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Study on Chaotic transport phenomena

混沌输运现象研究

基本信息

批准号：
16540351
负责人：
TOMINAGA Hirotaka
金额：
$ 2.08万
依托单位：
Saga University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16540351/
关键词：
Chaos Transport phenomena Projection operator method Memory function Fluctuation force Time-correlation function Power spectra 時間相関

项目摘要

This study is the fundamental research of chaotic transport processes, namely, we would like to clarify the problem that what kind of physical process exits under various dissipative structures due to chaos or turbulance. In other words, we would like to elucidate chaos dynamical system and turbulence in a point of the statistical thermodyanmical and more physical properties such as viscosity, energy dissipation, heat production and entropy production.Concretely, we have performed the projection operator method to the nonlinear deterministic equations which bring about chaos or turbulence. Then we have obtained the statistical differential equations with the fluctuating force, leading to the transport coefficients. We have tried to certify the existence of the chaotic transport processes together with the chaotic transport coefficients, and elucidate its physical meanings.First, we have treated the Duffing oscillators as a typical dissipative dynamical chaotic system and the Henon-Heiles system as a typical conservative chaotic system. We have calculated the memory function and memory spectra with frequencies and obtained the relation between the power spectra of the state variables and the memory spectra. To sum up, we have clarified that main peaks in the power specara of the state variables, which produced by chaos, may be represented by the superposition of the asymmetric Lorentzians and the structure of the peak have a definite relationship with the memory spectra.

本研究是混沌输运过程的基础研究，即我们想要弄清楚在各种耗散结构下由于混沌或湍流导致的物理过程存在什么样的问题。换句话说，我们希望从统计热力学和更多的物理性质如粘度、能量耗散、产热和熵产等方面阐明混沌动力系统和湍流。具体地说，我们对引起混沌或湍流的非线性确定性方程应用了投影算子法。在此基础上，我们得到了脉动力下的统计微分方程，从而得到了输运系数。我们试图证明混沌输运过程和混沌输运系数的存在性，并阐明其物理意义。首先，我们将Duffing振子视为典型的耗散动力混沌系统，将Henon-Heiles系统视为典型的保守混沌系统。计算了随频率变化的记忆函数和记忆谱，得到了状态变量的功率谱与记忆谱的关系。综上所述，我们阐明了混沌产生的状态变量幂谱中的主峰可以用不对称洛伦兹子的叠加来表示，并且峰的结构与记忆谱有一定的关系。