Singularities in Fluids, Plasmas and Optics

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.

I. Singularities in Fluids.- Well-posed Numerical Calculations for Free-Surface Flows.- On the Well-Posedness of Two Fluid Interfacial Flows with Surface Tension.- Can Three-Dimensional Ideal Flows Become Singular in a Finite Time?.- Singularity Formation for Models of Axi-Symmetric Swirling Flow.- Complex Analytic Branching Structures in Porous Media Convection.- Singularities of the Velocity Field and Interaction Locality of Turbulence.- Solitons, Euler’s Equation, and the Geometry of Curve Motion.- Asymptotic and Numerical Results for Blowing-up Solutions to Semilinear Heat Equations.- Scaling of a Singularity of Euler.- The Rayleigh Centrifugal Instability for Vortex Rings with Swirl.- Dynamics of Magnetic Vortex Rings.- Morphology and Singularities of Vortex Flows.- Topological Transitions in Hele-Shaw Flow.- II. Singularities in Optics and Plasmas.- Separatrices and Singularities.- Nonlinear Dynamics of Ultra-Cold Gas.- The Interaction Representation for Nonlinear Schrodinger Equation Penleve Problem.- Self-Similar Regimes of Subsonic Langmuir Wave Collapse.- Asymptotic Profiles of Blow-up Solutions of the Nonlinear Schrödinger Equation.- Modulational Stability of Periodic Solutions of the Kuramoto-Sivashinsky Equation.- Dynamic Rescaling for Tracking Point Singularities: Application to Nonlinear Schrödinger Equation and Related Problems.- Dynamic Self-Focusing of Structured Laser Beams in Plasma.- Experimental Manifestation of Strong Langmuir Turbulence.- On Long-Lived Singularities in the Nonlinear Shroedinger Equation.- On Collapsing Solutions of the Nonlinear Schroedinger Equation in Supercritical Case.- Sharp Criteria for Wave Collapse and Wave Collapse Ideology in Application to Optical Pulses Compression.- Fluid Analogies in Optics.