二阶六维Hamilton守恒格式的构造
Construction of second-order six-dimensional Hamiltonian-conserving scheme
摘要：
分析表明，Bacchini，Ripperda，Chen和Sironi的能量守恒隐式非辛格式对六维守恒Hamilton系统的数值解具有一阶精度.基于此，提出了一种新的二阶能量守恒隐式格式。数值模拟的银河系模型托管BL Lacertae对象和磁化旋转黑洞背景支持这些分析结果。采用适当时间步长的新方法研究了参数变化对两个物理模型中混沌现象的影响。随着星系核质量、内部微扰参数和椭圆星系势的各向异性的增大，星系模型中容易出现混沌。磁化Kerr时空周围的带电粒子的动力学在粒子能量较大、粒子初始角动量较小和磁场较强时容易发生混沌。当黑洞自旋增大时，混沌性质并不一定减弱。新方法可用于任何六维哈密顿问题，包括具有现成的（3+1）分裂坐标的全局双曲时空。
英文摘要：
It is shown analytically that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of this, a new second-order energy-conserving implicit scheme is proposed. Numerical simulations of Galactic model hosting a BL Lacertae object and magnetized rotating black hole background support these analytical results. The new method with appropriate time steps is used to explore the effects of varying the parameters on the presence of chaos in the two physical models. Chaos easily occurs in the Galactic model as the mass of the nucleus, the internal perturbation parameter, and the anisotropy of the potential of the elliptical galaxy increase. The dynamics of charged particles around the magnetized Kerr spacetime is easily chaotic for larger energies of the particles, smaller initial angular momenta of the particles, and stronger magnetic fields. The chaotic properties are not necessarily weakened when the black hole spin increases. The new method can be used for any six-dimensional Hamiltonian problems, including globally hyperbolic spacetimes with readily available (3+1) split coordinates.
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