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Two-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect

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Progress in Natural Science:Materials International 2007年第12期17卷 1389-1396页

作者： Hu Jun1 and Yin Xieyuan2.1. institute of applied {2. and Computational Mathematics, Beijing 100088, china 2. Department of Modern Mechanics, University of Science and technology of china, Hefei 2.002., china) institute of applied {2. and Computational Mathematics Beijing 100088 China Department of Modern Mechanics University of Science and Technology of China Hefei 230027 China

Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect are directly simulated by a mixed finite element method. A temperature perturbation is used as an initial disturbed source for the basic parallel flows. The whole spatio-temporal evolution of the binary fluid flows is exhibited: initially only the disturbed mode with the wavenumber k=π is amplified while others are damped, and continuously the amplified mode grows further and the nonlinear effect becomes important; after a nonlinear evolution transition the flow system evolves finally into a periodic right traveling wave.

关键词： Poiseuille-Rayleigh-Bénard flow Soret effect through-flow.

NONEQUILIBRIUM STATISTICAL FOUNDATION OF FATIGUE FRACTURE

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Acta Mechanica Sinica 1990年第1期6卷 35-44页

作者： xing Xiusan, Department of applied {2., Beijing institute of technology, Beijing, 100081, china Department of applied physics Beijing Institute of Technology Beijing China

The physical foundation of statistical law of fatigue fracture is discussed. The universal forms of the microcrack growth rate, fluctuation growth coefficient and distribution function and fatigue life distribution fu... 详细信息

关键词： microcrack evolution equation microscopic mechanism microcrack distribution function fatigue life distribution function

Dynamic information theory and information description of dynamic systems

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Science china(physics,Mechanics & Astronomy) 2010年第4期53卷 607-627页

作者： xing XiuSan Department of physics, Beijing {2. of technology, Beijing 100081, china Department of physics Beijing Institute of Technology Beijing China

In this paper, we develop dynamic statistical information theory established by the author. Starting from the ideas that the state variable evolution equations of stochastic dynamic systems, classical and quantum nonequilibrium statistical physical systems and special electromagnetic field systems can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derive the evolution equations of dynamic information and dynamic entropy that describe the evolution laws of dynamic information. These four kinds of evolution equations are of the same mathematical type. They show in unison when information transmits in coordinate space outside the systems that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes, and that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes. When space noise can be neglected, an information wave will appear. If we only consider the information change inside the systems, dynamic information evolution equations reduce to information equations corresponding to the dynamic equations which describe evolution laws of the above dynamic systems. This reveals that the evolution laws of respective dynamic systems can be described by information equations in a unified fashion. Hence, the evolution processes of these dynamic systems can be abstracted as the evolution processes of information. Furthermore, we present the formulas for information flow, information dissipation rate, and entropy production rate. We prove that the information production probably emerges in a dynamic system with internal attractive interaction between the elements, and derive a formula for this information production

关键词： dynamic information evolution equation informationization of dynamic equation information wave information flow and force information dissipation and production degradation and evolution

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

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Science china(physics,Mechanics & Astronomy) 2010年第12期53卷 2194-2215页

作者： xing XiuSan Department of physics, Beijing {2. of technology, Beijing 100081, china Department of physics Beijing Institute of Technology Beijing China

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or anothe

关键词： stochastic velocity type’s Langevin equation in 6N dimensional phase space drift-diffusion duality nonequilibrium entropy evolution equation entropy diffusion formula for entropy production rate entropy change from internal interaction a

Void damage model and service life prediction for solid high polymer

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Chinese Science Bulletin 2001年第21期46卷 1842-1845页

作者： SHEN TingfangDepartment of applied physics, Beijing {2. of technology, Beijing 100081, china Department of applied physics Beijing Institute of Technology Beijing China

Based on the analysis of three void damage variety models, this note presents (i) a method that regards the void content as a damage variation of the grain and (ii) a geometric model for micro-unit of void damage. Equations of the void damage variety containing void content are analyzed. This work is focused on the measurement of internal damage level and the damage variety estimation is directly related to the life predication in the practical engineering applications. Nowadays, the critical service life of the solid grain/polymers is usually presumed at domestic and international level. The strength or strain reduction of 2.% or the stabilizer consumption of 50% is generally regarded as a critical storage life of the solid grain/polymers, and the service life is predicted by the extrapolation method on An-henius formula. The applications, however, show that the above method is unreliable and has significant errors. With the aid of the discontiguous automatic measuring device of real time volume

关键词： void content void damage thermal aging service life damage mechanics.

