Dynamic structures of the time correlation functions of chaotic nonequilibrium fluctuations

Hazime Mori, Makoto Okamura

研究成果: ジャーナルへの寄稿記事

10 引用 (Scopus)

抄録

Using the projection operator formalism we explore the decay form of the time correlation function Un (t) un (t) un (0) of the state variable u n (t) in the chaotic Kuramoto-Sivashinsky equation. The decay form turns out to be the algebraic decay 1 [1+ (na t) 2] in the initial regime t ne and the exponential decay exp (a ne t) in the final regime t>1â• I ne. The memory function Î"n (t) that represents the chaos-induced transport is found to obey the Gaussian decay exp [a (ng t) 2] in the case of large wave numbers, but the 3/2 power decay exp [a (I n3 t) 3a 2] in the case of small wave numbers. The power spectrum of u n (t) is given by the real part Una (ω) of the Fourier-Laplace transform of Un (t) and has a dominant peak at ω=0. This peak within the linewidth ne (ane) is given by the Lorentzian spectrum ne 2 a (ω2 + ne 2). However, the wings of the peak outside the width ne turn out to take the exponential spectrum exp (na). Thus it is found that the exponential decay exp (ne t) appears to lead to the universal Lorentzian peak, while the algebraic decay 1 [1+ (na t) 2] arises to bring about the exponential wing.

元の言語英語
記事番号061104
ジャーナルPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
76
発行部数6
DOI
出版物ステータス出版済み - 12 5 2007

Fingerprint

Time Correlation Functions
Non-equilibrium
Decay
Fluctuations
decay
Exponential Decay
wings
Memory Function
Kuramoto-Sivashinsky Equation
Projection Operator
Linewidth
Power Spectrum
Laplace transform
Fourier transform
Chaos
chaos
power spectra
projection
formalism
operators

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

これを引用

@article{07e13b8a8f724858a35259d129a5f498,
title = "Dynamic structures of the time correlation functions of chaotic nonequilibrium fluctuations",
abstract = "Using the projection operator formalism we explore the decay form of the time correlation function Un (t) un (t) un (0) of the state variable u n (t) in the chaotic Kuramoto-Sivashinsky equation. The decay form turns out to be the algebraic decay 1 [1+ (na t) 2] in the initial regime t ne and the exponential decay exp (a ne t) in the final regime t>1{\^a}• I ne. The memory function {\^I}{"}n (t) that represents the chaos-induced transport is found to obey the Gaussian decay exp [a (ng t) 2] in the case of large wave numbers, but the 3/2 power decay exp [a (I n3 t) 3a 2] in the case of small wave numbers. The power spectrum of u n (t) is given by the real part Una ({\"I}‰) of the Fourier-Laplace transform of Un (t) and has a dominant peak at {\"I}‰=0. This peak within the linewidth ne (ane) is given by the Lorentzian spectrum ne 2 a ({\"I}‰2 + ne 2). However, the wings of the peak outside the width ne turn out to take the exponential spectrum exp (na). Thus it is found that the exponential decay exp (ne t) appears to lead to the universal Lorentzian peak, while the algebraic decay 1 [1+ (na t) 2] arises to bring about the exponential wing.",
author = "Hazime Mori and Makoto Okamura",
year = "2007",
month = "12",
day = "5",
doi = "10.1103/PhysRevE.76.061104",
language = "English",
volume = "76",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "6",

}

TY - JOUR

T1 - Dynamic structures of the time correlation functions of chaotic nonequilibrium fluctuations

AU - Mori, Hazime

AU - Okamura, Makoto

PY - 2007/12/5

Y1 - 2007/12/5

N2 - Using the projection operator formalism we explore the decay form of the time correlation function Un (t) un (t) un (0) of the state variable u n (t) in the chaotic Kuramoto-Sivashinsky equation. The decay form turns out to be the algebraic decay 1 [1+ (na t) 2] in the initial regime t ne and the exponential decay exp (a ne t) in the final regime t>1â• I ne. The memory function Î"n (t) that represents the chaos-induced transport is found to obey the Gaussian decay exp [a (ng t) 2] in the case of large wave numbers, but the 3/2 power decay exp [a (I n3 t) 3a 2] in the case of small wave numbers. The power spectrum of u n (t) is given by the real part Una (ω) of the Fourier-Laplace transform of Un (t) and has a dominant peak at ω=0. This peak within the linewidth ne (ane) is given by the Lorentzian spectrum ne 2 a (ω2 + ne 2). However, the wings of the peak outside the width ne turn out to take the exponential spectrum exp (na). Thus it is found that the exponential decay exp (ne t) appears to lead to the universal Lorentzian peak, while the algebraic decay 1 [1+ (na t) 2] arises to bring about the exponential wing.

AB - Using the projection operator formalism we explore the decay form of the time correlation function Un (t) un (t) un (0) of the state variable u n (t) in the chaotic Kuramoto-Sivashinsky equation. The decay form turns out to be the algebraic decay 1 [1+ (na t) 2] in the initial regime t ne and the exponential decay exp (a ne t) in the final regime t>1â• I ne. The memory function Î"n (t) that represents the chaos-induced transport is found to obey the Gaussian decay exp [a (ng t) 2] in the case of large wave numbers, but the 3/2 power decay exp [a (I n3 t) 3a 2] in the case of small wave numbers. The power spectrum of u n (t) is given by the real part Una (ω) of the Fourier-Laplace transform of Un (t) and has a dominant peak at ω=0. This peak within the linewidth ne (ane) is given by the Lorentzian spectrum ne 2 a (ω2 + ne 2). However, the wings of the peak outside the width ne turn out to take the exponential spectrum exp (na). Thus it is found that the exponential decay exp (ne t) appears to lead to the universal Lorentzian peak, while the algebraic decay 1 [1+ (na t) 2] arises to bring about the exponential wing.

UR - http://www.scopus.com/inward/record.url?scp=36849014293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849014293&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.76.061104

DO - 10.1103/PhysRevE.76.061104

M3 - Article

AN - SCOPUS:36849014293

VL - 76

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 061104

ER -