Modeling multidimensional effects in the propagation of radiative shocks

Radiative shocks (also called supercritical shocks) are high Mach number shock waves that photoionize the medium ahead of the shock front and give rise to a radiative precursor. They are generated in the laboratory using high-energy or high-power lasers and are frequently present in a wide range of astronomical objects. Their modelisation in one dimension has been the subject of numerous studies, but generalization to three dimensions is not straightforward. We calculate analyticaly the absorption of radiation in a grey uniform cylinder and show how it decreases with $\chi R$, the product of the opacity $\chi$ and of the cylinder radius $R$. Simple formulas, whose validity range increases when $\chi R$ diminishes, are derived for the radiation field on the axis of symmetry. Numerical calculations in three dimensions of the radiative energy density, flux and pressure created by a stationary shock wave show how the radiation decreases whith $R$. Finally, the bidimensional structures of both the precursor and the radiation field are calculated with time-dependent radiation hydrodynamics numerical simulations and the influence of two-dimensional effects on the electron density, the temperature, the shock velocity and the shock geometry are exhibited. These simulations show how the radiative precursor shortens, cools and slows down when $R$ is decreased

Correction to: Clinical recommendations for cardiovascular magnetic resonance mapping of T1, T2, T2* and extracellular volume: A consensus statement by the Society for Cardiovascular Magnetic Resonance (SCMR) endorsed by the European Association for Cardiovascular Imaging (EACVI).

CORRECTION TO: J CARDIOVASC MAGN RESON (2017) 19: 75. DOI: 10.1186/S12968-017-0389-8: In the original publication of this article [1] the "Competing interests" section was incorrect. The original publication stated the following competing interests

Analytical modeling of the steady radiative shock

In a paper dated 2000 [1], a fully analytical theory of the radiative shock has been presented. This early model had been used to design [2] radiative shock experiments at the Laboratory for the Use of Intense Lasers (LULI) [3–5]. It became obvious from numerical simulations [6, 7] that this model had to be improved in order to accurately recover experiments. In this communication, we present a new theory in which the ionization rates in the unshocked ($\bar{Z_1}$) and shocked ($\bar{Z_2} \neq \bar{Z_1}$) material, respectively, are included. Associated changes in excitation energy are also taken into account. We study the influence of these effects on the compression and temperature in the shocked medium

Delta(3)-Aryl/heteroaryl substituted heterocycles via sequential Pd-catalysed termolecular cascade/ring closing metathesis (RCM)

WOS: 000232676900003A novel sequential Pd-catalysed termolecular allenylation cascade/Ru catalysed RCM process affords a diverse range of Delta(3)-aryl/ heteroaryl substituted five-seven membered nitrogen and oxygen heterocycles. Further elaboration, via 1,3-dipolar cycloaddition, in selected cases, afforded fused heterocyclic ring systems. (c) 2005 Elsevier Ltd. All rights reserved

Shock Wave Analysis from Laboratory Experiments: Application to Laboratory Astrophysics

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