用于研究开放系统传输的保守系统混沌测量

Asen Mokrani, Cathy Castelain, Hassan Peerhossaini
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引用次数: 10

摘要

由于缺乏适用于保守系统的数学标准,对这种措施的评估已被证明是特别困难的。现有的工具主要是基于对吸引子“奇异性”的描述。因此,这些渐近测度仅限于耗散系统。我们已经调整了这些工具中的一些,以便将它们应用于保守系统,基于系统的短时间观测而不是渐近观测。在这项研究中,我们以交替的迪安流为基准,并在此基础上构建了数学工具。而不是观察吸引子,我们建议观察由注入流上游的示踪丝的横截面形成的图像。用流动的数值模型模拟了这种图像。利用图像,我们评估了“信息维”和“积分相关维”。由于我们使用短时间观测,因此尺寸取决于注入灯丝的初始位置。然而,它们的进化遵循了在图像上观察到的明显的无序。作为混沌行为的全局度量,我们建议计算所有注入位置的维数的平均值,定义为“平均积分相关维数”。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mesure du chaos dans les systèmes conservatifs en vue de l'étude des transferts dans les systèmes ouverts

Assessment of such a measure has been revealed to be especially difficult due to the lake of mathematical criteria applicable to conservative systems. Existing tools are mainly based on the characterization of the ‘strangeness’ of the attractors. These asymptotic measures are thus limited to dissipative systems. We have adapted some of these tools in order to apply them to conservative systems, based on short time observations of the system instead of asymptotic observations. In this study we have used the alternating Dean flow as a benchmark and on the basis of which the mathematical tools have been constructed. Instead of observing an attractor, we suggest observing the image formed by the cross section of a tracer filament injected upstream of the flow. Such an image is simulated by using a numerical model for the flow. With the image, we evaluate the ‘information dimension’ as well as the ‘integral correlation dimension’. Since we use short time observations, the dimensions depend on the initial position of the injected filament. However, their evolution follows the apparent disorder observed on the images. As a global measure of the chaotic behavior, we suggest calculating the mean value of the dimensions for all injection positions defined as ‘mean integral correlation dimensions’.

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