Modeling Macroscopic Nonlinear Space-Time Phenomena
Summary :
Modeling in terms of cell dynamical systems (CDS) is advocated as an efficient tool to sort out correct guesses about the mathematical essence of macroscopic nonlinear phenomena with space-time patterns. CDS is a map from a discrete pattern at time t to the one at t+1. With the aid of segregation processes, the CDS modeling is illustrated. Numerical schemes are introduced which are often stable for fairly large increments to bridge conventional partial differential equation (PDE) models and CDS models. Although these schemes with large increments usually do not give correct solutions to the original PDE, they could still give quantitatively accurate results for macroscopic observables. Thus it is meaningful to discuss qualitatively accurate schemes.
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- IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.6 pp.1379-1387
- Publication Date
- 1991/06/25
- Publicized
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- Special Section INVITED PAPER (Special Issue on Nonlinear Theory and Its Applications)
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Yoshitsugu OONO, "Modeling Macroscopic Nonlinear Space-Time Phenomena" in IEICE TRANSACTIONS on Fundamentals,
vol. E74-A, no. 6, pp. 1379-1387, June 1991, doi: .
Abstract: Modeling in terms of cell dynamical systems (CDS) is advocated as an efficient tool to sort out correct guesses about the mathematical essence of macroscopic nonlinear phenomena with space-time patterns. CDS is a map from a discrete pattern at time t to the one at t+1. With the aid of segregation processes, the CDS modeling is illustrated. Numerical schemes are introduced which are often stable for fairly large increments to bridge conventional partial differential equation (PDE) models and CDS models. Although these schemes with large increments usually do not give correct solutions to the original PDE, they could still give quantitatively accurate results for macroscopic observables. Thus it is meaningful to discuss qualitatively accurate schemes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_6_1379/_p
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@ARTICLE{e74-a_6_1379,
author={Yoshitsugu OONO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Modeling Macroscopic Nonlinear Space-Time Phenomena},
year={1991},
volume={E74-A},
number={6},
pages={1379-1387},
abstract={Modeling in terms of cell dynamical systems (CDS) is advocated as an efficient tool to sort out correct guesses about the mathematical essence of macroscopic nonlinear phenomena with space-time patterns. CDS is a map from a discrete pattern at time t to the one at t+1. With the aid of segregation processes, the CDS modeling is illustrated. Numerical schemes are introduced which are often stable for fairly large increments to bridge conventional partial differential equation (PDE) models and CDS models. Although these schemes with large increments usually do not give correct solutions to the original PDE, they could still give quantitatively accurate results for macroscopic observables. Thus it is meaningful to discuss qualitatively accurate schemes.},
keywords={},
doi={},
ISSN={},
month={June},}
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TY - JOUR
TI - Modeling Macroscopic Nonlinear Space-Time Phenomena
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1379
EP - 1387
AU - Yoshitsugu OONO
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1991
AB - Modeling in terms of cell dynamical systems (CDS) is advocated as an efficient tool to sort out correct guesses about the mathematical essence of macroscopic nonlinear phenomena with space-time patterns. CDS is a map from a discrete pattern at time t to the one at t+1. With the aid of segregation processes, the CDS modeling is illustrated. Numerical schemes are introduced which are often stable for fairly large increments to bridge conventional partial differential equation (PDE) models and CDS models. Although these schemes with large increments usually do not give correct solutions to the original PDE, they could still give quantitatively accurate results for macroscopic observables. Thus it is meaningful to discuss qualitatively accurate schemes.
ER -
English
