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
36 papers
Convergent series of Stokes wave of arbitrary height in deep water via machine learning
Chong Lin, Shijun Liao
Permanent gravity waves propagating in deep water, spanning amplitudes from infinitesimal to their theoretical limiting values, remain a classical yet challenging problem due to it…
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…
Physical significance of artificial numerical noise in direct numerical simulation of turbulence
Shijun Liao, Shijie Qin
Using clean numerical simulation (CNS) in which artificial numerical noise is negligible over a finite, sufficiently long interval of time, we provide evidence, for the first time,…
Noise-expansion cascade: an origin of randomness of turbulence
Shijun Liao, Shijie Qin
Randomness is one of the most important characteristics of turbulence, but its origin remains an open question. By means of a ``thought experiment'' via several clean numerical exp…
HAM-Schrödingerisation: a generic framework of quantum simulation for any nonlinear PDEs
Shijun Liao
Recently, Jin et al. proposed a quantum simulation technique for ANY linear partial differential equations (PDEs), called Schrödingerisation [1,2,3]. In this paper, the Schrödinger…
Is a direct numerical simulation (DNS) of Navier-Stokes equations with small enough grid spacing and time-step definitely reliable/correct?
Shejie Qin, Yu Yang, Yongxiang Huang +3
Traditionally, results given by the direct numerical simulation (DNS) of Navier-Stokes equations are widely regarded as reliable benchmark solutions of turbulence, as long as grid…
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…
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…
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…
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…
Shape of spreading and leveling gravity currents in a Hele-Shaw cell with flow-wise width variation
Zhong Zheng, Aditya A. Ghodgaonkar, Ivan C. Christov
We study the spreading and leveling of a gravity current in a Hele-Shaw cell with flow-wise width variations as an analog for flow {in fractures and horizontally heterogeneous aqui…
Prediction of structure-dependent thermal transport behavior in self-folded graphene film validated by molecular dynamics simulation
Anran Wei, Fenglin Guo
Understanding the relationship between the microstructures and overall properties is one of the basic concerns for the material design and applications. As a ubiquitous structural…
Shape Deformation and Drag Variation of a Coupled Rigid-flexible System in a Flowing Soap Film
Song Gao, Song Pan, Huaicheng Wang +1
We experimentally study the flow past a rigid plate with an attached closed filament acting as a deformable afterbody in the soap film. The complex fluid-structure interactions due…
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 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…
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…
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…
-log-convexity from linear transformations and polynomials with only real zeros
Bao-Xuan Zhu
In this paper, we mainly study the stability of iterated polynomials and linear transformations preserving the strong -log-convexity of polynomials Let be…
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…
Gas-like adhesion of two-dimensional materials onto solid surfaces
Zhengrong Guo, Tienchong Chang, Xingming Guo +1
The adhesion of two-dimensional (2D) materials to other surfaces is so far believed to be a solid-solid mechanical contact. Here, we conduct both atomistic simulations and theoreti…