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25 November 2021, Volume 38 Issue 6 Previous Issue    Next Issue
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Modeling and Analysis Methods for Complex Fields Based on Phase Space Aiguo XU, Jiahui SONG, Feng CHEN, Kan XIE, Yangjun YING 2021, 38(6): 631-660.  DOI: 10.19596/j.cnki.1001-246x.8379 Abstract ( )   HTML ( )   PDF (39020KB) ( )   We review two modeling and analysis methods based on phase space and their applications. The first is Minkowski functionals-based Morphological Analysis Method (Min-MAM), and the second is Discrete Boltzmann modeling and analysis Method (DBM). Both of them are developed from phase space description in statistical physics. Based on independent behavior characteristic quantities, a phase space is constructed, and the phase space and its subspaces are used to describe behavior characteristics of a system. A given point in the phase space corresponds to a set of behavior characteristics of the system. The distance d between two points is used to describe the difference of two groups of behavioral characteristics, and its reciprocal, S=1/d, is used to describe similarity of two groups of behavioral characteristics. Mean value of the distance between two points over a period of time, ${\bar d}$, is used to describe difference between two kinetic processes, and its reciprocal, Sp=1/${\bar d}$, is used to describe similarity of two kinetic processes, Historically, Min-MAM appeared earlier. Receiving its inspiration is the key step in the development of discrete Boltzmann method towards phase space description method. Min-MAM is independent of data sources, so results obtained with discrete Boltzmann simulation can be further understood on another level or perspective by using Min-MAM, in addition to its own analysis functions. In the study of complex media kinetics, these two methods, from different perspectives, provide information that can be stratified and studied quantitatively.

Research Reports

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Numerical Simulation on Instability of Vertical Liquid Drainage Han XIAO, Chunxi LI, Haozhe SU, Xuemin YE 2021, 38(6): 661-671.  DOI: 10.19596/j.cnki.1001-246x.8332 Abstract ( )   HTML ( )   PDF (15118KB) ( )   To analyze instability on surface of liquid film in a wire-frame drainage experiment, we establish a three-dimensional mathematical model for drainage process of a wire-frame containing insoluble surfactants, and simulate instability at bottom of the liquid film. Influence of factors including Marangoni effect, dilational viscosity and disturbance wave number are analyzed. It shows that bottom perturbation is severe at beginning of drainage, then quickly weakens, and gradually increases in the late drainage. Perturbation at the beginning is caused by initial perturbation, and instability at the late of the drainage is related to the distribution of surfactant. A weaker Marangoni effect enhances the surface disturbance, while a stronger Marangoni effect inhibits the bottom perturbation, making the liquid film rigid and causing surface countercurrent. Higher dilational viscosity slows down the drainage process and reduces the surface velocity. It suppresses the countercurrent phenomenon caused by the Marangoni effect. A greater disturbance wave number makes the perturbation stronger in the early stage of drainage, while it does not affect the stability of late stage of the drainage.

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Droplet Upward Movement on an Inclined Surface Under Wetting Gradient: Lattice Boltzmann Simulation Lu CHEN, Ming GAO, Jia LIANG, Dongmin WANG, Yugang ZHAO, Lixin ZHANG 2021, 38(6): 672-682.  DOI: 10.19596/j.cnki.1001-246x.8325 Abstract ( )   HTML ( )   PDF (14156KB) ( )   A lattice Boltzmann method based on Shan-Chen pseudo-potential model was used to simulate the process of a droplet overcoming gravity and moving upward on a inclined plane with wetting gradient. Effects of wetting gradient, droplet size, Bond number and surface inclination angle on droplet motion were investigated. It shows that velocity vector appears in the droplet moving upwards along the slope. The greater the wetting gradient is, the faster the droplet moves, and the longer the wetting length is, and the faster the dynamic contact angle decreases. Droplet size and Bond number have weak influence on droplet motion, but there is a critical Bond number, beyond which the droplet moves down along the gradient wetting surface. The surface inclination angle has a significant effect on the droplet motion. As the inclination angle increases, the droplet motion speed and wetting length are significantly reduced.

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Lattice Boltzmann Method for One-dimensional Riesz Spatial Fractional Convection-Diffusion Equations Xuedan WEI, Houping DAI, Mengjun LI, Zhoushun ZHENG 2021, 38(6): 683-692.  DOI: 10.19596/j.cnki.1001-246x.8318 Abstract ( )   HTML ( )   PDF (3766KB) ( )   A D1Q3 evolution model of lattice Boltzmann method (LBM) is established to numerically solve a class of spatial fractional convection-diffusion equation in Riesz sense. By discretizing the integral term of fractional order operator, the fractional convection-diffusion equation is transformed into a standard one with Riesz derivative. With Taylor expansion, Chapman-Enskog and multi-scales expansion, equilibrium distribution functions of the model are derived in all directions. Furthermore, the macroscopic equation to be solved is recovered correctly. Finally, numerical experiments are carried out to verify the model.