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1, Guo Boling2.and Cheng Caozong1(1. College of applied Sciences, Beijing University of technology, Beijing 10002.,{2. 2. Center for Nonlinear Studies, institute of applied physics and Computational Mathematics, Beijing 100088,{2.) College of applied Sciences Beijing University of Technology Beijing 100022 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method

A complex variable meshless method for fracture problems

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Science china(physics,Mechanics & Astronomy) 2006年第1期49卷 46-59页

作者： CHENG Yumin1 & LI Jiuhong2.1. Shanghai institute of applied Mathematics and Mechanics, Shanghai University, Shanghai 2.0072.{2. 2. Department of Building Engineering, Xi’an University of technology, Xi’an 710048,{2. Shanghai institute of applied Mathematics and Mechanics Shanghai University Shanghai China Department of Building Engineering Xi’an University of Technology Xi’an China

Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approxi- mation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable meshless method for fracture problems is presented, and the formulae of the complex variable meshless method are obtained. The complex variable meshless method in this paper has greater precision and computational efficiency than the conventional meshless method. Some examples are given.

关键词： moving least-square approximation, complex variable moving least-square approximation, meshless method, complex variable meshless method, fracture.

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Science china Chemistry 2004年第6期47卷 466-479页

作者： SONG Huajie1,2. XIAO Heming1 & DONG Haishan2.1. Department of Chemistry, Nanjing University of Science and technology, Nanjing 2.0094, china 2. {2. of Chemical Materials, china Academy of Engineering physics, Mianyang 62.900, china Department of Chemistry Nanjing University of Science and Technology Nanjing China institute of Chemical Materials China Academy of Engineering Physics Mianyang China

The symmetry-adapted perturbation theory (SAPT) that has the ability in decompo- sition of the total interaction energy into physically meaningful components is used to provide a more fundamental understanding of intermolecular forces. This work was motivated by the diffi- culty of standard SAPT in computing the intermolecular interactions for large energetic dimer systems. SAPT based on Kohn-Sham orbitals (SAPT(DFT)) proves computationally efficient for these large systems, but has been shown to perform poorly for interaction energy components. The deficiencies of SAPT(DFT) result from wrong asymptotical behaviors of commonly used exchange-correlation potentials. To remove the deficiencies, two asymptotic corrections by means of van Leeuwen and Baerends (LB) model potential and Fermi-Amaldi (FA) type potential were applied into three small test systems comprising He2. HF2.and (N2.2.and a set of larger ni- tramide dimers at several separations. The results showed that when utilizing newly developed frequency-dependent density susceptibilities (FDDS) technique for computing dispersion energy, the FA asymptotic correction is very effective to circumvent these deficiencies in SAPT(DFT) and yields a good accuracy over the LB correction. The FA corrected SAPT(DFT) approach is capa- ble of correctly predicting all the quantitative trends in binding energies for all test cases and substantially reduces computational cost as compared with the standard SAPT calculations. The successful application of the approach to nitramide dimer demonstrates that it potentially pro- vides a good means to calculate accurately intermolecular forces in larger system such as en- ergetic systems.

关键词： intermolecular interaction, density functional theory (DFT), symmetry adapted perturbation theory (SAPT), asymptotic correction, frequency-dependent density susceptibilities (FDDS).

Numerical and experimental investigation of the fracture behavior of shock loaded alumina

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Science china(physics,Mechanics & Astronomy) 2010年第2期53卷 244-252页

作者： REN HuiLan1,SHU XueFeng2.& LI Ping3 1 State Key Laboratory of Explosion Science and technology,Beijing institute of technology,Beijing 100081,china 2.institute of applied Mechanics and Biomedical Engineering,Taiyuan University of technology,Taiyuan 03002.,china 3 Labroratory for Shock Wave and Detonation physics Research,institute of Fluid physics,CAEP,Mianyang 610059,china State Key Laboratory of Explosion Science and technology Beijing Institute of Technology Beijing China institute of applied Mechanics and Biomedical Engineering Taiyuan University of Technology Taiyuan China Labroratory for Shock Wave and Detonation physics Research Institute of Fluid Physics CAEP Mianyang China

Plate impact expeiments are conducted to investigate the dynamic behavior of alumina by using one stage light gas gun. A ve-locity interferometer system for reflectors (VISAR) is used to obtain Hugoniot elastic limit and the free surface velocity profile,which consists of an elastic wave followed immediately by a dispersive inelastic wave. The stress histories under different impact velocities are measured by in-material manganin gauges. Based on the experimental data a Hugoniot curve is fitted,which shows the compressive characteristics that alumina changes typically from elastic to "plastic" ,and under higher pressure it will be transferred to similar-fluid state. The turning point of the Hugoniot curve from a high pressure region to a low pressure region is about 11.4 GPa. The fracture process of alumina is simulated by way of finite element code. After the analysis of the fracture mechanism,the numerical results show an important role played by the nucleation and the growth of the cracks in the macro-scopic fracture of the alumina target. The numerical predictions of stress histories are compared with the experimental results,which indicates consistency between them.

关键词： plate impact experiment hugoniot curve fracture characteristics numerical simulation