不连续流的对称性与流体动力学中的对偶Rankine-Hugoniot条件
Symmetries of Discontinuous Flows and the Dual Rankine-Hugoniot Conditions in Fluid Dynamics
摘要：
最近的研究表明，对于光滑亚音速流，多方流体的最大运动学不变性群是SL（2，R）与静态Galilei群G的半直积。这一结果旨在为最近观察到的超新星爆炸和等离子体内爆之间有趣的相似性提供理论解释。在本文中，我们将这一结果扩展到讨论不连续流的对称性，考虑到冲击波，这是爆炸和内爆背后的驱动力，进一步验证了解释。这是通过构造一组新的朗肯-雨果尼奥条件来实现的，这些条件遵循诺特守恒定律。新的集合是标准Rankine-Hugoniot条件的对偶，并且通过SL（2，R）变换与它们相关。熵的条件，即激波需要满足的物理原因，也被认为是保持不变的变换。
英文摘要：
It has recently been shown that the maximal kinematical invariance group of polytropic fluids, for smooth subsonic flows, is the semidirect product of SL(2,R) and the static Galilei group G. This result purports to offer a theoretical explanation for an intriguing similarity, that was recently observed, between a supernova explosion and a plasma implosion. In this paper we extend this result to discuss the symmetries of discontinuous flows, which further validates the explanation by taking into account shock waves, which are the driving force behind both the explosion and implosion. This is accomplished by constructing a new set of Rankine-Hugoniot conditions, which follow from Noether's conservation laws. The new set is dual to the standard Rankine-Hugoniot conditions and is related to them through the SL(2,R) transformations. The entropy condition, that the shock needs to satisfy for physical reasons, is also seen to remain invariant under the transformations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
