Eigen Analysis of Moment Vector Equation for Interacting Chaotic Elements Described by Nonlinear Boltzmann Equation

Hideki SATOH

doi:10.1587/transfun.E97.A.331

Eigen Analysis of Moment Vector Equation for Interacting Chaotic Elements Described by Nonlinear Boltzmann Equation

Hideki SATOH

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A macroscopic structure was analyzed for a system comprising multiple elements in which the dynamics is affected by their distribution. First, a nonlinear Boltzmann equation, which has an integration term with respect to the distribution of the elements, was derived. Next, the moment vector equation (MVE) for the Boltzmann equation was derived. The average probability density function (pdf) in a steady state was derived using eigen analysis of the coefficient matrix of the MVE. The macroscopic structure of the system and the mechanism that provides the average pdf and the transient response were then analyzed using eigen analysis. Evaluation of the average pdf and transient response showed that using eigen analysis is effective for analyzing not only the transient and stationary properties of the system but also the macroscopic structure and the mechanism providing the properties.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.1 pp.331-338

Publication Date: 2014/01/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E97.A.331

Type of Manuscript: PAPER

Category: Nonlinear Problems

Authors

Hideki SATOH
Future University Hakodate

Keyword

nonlinear interaction, Boltzmann equation, MVE, eigen analysis

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Hideki SATOH, "Eigen Analysis of Moment Vector Equation for Interacting Chaotic Elements Described by Nonlinear Boltzmann Equation" in IEICE TRANSACTIONS on Fundamentals, vol. E97-A, no. 1, pp. 331-338, January 2014, doi: 10.1587/transfun.E97.A.331.
Abstract: A macroscopic structure was analyzed for a system comprising multiple elements in which the dynamics is affected by their distribution. First, a nonlinear Boltzmann equation, which has an integration term with respect to the distribution of the elements, was derived. Next, the moment vector equation (MVE) for the Boltzmann equation was derived. The average probability density function (pdf) in a steady state was derived using eigen analysis of the coefficient matrix of the MVE. The macroscopic structure of the system and the mechanism that provides the average pdf and the transient response were then analyzed using eigen analysis. Evaluation of the average pdf and transient response showed that using eigen analysis is effective for analyzing not only the transient and stationary properties of the system but also the macroscopic structure and the mechanism providing the properties.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.331/_p

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@ARTICLE{e97-a_1_331,
author={Hideki SATOH, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Eigen Analysis of Moment Vector Equation for Interacting Chaotic Elements Described by Nonlinear Boltzmann Equation},
year={2014},
volume={E97-A},
number={1},
pages={331-338},
abstract={A macroscopic structure was analyzed for a system comprising multiple elements in which the dynamics is affected by their distribution. First, a nonlinear Boltzmann equation, which has an integration term with respect to the distribution of the elements, was derived. Next, the moment vector equation (MVE) for the Boltzmann equation was derived. The average probability density function (pdf) in a steady state was derived using eigen analysis of the coefficient matrix of the MVE. The macroscopic structure of the system and the mechanism that provides the average pdf and the transient response were then analyzed using eigen analysis. Evaluation of the average pdf and transient response showed that using eigen analysis is effective for analyzing not only the transient and stationary properties of the system but also the macroscopic structure and the mechanism providing the properties.},
keywords={},
doi={10.1587/transfun.E97.A.331},
ISSN={1745-1337},
month={January},}

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TY - JOUR
TI - Eigen Analysis of Moment Vector Equation for Interacting Chaotic Elements Described by Nonlinear Boltzmann Equation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 331
EP - 338
AU - Hideki SATOH
PY - 2014
DO - 10.1587/transfun.E97.A.331
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2014
AB - A macroscopic structure was analyzed for a system comprising multiple elements in which the dynamics is affected by their distribution. First, a nonlinear Boltzmann equation, which has an integration term with respect to the distribution of the elements, was derived. Next, the moment vector equation (MVE) for the Boltzmann equation was derived. The average probability density function (pdf) in a steady state was derived using eigen analysis of the coefficient matrix of the MVE. The macroscopic structure of the system and the mechanism that provides the average pdf and the transient response were then analyzed using eigen analysis. Evaluation of the average pdf and transient response showed that using eigen analysis is effective for analyzing not only the transient and stationary properties of the system but also the macroscopic structure and the mechanism providing the properties.
ER -