One-dimensional self-similar unsteady flows behind a spherical or cylindrical shock wave driven out by a piston moving with time according to a power law in a dusty gas is investigated. The medium is assumed to be the mixture of small solid particles of micro-size and a non-ideal gas. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by the inner surface (piston). It is assumed that the equilibrium flow-conditions are maintained and the moving piston continuously supplies the variable energy input. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both cases, when the flow between the shock and the piston is isothermal or adiabatic. The shock waves in non-ideal dusty gas can be important for the description of shocks in supernova explosions, in the study of a flare produced shock in the solar wind, the central part of starburst galaxies, nuclear explosion, rupture of the pressurized vessel, in the analysis of data from exploding wire experiments, and cylindrically symmetric hypersonic flow problems associated with meteors or re-entry vehicles, etc. The findings of the present work provided a clear picture of whether and how the non-idealness of the gas and the presence of the magnetic field affect the propagation of shock and the flow behind it. It is interesting to note that in the presence of azimuthal magnetic field, the pressure and density vanish at the piston and hence a vacuum is formed at the center of symmetry for both the isothermal and adiabatic flows, which is in excellent agreement with the laboratory condition to produce the shock wave.

中文翻译：

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非理想气体和固体小颗粒混合物中活塞在方位或轴向磁场影响下驱动的冲击波

研究了在含尘气体中根据幂律随时间移动的活塞驱动的球形或圆柱形激波后面的一维自相似非定常流动。假定介质是微小尺寸的固体小颗粒和非理想气体的混合物。固体颗粒均匀分布在混合物中，假设冲击波是由内表面（活塞）驱动的。假设保持平衡流动条件并且移动活塞连续提供可变能量输入。相似解仅在周围介质密度恒定时才存在。在这两种情况下，当激波和活塞之间的流动是等温或绝热时，都会得到解决方案。非理想含尘气体中的冲击波对于描述超新星爆炸中的冲击很重要，在研究太阳风中耀斑产生的冲击、星暴星系的中心部分、核爆炸、加压容器破裂、在分析爆炸丝实验数据以及与流星或再入飞行器相关的圆柱对称高超音速流动问题等方面。目前工作的发现清楚地说明了气体和气体的非理想性是否以及如何磁场的存在会影响激波的传播及其背后的流动。有趣的是，在存在方位磁场的情况下，活塞处的压力和密度消失，因此等温流和绝热流的对称中心都会形成真空，