79 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Shanghai Jiao Tong UniversityCN36 papers
- Shanghai Ocean UniversityCN8 papers
- Collaborative Innovation Centre for Advanced Ship and Deep-Sea ExplorationCN5 papers
- King Abdulaziz UniversitySA5 papers
- Qinghai UniversityCN4 papers
- State Key Laboratory of Plateau Ecology and Agriculture2 papers
- Beijing University of Posts and TelecommunicationsCN1 paper
- Brown UniversityUS1 paper
- Chinese Academy of SciencesCN1 paper
- École Centrale de NantesFR1 paper
- Hong Kong Polytechnic UniversityHK1 paper
- Hong Kong University of Science and TechnologyHK1 paper
11 papers · 1 filter
Ultra-chaotic property of Navier-Stokes turbulence
Shijie Qin, Kun Xu, Shijun Liao
A chaotic system is called ultra-chaos when its statistics have sensitivity dependence on initial condition and/or other small disturbances. In this paper, using two-dimensional tu…
A kind of Lagrangian chaotic property of the Arnold-Beltrami-Childress flow
Shijie Qin, Shijun Liao
Three-dimensional steady-state Arnold-Beltrami-Childress (ABC) flow has a chaotic Lagrangian structure, and also satisfies the Navier-Stokes (NS) equations with an external force p…
On the risks of using double precision in numerical simulations of spatio-temporal chaos
Tianli Hu, Shijun Liao
Due to the butterfly-effect, computer-generated chaotic simulations often deviate exponentially from the true solution, so that it is very hard to obtain a reliable simulation of c…
On the inherent self-excited macroscopic randomness of chaotic three-body system
Shijun Liao, Xiaoming Li
What is the origin of macroscopic randomness (uncertainty)? This is one of the most fundamental open questions for human being. In this paper, 10000 samples of reliable (convergent…
A comment on the arguments about the reliability and convergence of chaotic simulations
Shijun Liao
Yao and Hughes commented (Tellus-A, 60: 803 - 805, 2008) that "all chaotic responses are simply numerical noise and have nothing to do with the solutions of differential equations"…
Physical limit of prediction for chaotic motion of three-body problem
Shijun Liao
A half century ago, Lorenz found the "butterfly effect" of chaotic dynamic systems and made his famous claim that long-term prediction of chaos is impossible. However, the meaning…
On the mathematically reliable long-term simulation of chaos of Lorenz equation in the interval [0,10000]
Shijun Liao, Pengfei Wang
Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data, we have…
Chaotic motion of three-body problem : an origin of macroscopic randomness of the universe
Shijun Liao
The famous three-body problem is investigated by means of a numerical approach with negligible numerical noises in a long enough time interval, namely the Clean Numerical Simulatio…
On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems
S. J. Liao
In this paper, an extremely accurate numerical algorithm, namely the "clean numerical simulation" (CNS), is proposed to accurately simulate the propagation of micro-level inherent…
Chaos: a bridge from microscopic uncertainty to macroscopic randomness
S. J. Liao
It is traditionally believed that the macroscopic randomness has nothing to do with the micro-level uncertainty. Besides, the sensitive dependence on initial condition (SDIC) of Lo…
On the reliability of computed chaotic solutions of nonlinear differential equations
Shijun Liao
In this paper a new concept, namely the critical predictable time , is introduced to give a more precise description of computed chaotic solutions of nonlinear differential eq…