Singularities

Singularities: formation, structure, and propagation

by Eggers, J., (Jens G.)

Type Book
Rate 0.0 /5

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…

Read More ↓
Details
Files
Reviews
Download

Title Statements

  • Full title :Singularities : formation, structure, and propagation / J. Eggers, University of Bristol, M.A. Fontelos, Consejo Superior de Investigaciones Cientificas, Madrid.

Summary

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.

Read More ↓

Edition Statements

  • Publication Date:2015.

Publication Statements

The Physical Object

  • Description:xvi, 453 pages : : illustrations (some color) ; : 24 cm.

Edition Identifiers

  • ISBN:9781107098411, 1107098416, 9781107485495, 1107485495
  • oclc:ocn908310930
  • LC Classification:QA614.58
  • Dewey Decimal:514/.746

Table of Contents

1.What are singularities all about? -- 1.1.Drop pinch-off: scaling and universality -- 1.2.Stationary cusps: persistent singularities -- 1.3.Shock waves: propagation -- Exercises -- 2.Blowup -- 2.1.A scalar example -- 2.2.Crossover -- 2.3.Regularization: saturation -- 2.4.What is special about power laws? -- Exercises -- 3.Similarity profile -- 3.1.The spatial structure of blowup -- 3.2.Stability -- 3.3.Similarity solutions and the dynamical system -- 3.4.Regularization -- 3.5.Continuation -- 3.5.1.Similarity description -- Exercises -- 4.Continuum equations -- 4.1.General ideas -- 4.2.The Navier[--]Stokes equation -- 4.3.Boundary conditions -- 4.4.Free surface motion -- 4.5.Special limits -- 4.5.1.Potential flow -- 4.5.2.Two-dimensional flow -- 4.5.3.Stokes flow -- 4.6.Elasticity -- Exercises -- 5.Local singular expansions -- 5.1.Potential flow in a corner -- 5.2.Potential flow around a two-dimensional airfoil -- 5.3.Stokes waves -- 5.4.Electric fields near tips: Taylor cones -- 5.5.Mixed boundary conditions -- 5.6.Viscous flow in corners and Moffatt eddies -- Exercises -- 6.Asymptotic expansions of PDEs -- 6.1.Thin film equation -- 6.1.1.Hele-Shaw flow -- 6.2.Slender jets -- Exe…

Read More ↓

Subjects

Singularités (Mathématiques) Singularities (Mathematics)

Writers

Eggers, J., (Jens G.) Fontelos, M. A., (Marco Antonio)

More from this Series

Rate & Review

0.0/5
(0 people Voted)

No reviews yet. Be the first to rate this work.

Files & Downloads

  • Singularities: Formation, Structure, and Propagat…

    PDF · 28.7 MB · updated
    Login →

  • Singularities: Formation, Structure, and Propagat…

    PDF · 7.0 MB · updated
    Login →
Log in to request a copy