ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS

1.IntrodnctionWegiveaproofofthestrongconvergenceinofthesolutionoftheparabolicapproximationtowardstheentropicsolutiontothescalarconservationlawwhereuo(RN),udenotessomeapproximationofuosuchthatandthefluxfsatisfiesTheconvergenceoftheapproximatesolutions...     

Full-trajectory diagnosis of laser-driven radiative blast waves in search of thermal plasma instabilities

Experimental investigations into the dynamics of cylindrical, laser-driven, high-Mach-number shocks are used to study the thermal cooling instability predicted to occur in astrophysical radiative blast waves. A streaked Schlieren technique measures the full blast-wave trajectory on a single-shot basis, which is key for observing shock velocity oscillations. Electron density profiles and deceleration parameters associated with radiative blast waves were recorded, enabling the calculation of important blast-wave parameters including the fraction of radiated energy, epsilon, as a function of time for comparison with radiation-hydrodynamics simulations.     

Spatial coherence of short wavelength high-order harmonics

Received: 12 May 1997     

Production of periodically modulated laser-driven blast waves in a clustering gas

To study hydrodynamic behavior on thin shell high Mach number blast waves, experiments have been performed in which spatially tailored shock waves have been launched in a gas of clusters using an intense 35 fs laser pulse. The target medium was first modified by destroying clusters in specific locations using a spatially modulated laser focus. Under subsequent intense laser irradiation, the efficient absorption properties of the remaining clustered regions compared to those regions with no clusters led to a pattern of hot and cold plasma resulting in a cylindrical blast wave with a periodic modulation imprinted on the shock front. This technique may provide a method for studying thin shell instabilities in strongly radiative blast waves.     

Observation of a velocity domain cooling instability in a radiative shock

We report on experimental investigations into strong, laser-driven, radiative shocks in cluster media. Cylindrical shocks launched with several joules of deposited energy exhibit strong radiative effects including rapid deceleration, radiative preheat, and shell thinning. Using time-resolved propagation data from single-shot streaked Schlieren measurements, we have observed temporal modulations on the shock velocity, which we attribute to the thermal cooling instability, a process which is believed to occur in supernova remnants but until now has not been observed experimentally.     

ON LACUNARY STATISTICAL CONVERGENCE OF ORDER α

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nαθ(p)-summability. Furthermore, some relations between the spaces Nαθ(p) and Sαθare examined.