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Clean Numerical Simulation

Af: Shijun Liao Engelsk Hardback
SPAR
kr 141

Clean Numerical Simulation

Af: Shijun Liao Engelsk Hardback

This book describes the basic principles of Clean Numerical Simulation (CNS) proposed by the author in 2009, as well as several of its applications. Unlike conventional algorithms, CNS gives in a sufficiently long interval of time a convergent chaotic trajectory whose numerical noise is much lower than the true physical solution, so that one can gain accurately. Thus, CNS provides for the first time an ability to check statistics stability of chaos, leading to a completely new concept of "ultra-chaos," which has both trajectory instability and statistics instability, and thus is of a higher disorder.

Notably, it is impossible to repeat experimental results of ultra-chaos even in the statistical sense. However, the reproducibility of physical experiments forms a cornerstone for modern science. Thus, ultra-chaos reveals an incompleteness of the modern science paradigm. In addition, it also reveals statistics stability as a precondition for use of conventional algorithms, including direct numerical simulation (DNS). In Clean Numerical Simulation, several conjectures and open problems are proposed, including a modified fourth Clay millennium problem.

Indeed, CNS opens the door for us to enter the "clean" numerical world of chaos and turbulence.

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This book describes the basic principles of Clean Numerical Simulation (CNS) proposed by the author in 2009, as well as several of its applications. Unlike conventional algorithms, CNS gives in a sufficiently long interval of time a convergent chaotic trajectory whose numerical noise is much lower than the true physical solution, so that one can gain accurately. Thus, CNS provides for the first time an ability to check statistics stability of chaos, leading to a completely new concept of "ultra-chaos," which has both trajectory instability and statistics instability, and thus is of a higher disorder.

Notably, it is impossible to repeat experimental results of ultra-chaos even in the statistical sense. However, the reproducibility of physical experiments forms a cornerstone for modern science. Thus, ultra-chaos reveals an incompleteness of the modern science paradigm. In addition, it also reveals statistics stability as a precondition for use of conventional algorithms, including direct numerical simulation (DNS). In Clean Numerical Simulation, several conjectures and open problems are proposed, including a modified fourth Clay millennium problem.

Indeed, CNS opens the door for us to enter the "clean" numerical world of chaos and turbulence.

Produktdetaljer
Sprog: Engelsk
Sider: 144
ISBN-13: 9781032288093
Indbinding: Hardback
Udgave:
ISBN-10: 1032288094
Udg. Dato: 5 sep 2023
Længde: 15mm
Bredde: 158mm
Højde: 243mm
Forlag: Taylor & Francis Ltd
Oplagsdato: 5 sep 2023
Forfatter(e): Shijun Liao
Forfatter(e) Shijun Liao


Kategori Differentialregning & ligninger


Sprog Engelsk


Indbinding Hardback


Sider 144


Udgave


Længde 15mm


Bredde 158mm


Højde 243mm


Udg. Dato 5 sep 2023


Oplagsdato 5 sep 2023

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