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Computation and Optimal Perturbation of Finite-Time Coherent Sets for Aperiodic Flows Without Trajectory Integration
SIAM Journal on Applied Dynamical Systems ( IF 2.1 ) Pub Date : 2020-07-22 , DOI: 10.1137/19m1261791
Gary Froyland , Péter Koltai , Martin Stahn

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1659-1700, January 2020.
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.


中文翻译:

无轨迹积分的非周期性有限时间相干集的计算和最优摄动

SIAM应用动力系统杂志,第19卷第3期,第1659-1700页,2020年1月。
了解动力学系统的宏观行为是揭示复杂流中的传输机制的重要工具。将状态空间分解为相干集合是揭示这种基本的宏观演变的一种流行方法。为了从非周期时间相关动力系统计算相干集,我们考虑了增强时空流形上的相关传递算符及其无穷小生成器。这种时空发生器方法避免了轨迹整合,并为非周期性演化创建了一个方便的线性化方法。可以进一步利用此线性化来创建简单有效的频谱优化方法,以减少或增强相干性。
更新日期:2020-07-23
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