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Singularities Formation Structure and Propagation 1st Edition by Jens Eggers, Marco Antonio Fontelos 9781107098411 1107098416

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Singularities Formation Structure and Propagation 1st Edition Jens Eggers Digital Instant Download

Author(s): Jens Eggers, Marco Antonio Fontelos
ISBN(s): 9781107098411, 1107098416
Edition: 1
File Details: PDF, 7.02 MB
Year: 2015
Language: english
SKU: EB-6984002 Category: Tags: ,

Singularities Formation Structure and Propagation 1st Edition by Jens Eggers, Marco Antonio Fontelos – Ebook PDF Instant Download/Delivery: 9781107098411, 1107098416

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Product details:

ISBN 10: 1107098416

ISBN 13: 9781107098411

Author: Jens Eggers, Marco Antonio Fontelos

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.

Table of contents:

Part I: Setting the Scene

  1. What Are Singularities All About?

  2. Blowup

  3. Similarity Profile

  4. Continuum Equations

  5. Local Singular Expansions

  6. Asymptotic Expansions of PDEs

Part II: Formation of Singularities
7. Drop Breakup
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

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Tags: Jens Eggers, Marco Antonio Fontelos, Singularities, Propagation