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Singularities in Fluids, Plasmas and Optics

  • Book
  • © 1993

Overview

Editors:
  1. Russel E. Caflisch

    1. Department of Mathematics, University of California at Los Angeles, Los Angeles, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. George C. Papanicolaou

    1. Courant Institute of Mathematical Sciences, New York University, New York, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nato Science Series C: (ASIC, volume 404)

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Table of contents (26 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Singularities in Fluids

    1. Well-posed Numerical Calculations for Free-Surface Flows

      • Greg Baker, Saleh Tanveer
      Pages 1-10

    2. On the Well-Posedness of Two Fluid Interfacial Flows with Surface Tension

      • J. Thomas Beale, Thomas Y. Hou, John S. Lowengrub
      Pages 11-38

    3. Can Three-Dimensional Ideal Flows Become Singular in a Finite Time?

      • M. E. Brachet, M. Meneguzzi, A. Vincent, H. Politano, P. L. Sulem
      Pages 39-51

    4. Singularity Formation for Models of Axi-Symmetric Swirling Flow

      • Russel E. Caflisch, Peter Smereka
      Pages 53-64

    5. Complex Analytic Branching Structures in Porous Media Convection

      • Thierry Dombre
      Pages 65-74

    6. Singularities of the Velocity Field and Interaction Locality of Turbulence

      • G. E. Falkovich
      Pages 75-91

    7. Solitons, Euler’s Equation, and the Geometry of Curve Motion

      • Raymond E. Goldstein, Dean M. Petrich
      Pages 93-109

    8. Asymptotic and Numerical Results for Blowing-Up Solutions to Semilinear Heat Equations

      • Joseph. B. Keller, John S. Lowengrub
      Pages 111-129

    9. Scaling of a Singularity of Euler

      • R. M. Kerr
      Pages 131-135

    10. The Rayleigh Centrifugal Instability for Vortex Rings with Swirl

      • Alexander Lifschitz
      Pages 137-149

    11. Dynamics of Magnetic Vortex Rings

      • N. Papanicolaou
      Pages 151-158

    12. Morphology and Singularities of Vortex Flows

      • Alain Pumir, Eric D. Siggia
      Pages 159-166

    13. Topological Transitions in Hele-Shaw Flow

      • Michael J. Shelley, Raymond E. Goldstein, Adriana I. Pesci
      Pages 167-188

  3. Singularities in Optics and Plasmas

    1. Separatrices and Singularities

      • A. Bhattacharjee
      Pages 189-195

    2. Nonlinear Dynamics of Ultra-Cold Gas

      • V. Flambaum, E. Kuznetsov
      Pages 197-203

    3. The Interaction Representation for Nonlinear Schrodinger Equation Penleve Problem

      • G. M. Fraiman
      Pages 205-212

    4. Self-Similar Regimes of Subsonic Langmuir Wave Collapse

      • V. M. Malkin, V. N. Khudik
      Pages 213-219

    5. Asymptotic Profiles of Blow-Up Solutions of the Nonlinear Schrödinger Equation

      • Hayato Nawa
      Pages 221-253

    6. Modulational stability of periodic solutions of the Kuramoto-Sivashinsky equation

      • Demetrios T. Papageorgiou, George C. Papanicolaou, Yiorgos S. Smyrlis
      Pages 255-263
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Keywords

About this book

Singularities in Fluids, Plasmas and Optics, which contains the proceedings of a NATO Workshop held in Heraklion, Greece, in July 1992, provides a survey of the state of the art in the analysis and computation of singularities in physical problems drawn from fluid mechanics, plasma physics and nonlinear optics. The singularities include curvature singularities on fluid interfaces, the onset of turbulence in 3-D inviscid flows, focusing singularities for laser beams, and magnetic reconnection. The highlights of the book include the nonlinear Schrödinger equation for describing laser beam focusing, the method of complex variables for the analysis and computation of singularities on fluid interfaces, and studies of singularities for the 3-D Euler equations. The book is suitable for graduate students and researchers in these areas.

Editors and Affiliations

  • Department of Mathematics, University of California at Los Angeles, Los Angeles, USA

    Russel E. Caflisch

  • Courant Institute of Mathematical Sciences, New York University, New York, USA

    George C. Papanicolaou

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