In this paper, we study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscous compressible fluids without heat conduction will blow up in finite time, as long as the initial data has an isolated mass group (see Definition 2.2). The results hold regardless of either the size of the initial data or the far fields being vacuum or not. This improves the blowup results of Xin [22] by removing the crucial assumptions that the initial density has compact support and the smooth solution has finite total energy. Furthermore, the analysis here also yields that any classical solutions of viscous compressible fluids without heat conduction in bounded domains or periodic domains will blow up in finite time, if the initial data have an isolated mass group satisfying some suitable conditions.

The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods. The hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical phenomenon. In this paper, a matrix-based stability analysis for 2-D Euler equations is performed to explore the cause of instability of numerical schemes. By combining the Roe with HLL flux in different directions and different flux components, we give an interesting explanation to the linear numerical instability. Based on such analysis, some hybrid schemes are compared to illustrate different mechanisms in controlling shock instability. Numerical experiments are presented to verify our analysis results. The conclusion is that the scheme of restricting directly instability source is more stable than other hybrid schemes.

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The adsorption and catalytic activation of O on single atom iron catalysts with graphene-based substrates were investigated systematically by density functional theory calculation. It is found that the support effects of graphene-based substrates have a significant influence on the stability of the single atom catalysts, the adsorption configuration, the electron transfer mechanism, the adsorption energy and the energy barrier. The differences in the stable adsorption configuration of O on single atom iron catalysts with different graphene-based substrates can be well understood by the symmetrical matching principle based on frontier molecular orbital analysis. There are two different mechanisms of electron transfer, in which the Fe atom acts as the electron donor in single vacancy graphene-based substrates while the Fe atom mainly acts as the bridge for electron transfer in double vacancy graphene-based substrates. The Fermi softness and work function are good descriptors of the adsorption energy and they can well reveal the relationship between electronic structure and adsorption energy. This single atom iron catalyst with single vacancy graphene modified by three nitrogen atoms is a promising non-noble metal single atom catalyst in the adsorption and catalytic oxidation of O. Furthermore, the findings can lay the foundation for the further study of graphene-based support effects and provide a guideline for the development and design of new non-noble-metal single atom catalysts.

Nitric oxide (NO) emitted from coal-fired power plants has raised global concerns.

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