无轨迹积分非周期流有限时间相干集的计算和最优扰动
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration
摘要：
理解动力系统的宏观行为是解开复杂流动中输运机制的重要工具。将状态空间分解为相干集合是揭示这种本质的宏观演化的流行方法。为了计算非周期时变动力系统的相干集，我们考虑了增广时空流形上的相关转移算子及其无穷小生成元。这种时空发生器方法避免了轨迹积分，并创建了一个方便的线性化的非周期性演变。这种线性化可以被进一步利用，以创建一个简单而有效的频谱优化方法，用于减少或增强相干性。我们得到明确的解决方案，这些最优化问题使用拉格朗日乘子，并说明这种技术，通过增加和减少混合的空间区域，通过小的速度场扰动。
英文摘要：
Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular way to reveal this essential macroscopic evolution. To compute coherent sets from an aperiodic time-dependent dynamical system we consider the relevant transfer operators and their infinitesimal generators on an augmented space-time manifold. This space-time generator approach avoids trajectory integration, and creates a convenient linearization of the aperiodic evolution. This linearization can be further exploited to create a simple and effective spectral optimization methodology for diminishing or enhancing coherence. We obtain explicit solutions for these optimization problems using Lagrange multipliers and illustrate this technique by increasing and decreasing mixing of spatial regions through small velocity field perturbations.
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