Academic Journal
Memory Function Approach to Chaos and Turbulence and the Continued Fraction Expansion: Memory function approach to chaos and turbulence and the continued fraction expansion
| Title: | Memory Function Approach to Chaos and Turbulence and the Continued Fraction Expansion: Memory function approach to chaos and turbulence and the continued fraction expansion |
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| Authors: | Hazime Mori, Ryuji Ishizaki, Nobuyuki Mori, Hirotaka Tominaga, Shoichi Kuroki |
| Source: | Progress of Theoretical Physics. 111:635-660 |
| Publisher Information: | Oxford University Press (OUP), 2004. |
| Publication Year: | 2004 |
| Subject Terms: | Stochastic methods applied to problems in equilibrium statistical mechanics, 0103 physical sciences, 01 natural sciences |
| Description: | Summary: The chaotic orbits of dynamical systems are deterministic and predictable on short timescales \(\tau_r\), but they become stochastic and random on long timescales \(\tau_M\) (\(\gg\tau_r\)) due to the orbital instability of chaos. This randomization of chaotic orbits has been formulated recently by deriving a non-Markovian stochastic equation for macrovariables in terms of a fluctuating force and a memory function. In order to develop this memory function approach to chaos and turbulence, we explore the following problems by studying the Duffing oscillator and the Navier-Stokes equation for an incompressible fluid: 1) the physical meaning of the projection of macrovariables \(A(t)\) onto \(A(0)\); 2) the method of calculating the short-lived motion with short timescale \(\tau_r\), which determines the memory functions and the macroscopic transport coefficients due to chaos and turbulence; 3) the continued fraction expansion of the memory function, and the order estimation of short timescales \(\tau_r\) and long timescales \(\tau_M\); 4) the relation between the memory function and the time correlation function of a nonlinear force, which gives computable theoretical expressions for the macroscopic transport coefficients. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1347-4081 0033-068X |
| DOI: | 10.1143/ptp.111.635 |
| Access URL: | https://academic.oup.com/ptp/article-pdf/111/5/635/5301749/111-5-635.pdf https://zbmath.org/2111961 https://doi.org/10.1143/ptp.111.635 https://ui.adsabs.harvard.edu/abs/2004PThPh.111..635M/abstract https://paperity.org/p/34417018/memory-function-approach-to-chaos-and-turbulence-and-the-continued-fraction-expansion http://ci.nii.ac.jp/naid/110001196166 https://academic.oup.com/ptp/article/111/5/635/1874913 |
| Accession Number: | edsair.doi.dedup.....4c46eadfddc02d14901ddcbaa0df137c |
| Database: | OpenAIRE |
| ISSN: | 13474081 0033068X |
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| DOI: | 10.1143/ptp.111.635 |