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Numerical Investigation of Gas Entrapment in Polymer Filling Process Puyang GAO 2021, 38(6): 693-706.  DOI: 10.19596/j.cnki.1001-246x.8327 Abstract ( )   HTML ( )   PDF (13054KB) ( )   The complicated gas entrapment problem in polymer filling process is studied. The moving melt interface is captured with a level set method. An XPP (eXtended Pom-Pom) constitutive model is utilized for the description of viscoelastic fluid. The governing equations of flow field are solved with a coupled continuous and discontinuous Galerkin method. The XPP constitutive equation, level set and its re-initialization equations are solved with an implicit discontinuous Galerkin method. Good agreement between experimental and numerical results illustrates validity of the combined algorithm. Influence of injection velocity and gate size on gas entrapment in a cavity with irregular insert was investigated. Entrapped gas is easier to appear as the injection velocity is higher and the gate size is smaller.

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Adsorption Characteristics of N2 on Shale Kerogen Yuanqiang ZHU, Saisai JIN, Qingqing SUN 2021, 38(6): 707-712.  DOI: 10.19596/j.cnki.1001-246x.8333 Abstract ( )   HTML ( )   PDF (7552KB) ( )   Density functional theory wB97XD method, RDG function method and counterpoise correction theory were used to study adsorption characteristics of N2 on shale kerogen C28H14O and nitrogen-doped shale kerogen C27H14ON. It shows that the active adsorption site is located on the central position above the benzene ring for N2 adsorbed on both kerogen C28H14O and nitrogen-doped kerogen C27H14ON. The adsorption energy is in the range of 8~10 kJ·mol-1, which shows that the main interaction between nitrogen molecule and kerogens is van der Waals interaction and steric repulsion. Nitrogen doping changes the geometric configuration and electron cloud distribution of kerogen. As a result, the nitrogen-containing heterocycle is no longer a stable active site. The adsorption energy is a little lower than that of N2 adsorbed on C28H14O, but it is still in the range of 8~10 kJ·mol-1. The main interaction force between N2 and C27H14ON is still van der Waals interaction and steric repulsion. This work is significant for understanding adsorption characteristics of small molecules on kerogens. It provides theoretical support for the exploring of shale gas.

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Helicon Waves Propagation and Absorption: Effect of Axial Length of Helical Antenna Dan DU, Shuai LI, Puqiong YANG, Jun FENG, Dong XIANG, Xueyu GONG 2021, 38(6): 713-721.  DOI: 10.19596/j.cnki.1001-246x.8323 Abstract ( )   HTML ( )   PDF (5331KB) ( )   Helicon waves propagation and absorption of helical antenna is studied by solving Maxwell equations with finite element method and experimental parameters of H-1 stellarator. As axial length of helical antenna increases, total radiation resistance and radiation energy of the antenna increase as well. In H-1 plasma, helical antenna mainly excites m=±1 waves, and the m=-1 waves spread generally at the plasma boundary. Energy of the excited modes of full-wavelength helical antenna is mainly deposited at plasma boundary, which causes inhomogeneous radial energy absorption and heating. Excited waves of half-wavelength helical antenna penetrate deeply into the bulk plasma, which leads to relatively uniform radial energy absorption and heating.

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Dissociation Properties of Acrolein in External Electric Field Zhuoyan ZHOU, Yuzhu LIU, Yu CHEN, Xinyang ZHANG, Zhuoyi SUN 2021, 38(6): 722-728.  DOI: 10.19596/j.cnki.1001-246x.8331 Abstract ( )   HTML ( )   PDF (8126KB) ( )   Based on HF(Hartree-Fock) calculation method with 3-21G basis set, we discussed structural and dissociation characteristics of C3H4O gas molecules under different external fields (from -10.28 V·nm-1 to 10.28 V·nm-1). It is found that as the electric field increases along the direction of molecular conjugated single bond the total energy increases. The bond length of C-C double bond and C-C single bond decreases. The bond length of C-O double bond increases. The dipole moment decreases. Energy gap EG increases. The infrared absorption peak has both red shift and blue shift at different frequencies and the intensity of IR also changes. The molecular dissociation performance is as follows: The potential energy barrier decreases with the increase of the external electric field. As the electric field reaches 25.71 V·nm-1, the potential energy barrier almost disappears and the dissociation energy decreases gradually with the increase of the electric field, which indicating that the dissociation difficulty of C3H4O gas molecules under electric field decreases gradually. It provides reference for the study of dissociation characteristics of C3H4O gas molecules or mixtures containing C3H4O in external electric field.

