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Singularities in Fluids, Plasmas and Optics : NATO SCIENCE SERIES SERIES C: MATHEMATICAL AND PHYSICAL SCIENCES - Russel Caflisch

Singularities in Fluids, Plasmas and Optics

NATO SCIENCE SERIES SERIES C: MATHEMATICAL AND PHYSICAL SCIENCES

By: Russel Caflisch (Editor), George C. Papanicolaou (Editor)

Hardcover Published: 30th June 1993
ISBN: 9780792323334
Number Of Pages: 348

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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 Schr‚ÄĚdinger 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.

Preface
Well-posed Numerical Calculations for Free-Surface Flowsp. 1
On the Well-Posedness of Two Fluid Interfacial Flows with Surface Tensionp. 11
Can Three-Dimensional Ideal Flows Become Singular in a Finite Time?p. 39
Singularity Formation for Models of Axi-Symmetric Swirling Flowp. 53
Complex Analytic Branching Structures in Porous Media Convectionp. 65
Singularities of the Velocity Field and Interaction Locality of Turbulencep. 75
Solitons, Euler's Equation, and the Geometry of Curve Motionp. 93
Asymptotic and Numerical Results for Blowing-up Solutions to Semilinear Heat Equationsp. 111
Scaling of a Singularity of Eulerp. 131
The Rayleigh Centrifugal Instability for Vortex Rings with Swirlp. 137
Dynamics of Magnetic Vortex Ringsp. 151
Morphology and Singularities of Vortex Flowsp. 159
Topological Transitions in Hele-Shaw Flowp. 167
Separatrices and Singularitiesp. 189
Nonlinear Dynamics of Ultra-Cold Gasp. 197
The Interaction Representation for Nonlinear Schrodinger Equation Penleve Problemp. 205
Self-Similar Regimes of Subsonic Langmuir Wave Collapsep. 213
Asymptotic Profiles of Blow-up Solutions of the Nonlinear Schrodinger Equationp. 221
Modulational Stability of Periodic Solutions of the Kuramoto-Sivashinsky Equationp. 255
Dynamic Rescaling for Tracking Point Singularities: Application to Nonlinear Schrodinger Equation and Related Problemsp. 265
Dynamic Self-Focusing of Structured Laser Beams in Plasmap. 281
Experimental Manifestation of Strong Langmuir Turbulencep. 301
On Long-Lived Singularities in the Nonlinear Shroedinger Equationp. 309
On Collapsing Solutions of the Nonlinear Schroedinger Equation in Supercritical Casep. 317
Sharp Criteria for Wave Collapse and Wave Collapse Ideology in Application to Optical Pulses Compressionp. 323
Fluid Analogies in Opticsp. 333
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792323334
ISBN-10: 0792323335
Series: NATO SCIENCE SERIES SERIES C: MATHEMATICAL AND PHYSICAL SCIENCES
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 348
Published: 30th June 1993
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.78  x 2.54
Weight (kg): 0.77