J. Eggers

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.Preface; 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; References; Index.


Szczegóły: Singularities: Formation, Structure and Propagation - M. A. Fontelos, J. Eggers

Tytuł: Singularities: Formation, Structure and Propagation
Autor: M. A. Fontelos, J. Eggers
Producent: Cambridge University Press
ISBN: 9781107485495
Rok produkcji: 2015
Ilość stron: 470
Oprawa: Miękka
Waga: 0.74 kg


Recenzje: Singularities: Formation, Structure and Propagation - M. A. Fontelos, J. Eggers

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Singularities: Formation, Structure and Propagation

,

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.Preface; 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; References; Index.

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Cena 253,00 PLN
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Wysyłka: Niedostępna
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Szczegóły: Singularities: Formation, Structure and Propagation - M. A. Fontelos, J. Eggers

Tytuł: Singularities: Formation, Structure and Propagation
Autor: M. A. Fontelos, J. Eggers
Producent: Cambridge University Press
ISBN: 9781107485495
Rok produkcji: 2015
Ilość stron: 470
Oprawa: Miękka
Waga: 0.74 kg


Recenzje: Singularities: Formation, Structure and Propagation - M. A. Fontelos, J. Eggers

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