论文信息 - Moment invariants for the Vlasov equation

Moment invariants for the Vlasov equation

Moment invariants [functions of the moments of a Vlasov distribution that are invariant under Sp(6)] are classified using Young diagrams. The connection between the moment invariants and the Poincare invariants is established. An application using the moment invariants as phase space coordinates is considered for a matching section in a particle‐beam accelerator, and a Lie–Poisson numerical integration algorithm for the moment dynamics is proposed.

Darryl D. Holm | J. C. Scovel | W. P. Lysenko | J. Scovel | W. Lysenko

[1] V. Varadarajan. Lie groups, Lie algebras, and their representations , 1974 .

[2] Victor Guillemin,et al. Infinite dimensional primitive Lie algebras , 1970 .

[3] S. Sternberg,et al. The moment map and collective motion , 1980 .

[4] J. Marsden,et al. Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators , 1988 .

[5] Gerald W. Schwarz. On classical invariant theory and binary cubics , 1987 .

[6] M. Fischler. Young–tableau methods for Kronecker products of representations of the classical groups , 1981 .

[7] Gerald J. Janusz,et al. Linear Algebra and Group Representations. , 1985 .

[8] Ralph Abraham,et al. Foundations Of Mechanics , 2019 .

[9] P. Channell,et al. Integrators for Lie-Poisson or dynamical systems , 1991 .

[10] C. Itzykson,et al. UNITARY GROUPS: REPRESENTATIONS AND DECOMPOSITIONS , 1966 .

[11] H. Weyl. The Classical Groups , 1939 .

[12] M. Micu. CONSTRUCTION OF INVARIANTS FOR SIMPLE LIE GROUPS , 1964 .