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Theoretical Study of Electronic States Spectrum and Transition Property of OH+ Xingwei WANG, Xiaoshu SONG 2021, 38(6): 729-734.  DOI: 10.19596/j.cnki.1001-246x.8297 Abstract ( )   HTML ( )   PDF (1513KB) ( )   A highly accuracy internally multi-reference configuration interaction method (icMRCI) was used to calculate potential curves of low-lying electronic states and transition dipole moment of A3П-X3Σ- system for OH+ ion. Davidson correction (MRCI+Q) of energy and scalar relativistic effect were considered in the calculation. Based on potential energy curves of low-lying electronic states spectroscopic parameters were determined by solving one-dimensional radial Schr dinger equation of nuclear motion. Einstein coefficient and F-C factor of A3П-X3Σ- transition system are calculated by using the transition dipole moment. Moreover, radiative lifetimes of A3П(ν'=0-6) vibration states were studied. It shows that the radiative lifetimes are of the order of 10-6 s.

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Regulation of Light Absorption with Position of Au Particles in a Au@Carbon Sphere Composite Structure Jie SUN, Renzhai CHENG, Yun LI, Hongjie FANG, Hongbo WANG, Xiaolong CHEN 2021, 38(6): 735-741.  DOI: 10.19596/j.cnki.1001-246x.8314 Abstract ( )   HTML ( )   PDF (5548KB) ( )   Light absorption of Au nanoparticles@carbon sphere (AuNPs@CS) composite structure is investigated with finite difference time domain (FDTD) method. It shows that light absorption of AuNPs@CS composite structure is effectively controlled by position of Au nanoparticle.Two Au nanoparticles are selected and embedded on the surface of the carbon sphere at an optimal depth (0 nm). As the angle between the particle center of Au and the spheroid core of carbon sphere is 22.5° and 45°, light absorption is enhanced than that of a single carbon sphere; As the angles between them are 315°, 270°, 180° and 90°, the increment of light absorption decreases gradually; At an angle of 337.5° between them, the optical absorption is significantly lower than that of a single carbon sphere. It may be attributed to the change of Au nanoparticles position, which causes the change of light intensity and scattering direction of the surface plasmon. The light absorption of AuNPs@CS composite structure can be adjusted by varying the number and position of Au nanoparticle on the surface of carbon sphere.

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Dynamics Analysis and Circuit Simulation of A New Chaotic System with A Compound Power Function and Coexisting Attractors Qicheng XU, Changchun SUN 2021, 38(6): 742-748.  DOI: 10.19596/j.cnki.1001-246x.8335 Abstract ( )   HTML ( )   PDF (2104KB) ( )   A new three-dimensional continuous autonomous chaotic system with a compound power function is constructed. The equation of state of the system has only five terms, one of which is a compound power function with an exponent less than 1. The system has properties of simple structure, non-hyperbolic equilibrium point, coexistence of attractors, and exhibits complex dynamic behaviors. Firstly, dynamic behaviors including Lyapunov exponential spectrum, bifurcation diagram and Poincaré mapping are analyzed. It shows that the system has chaotic characteristics. Then, circuit design of the chaotic system is carried out. Circuit simulation results verify the theoretical analysis.

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Spiral Wave Dynamics of Excited Medium: Effect of Relative Refractory Furong GUAN, Chengqian LI, Minyi DENG 2021, 38(6): 749-756.  DOI: 10.19596/j.cnki.1001-246x.8321 Abstract ( )   HTML ( )   PDF (7399KB) ( )   Effect of relative refractory of excited medium on dynamical behavior of spiral waves is investigated in a cellular automata model. It is found that there is a critical interval in the excitation threshold. Spiral wave period in the critical interval increases suddenly and there is a maximum period. Under appropriate system size and number of states, the spiral wave period is not affected by refractoriness. It depends on the excitation threshold of the system only. Relative refractory state leads to Z-type meandering, small-scale irregular meandering, petal meandering, jagged meandering, windmill meandering and other complex spiral wave tip motions. Stable spiral wave, meandering spiral wave, and disappearing spiral wave are observed. Mechanisms of these phenomena are briefly analyzed.