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.
| ISBN: | 9781032288093 |
| Publication date: | 25th October 2023 |
| Author: | Shijun Liao |
| Publisher: | Chapman & Hall/CRC an imprint of CRC Press |
| Format: | Hardback |
| Pagination: | 188 pages |
| Series: | Advances in Applied Mathematics |
| Genres: |
Chaos theory Differential calculus and equations Mathematical physics Technology, Engineering, Agriculture, Industrial processes |
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.
Clean Numerical Simulation features in the following genres: Chaos theory, Differential calculus and equations, Mathematical physics, Technology, Engineering, Agriculture, Industrial processes
Clean Numerical Simulation is available in Hardback
Clean Numerical Simulation was written by Shijun Liao and published by Chapman & Hall/CRC an imprint of CRC Press
Clean Numerical Simulation has 188 pages
Yes it is part of Advances in Applied Mathematics series
£93.59