Singularities in Fluids, Plasmas, and Optics: Proceedings of a NATO Advanced Research Workshop July 6-10, 1992, Herkalion, Greece
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....
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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 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.
PrefaceWell-posed Numerical Calculations for Free-Surface Flows1On the Well-Posedness of Two Fluid Interfacial Flows with Surface Tension11Can Three-Dimensional Ideal Flows Become Singular in a Finite Time?39Singularity Formation for Models of Axi-Symmetric Swirling Flow53Complex Analytic Branching Structures in Porous Media Convection65Singularities of the Velocity Field and Interaction Locality of Turbulence75Solitons, Euler's Equation, and the Geometry of Curve Motion93Asymptotic and Numerical Results for Blowing-up Solutions to Semilinear Heat Equations111Scaling of a Singularity of Euler131The Rayleigh Centrifugal Instability for Vortex Rings with Swirl137Dynamics of Magnetic Vortex Rings151Morphology and Singularities of Vortex Flows159Topological Transitions in Hele-Shaw Flow167Separatrices and Singularities189Nonlinear Dynamics of Ultra-Cold Gas197The Interaction Representation for Nonlinear Schrodinger Equation Penleve Problem205Self-Similar Regimes of Subsonic Langmuir Wave Collapse213Asymptotic Profiles of Blow-up Solutions of the Nonlinear Schrodinger Equation221Modulational Stability of Periodic Solutions of the Kuramoto-Sivashinsky Equation255Dynamic Rescaling for Tracking Point Singularities: Application to Nonlinear Schrodinger Equation and Related Problems265Dynamic Self-Focusing of Structured Laser Beams in Plasma281Experimental Manifestation of Strong Langmuir Turbulence301On Long-Lived Singularities in the Nonlinear Shroedinger Equation309On Collapsing Solutions of the Nonlinear Schroedinger Equation in Supercritical Case317Sharp Criteria for Wave Collapse and Wave Collapse Ideology in Application to Optical Pulses Compression323Fluid Analogies in Optics333
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