论文标题
冷动力学系统和自相似性的平衡解决方案。 （ii）
Equilibrium solution for cold dynamical systems and self-similarity. (II)
论文作者
论文摘要
数值模拟展示了动态冷初始解决方案与自相似性之间的联系。但是，该链接的性质尚未完全理解。单独没有进一步对称的冷初始条件不会导致自相似性。在这里，我们表明，当系统接近平衡时，出现了新的对称性。在初始条件下，这种平衡对称性与冷对称性的组合导致了完全相似之处。结果，即使初始空间分布不是自相似的，我们也会观察到在平衡附近向自相似性的演变。详细讨论了3D中一维系统或球形对称系统的情况。还考虑了根据能量和其他积分的系统。解决了平衡时自相似溶液退化的问题。结果表明，系统中心的非常小的扰动能够打破这种脱落性并导致与特定自动相似溶液的收敛性。
Numerical simulations demonstrate a link between dynamically cold initial solutions and self-similarity. However the nature of this link is not fully understood. Cold initial conditions alone without further symmetry do not lead to self-similarity. Here we show that when the system approaches equilibrium a new symmetry appears. The combination of this equilibrium symmetry with the cold symmetry in the initial conditions leads to full self-similarity. As a consequence for any initially cold system even if the initial spatial distribution is not self-similar we will observe an evolution towards self-similarity near equilibrium. The case of one dimensional systems or spherically symmetric systems in 3D are discussed in detail. Systems depending on the energy and other integrals are also considered. The problem of the degeneracy of the self-similar solutions at equilibrium is tackled. It is shown that very small perturbations at the center of the system have the ability to break this degeneracy and lead to the convergence towards a specific auto-similar solution.
