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Asymptotics beyond All Orders

  • Book
  • © 1991

Overview

Editors:
  1. Harvey Segur

    1. University of Colorado, Boulder, USA

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  2. Saleh Tanveer

    1. Ohio State University, Columbus, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Herbert Levine

    1. University of California, San Diego, La Jolla, USA

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Part of the book series: NATO Science Series B: (NSSB, volume 284)

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Table of contents (30 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  3. The Geometric Model of Crystal Growth

    1. The Geometric Model of Crystal Growth — An Overview

      • Harvey Segur
      Pages 29-35

    2. Numerical Analysis of the Geometric Model for Dendritic Growth of Crystals

      • J. M. Hammersley, G. Mazzarino
      Pages 37-66

  4. Dendritic Crystal Growth

    1. Dendritic Crystal Growth: Overview

      • Herbert Levine
      Pages 67-73

    2. An Experimental Assessment of Continuum Models of Dendritic Growth

      • J. P. Gollub
      Pages 75-86

    3. A New Formulation for Dendritic Crystal Growth in two Dimensions

      • E. A. Coutsias, H. Segur
      Pages 87-104

  5. Directional Solidification of Solids

    1. Directional Growth of Dilute Mixtures and Lamellar Eutectics

      • K. Kassner, C. Misbah, H. Müller-Krumbhaar, Y. Saito, D. E. Temkin
      Pages 105-118

    2. A Flat Interface and its Unfolding Bifurcations

      • A. Libchaber, A. J. Simon, J.-M. Flesselles
      Pages 119-129

  6. Flow in a Hele-Shaw Cell (Also known as VISCOUS FINGERING)

    1. Viscous Displacement in a Hele-Shaw Cell

      • S. Tanveer
      Pages 131-153

    2. Saffman — Taylor Viscous Fingering in a Wedge

      • Martine Ben Amar, Roland Combescot
      Pages 155-173

    3. Saffman-Taylor Problem in Sector Geometry

      • Yuhai Tu
      Pages 175-186

  7. The Rapidly Forced Pendulum

    1. Exponentially Small Estimates for Separatrix Splittings

      • Jürgen Scheurle, Jerrold E. Marsden, Philip Holmes
      Pages 187-195

    2. Exponentially Small Phenomena in the Rapidly Forced Pendulum

      • Martin Kummer, James A. Ellison, A. W. Sáenz
      Pages 197-211

    3. Proof of an Asymptotic Symmetry of the Rapidly Forced Pendulum

      • Yi-Hua Chang
      Pages 213-221

  8. Ordinary Differential Equations

    1. Exponentially Small Oscillations in the Solution of an Ordinary Differential Equation

      • J. G. Byatt-Smith, A. M. Davie
      Pages 223-240

    2. Singular Perturbation of Solitons

      • Yves Pomeau
      Pages 241-246

    3. Reflection Coefficient Beyond All Orders for Singular Problems

      • Jishan Hu, Martin D. Kruskal
      Pages 247-253

    4. Laminar Flow in a Porous Channel

      • J. B. McLeod
      Pages 255-266
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Keywords

About this book

An asymptotic expansion is a series that provides a sequence of increasingly accurate approximations to a function in a particular limit. The formal definition, given by Poincare (1886, Acta Math. 8:295), is as follows. Given a function,

Editors and Affiliations

  • University of Colorado, Boulder, USA

    Harvey Segur

  • Ohio State University, Columbus, USA

    Saleh Tanveer

  • University of California, San Diego, La Jolla, USA

    Herbert Levine

Bibliographic Information

  • Book Title: Asymptotics beyond All Orders

  • Editors: Harvey Segur, Saleh Tanveer, Herbert Levine

  • Series Title: NATO Science Series B:

  • DOI: https://doi.org/10.1007/978-1-4757-0435-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1991

  • Softcover ISBN: 978-1-4757-0437-2Published: 02 June 2012

  • eBook ISBN: 978-1-4757-0435-8Published: 06 December 2012

  • Series ISSN: 0258-1221

  • Edition Number: 1

  • Number of Pages: 408

  • Number of Illustrations: 7 b/w illustrations

  • Topics: Theoretical, Mathematical and Computational Physics

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