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arXiv 1908.06247physics.flu-dyncond-mat.stat-mechnlin.CD
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驱动活性物质向Turbulence的转变

Transition to Turbulence in Driven Active Matter

Aritra Das, J. K. Bhattacharjee, T. R. Kirkpatrick

摘要:

最近建立了一个类Lorenz模型来研究受驱动的活性物质系统的流体动力学不稳定性。这个洛伦兹模型与标准模型的不同之处在于,所有三个方程都包含非线性项。附加的非线性项来自于活性物质对应力张量的贡献。在这项工作中,我们调查的非线性性质的洛伦兹模型分析和数值。该模型的显着特点是通过一套完整的倍周期分岔以上的Hopf点的反施密特数超过一个临界值。有趣的是,在这些施密特数上,一个奇异吸引子和稳定不动点在同宿点之外共存。在霍普夫点,奇异吸引子消失,留下高周期的周期轨道。这个周期状态通过一系列分岔成为预期的极限环,然后经历一系列倍周期分岔,导致形成一个奇异吸引子。这是第一种情况下,一个类似洛伦兹的模型已经显示了一组连续的倍周期分岔在一个物理相关的过渡到湍流。

英文摘要:

A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term comes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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