救助嵌入映射中的危机和不稳定维度可变性
Crisis and unstable dimension variability in the bailout embedding map
摘要：
$2-d$不可压缩流中惯性粒子的动力学可以用$4-d$救助嵌入映射来模拟。惯性粒子的密度相对于流体的密度是控制粒子的动力学行为的关键参数。我们在这里研究气溶胶的动力学行为，即比流动重的颗粒。在气溶胶的情况下，相空间出现了吸引子加宽和合并的危机。在时间序列中可以看到危机引起的不稳定性，并且爆发前时间的层流长度分布产生指数为$β=-1/3$的幂律。最大李雅普诺夫指数附近的危机波动为零，表明不稳定的尺寸变化（UDV）的系统。有限时间李雅普诺夫指数的概率分布的行为证实了不稳定的尺寸变化的存在。
英文摘要：
The dynamics of inertial particles in $2-d$ incompressible flows can be modeled by $4-d$ bailout embedding maps. The density of the inertial particles, relative to the density of the fluid, is a crucial parameter which controls the dynamical behaviour of the particles. We study here the dynamical behaviour of aerosols, i.e. particles heavier than the flow. An attractor widening and merging crisis is seen the phase space in the aerosol case. Crisis induced intermittency is seen in the time series and the laminar length distribution of times before bursts gives rise to a power law with the exponent $β=-1/3$. The maximum Lyapunov exponent near the crisis fluctuates around zero indicating unstable dimension variability (UDV) in the system. The presence of unstable dimension variability is confirmed by the behaviour of the probability distributions of the finite time Lyapunov exponents.
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