Vlasov-Vlasvre方程的Hamilton流体封闭：从水囊到N矩模型
Hamiltonian fluid closures of the Vlasov-Amp{è}re equations: from water-bags to N moment models
摘要：
利用水囊理论研究了Vlasov-Vlasvre系统的矩封闭问题，即高阶矩表示为低阶矩的函数，约束条件是所得到的流体系统保持Hamilton性。通过引入合适的热力学变量，建立了水囊形式主义和流体模型之间的联系，包括密度，流体速度，压力和更高的时刻。分别讨论了一个、两个和三个水囊的情况，给出了它们的哈密顿结构。在每种情况下，我们给出了相关的流体闭包，并讨论了它们的Casimir不变量。我们展示了如何将该方法扩展到任意数量的字段，即，任意数量的水袋和相关的时刻。由此产生的模型的热力学解释进行了讨论。最后，提出了一种推导哈密顿N场流体模型的一般方法。
英文摘要：
Moment closures of the Vlasov-Amp{è}re system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.
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。
