79 citations · 1k across the 43 of their papers we have counts for
43 papers
A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos
Shijie Qin, Shijun Liao
The background numerical noise is determined by the maximum of truncation error and round-off error. For a chaotic system, the numerical error g…
Large-scale influence of numerical noises as artificial stochastic disturbances on a sustained turbulence
Shijie Qin, Shijun Liao
We investigate the large-scale influence of numerical noises as tiny artificial stochastic disturbances on a sustained turbulence. Using the two-dimensional (2D) turbulent Rayleigh…
Avoiding small denominator problems by means of the homotopy analysis method
Shijun Liao
The so-called ``small denominator problem'' was a fundamental problem of dynamics, as pointed out by Poincaré. Small denominators appear most commonly in perturbative theory. The D…
Ultra-chaos: an insurmountable objective obstacle of reproducibility and replicability
Shijun Liao, Shijie Qin
In this paper, a new concept, i.e. ultra-chaos, is proposed for the first time. Unlike a normal-chaos, statistical properties such as the probability density functions (PDF) of an…
Influence of database noises to machine learning for spatiotemporal chaos
Yu Yang, Shijie Qin, Shijun Liao
A new strategy, namely the "clean numerical simulation" (CNS), was proposed (J. Computational Physics, 418:109629, 2020) to gain reliable/convergent simulations (with negligible nu…
Three-body problem -- from Newton to supercomputer plus machine learning
Shijun Liao, Xiaoming Li, Yu Yang
The famous three-body problem can be traced back to Newton in 1687, but quite few families of periodic orbits were found in 300 years thereafter. In this paper, we propose an effec…
Accurate predictions of chaotic motion of a free fall disk
Tianzhuang Xu, Jing Li, Zhihui Li +1
It is important to know the accurate trajectory of a free fall object in fluid (such as a spacecraft), whose motion might be chaotic in many cases. However, it is impossible to acc…
Satellites of the Broucke-Hadjidemetriou-Hénon family of periodic unequal-mass three-body orbits
Xiaoming Li, Shijun Liao
The Broucke-Hadjidemetriou-Hénon's (BHH) orbits are a family of periodic orbits of the three-body system with the simplest topological free group word , while the BHH satellites…
One family of 13315 stable periodic orbits of the non-hierarchical unequal-mass triple system
Xiaoming Li, Xiaochen Li, Shijun Liao
The three-body problem has been studied for more than three centuries [1,2], and has received much attention in recent years [3-5]. It shows complex dynamical phenomena due to the…
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…
A new non-perturbative approach in quantum mechanics for time-independent Schrödinger equations
Shijun Liao
A new non-perturbative approach is proposed to solve time-independent Schrödinger equations in quantum mechanics and chromodynamics (QCD). It is based on the homotopy analysis meth…
Collisionless periodic orbits in the free-fall three-body problem
Xiaoming Li, Shijun Liao
Although the free-fall three-body problem have been investigated for more than one century, however, only four collisionless periodic orbits have been found. In this paper, we repo…
A singularity-free analytic solution of rise dynamics of a liquid in a vertical cylindrical capillary
Xiaoxu Zhong, Bohua Sun, Shijun Liao
Capillary driven flow is a famous problem in fluid dynamics which dates back to Leonardo da Vinci. In this paper, we apply an analytic approximation method for highly nonlinear pro…
The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum
Xiaoming Li, Yipeng Jing, Shijun Liao
We present 1349 families of Newtonian periodic planar three-body orbits with unequal mass and zero angular momentum and the initial conditions in case of isosceles collinear config…
On the Limiting Stokes' Wave of Extreme Height in Arbitrary Water Depth
Xiaoxu Zhong, Shijun Liao
As mentioned by Schwartz (1974) and Cokelet (1977), it was failed to gain convergent results of limiting Stokes' waves in extremely shallow water by means of perturbation methods e…
Influence of round-off errors on the reliability of numerical simulations of chaotic dynamic systems
Shijie Qin, Shijun Liao
We illustrate that, like the truncation error, the round-off error has a significant influence on the reliability of numerical simulations of chaotic dynamic systems. Due to the bu…
More than six hundreds new families of Newtonian periodic planar collisionless three-body orbits
Xiaoming Li, Shijun Liao
The famous three-body problem can be traced back to Isaac Newton in 1680s. In the 300 years since this "three-body problem" was first recognized, only three families of periodic so…
On the homotopy analysis method for backward/forward-backward stochastic differential equations
Xiaoxu Zhong, Shijun Liao
In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differentia…
On the Generalized Wavelet-Galerkin Method
Zhaochen Yang, Shijun Liao
In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some…
On the origin of intrinsic randomness of Rayleigh-Benard turbulence
Zhiliang Lin, Lipo Wang, Shijun Liao
It is of broad interest to understand how the evolution of non-equilibrium systems can be triggered and the role played by external perturbations. A famous example is the origin of…
The influence of numerical noises on statistics computation of chaotic dynamic systems
Xiaoming Li, Shijun Liao
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependance on initial conditions (SDIC). Unfortunately, numer…
Clean Numerical Simulation: A New Strategy to Obtain Reliable Solutions of Chaotic Dynamic Systems
Xiaoming Li, Shijun Liao
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependence on initial conditions (SDIC). Unfortunately, numer…
Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally
Xiaochen Li, Xiaoming Li, Shijun Liao
A system of two-dimensional, two coupled Faraday interfacial waves is experimentally observed at the two interfaces of the three layers of fluids (air, pure ethanol and silicon oil…
Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure (II): Equations in Integral Form
Xiaoxu Zhong, Shijun Liao
In this paper, the homotopy analysis method (HAM) is successfully applied to solve the Von Karman's plate equations in the integral form for a circular plate with the clamped bound…