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The conditions for validity and the limitations of experiments intended to simulate astrophysical hydrodynamics are discussed, with application to some ongoing experiments. For systems adequately described by the Euler equations, similarity criteria required for properly scaled experiments are identiÐed. The conditions for the applicability of the Euler equations are formulated, based on the analysis of localization, heat conduction, viscosity, and radiation. Other considerations involved in such a scaling, including its limitations at small spatial scales, are discussed. The results are applied to experiments aimed at simulating three-dimensional hydrodynamics during supernova explosions and hydrodynamic instabilities in young supernova remnants. In addition, hydrodynamic situations with signiÐcant radiative e †ects are discussed.

We report evidence that the asymptotic low-energy power law slope alpha (below the spectral break) of BATSE gamma-ray burst photon spectra evolves with time rather than remaining constant. We find a high degree of positive correlation exists between the time-resolved spectral break energy E_pk and alpha. In samples of 18 "hard-to-soft" and 12 "tracking" pulses, evolution of alpha was found to correlate with that of the spectral break energy E_pk at the 99.7% and 98% confidence levels respectively. We also find that in the flux rise phase of "hard-to-soft" pulses, the mean value of alpha is often positive and in some bursts the maximum value of alpha is consistent with a value > +1. BATSE burst 3B 910927, for example, has a alpha_max equal to 1.6 +/- 0.3. These findings challenge GRB spectral models in which alpha must be negative of remain constant.Comment: 12 pages (including 6 figures), accepted to Ap

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We measure up to 2x10;{10} positrons per steradian ejected out the back of approximately mm thick gold targets when illuminated with short ( approximately 1 ps) ultraintense ( approximately 1x10;{20} W/cm;{2}) laser pulses. Positrons are produced predominately by the Bethe-Heitler process and have an effective temperature of 2-4 MeV, with the distribution peaking at 4-7 MeV. The angular distribution of the positrons is anisotropic. Modeling based on the measurements indicate the positron density to be approximately 10;{16} positrons/cm;{3}, the highest ever created in the laboratory.

We analyze the time profiles of individual gamma-ray burst (GRB) pulses, that are longer than 2 s, by modelling them with analytical functions that are based on physical first principles and well-established empirical descriptions of GRB spectral evolution. These analytical profiles are independent of the emission mechanism and can be used to model both the rise and decay profiles allowing for the study of the entire pulse light-curve. Using this method, we have studied a sample of 77 individual GRB pulses, allowing us to examine the fluence, pulse width, asymmetry, and rise and decay power-law distributions. We find that the rise phase is best modelled with a power law of average index r = 1.31 ± 0.11 and that the average decay phase has an index of d = 2.39 ± 0.12. We also find that the ratio between the rise and decay times (the pulse asymmetry) exhibited by the GRB pulse shape has an average value of 0.47 which varies little from pulse to pulse and is independent of pulse duration or intensity. Although this asymmetry is largely uncorrelated to other pulse properties, a statistically significant trend is observed between the pulse asymmetry and the decay power law index, possibly hinting at the underlying physics. We compare these parameters with those predicted to occur if individual pulse shapes are created purely by relativistic curvature effects in the context of the fireball model, a process that -2makes specific predictions about the shape of GRB pulses. The decay index distribution obtained from our sample shows that the average GRB pulse fades faster than the value predicted by curvature effects, with only 39% of our sample being consistent with the curvature model. We discuss several refinements of the relativistic curvature scenario that could naturally account for these observed deviations, such as symmetry breaking and varying relative time-scales within individual pulses.

We present two-dimensional inviscid hydrodynamic simulations of a protoplanetary disk with an embedded planet, emphasizing the evolution of potential vorticity (the ratio of vorticity to density) and its dependence on numerical resolutions. By analyzing the structure of spiral shocks made by the planet, we show that progressive changes of the potential vorticity caused by spiral shocks ultimately lead to the excitation of a secondary instability. We also demonstrate that very high numerical resolution is required to both follow the potential vorticity changes and identify the location where the secondary instability is first excited. Low-resolution results are shown to give the wrong location. We establish the robustness of a secondary instability and its impact on the planet's torque. After the saturation of the instability, the disk shows large-scale nonaxisymmetry, causing the torque on the planet to oscillate with large amplitude. The impact of the oscillating torque on the protoplanet's migration remains to be investigated.

We consider irrotational dust solutions of the Einstein equations. We define ``velocity-dominated'' singularities of these solutions. We show that a velocity-dominated singularity can be considered as a three-dimensional manifold with an invariantly and uniquely defined inner metric tensor, extrinsic curvature tensor, and scalar bang time function. We compute this structure for a variety of known exact models. The structure of the singularity uniquely determines the solution in a certain class of spatially inhomogeneous models. We briefly discuss the b boundary (Schmidt boundary). In an appendix we generalize conformal transformations to ``stretch'' transformations and calculate the curvature form of a stretched metric.