With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding （2＋1）-dimensional integrable hierarchy...With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding （2＋1）-dimensional integrable hierarchy is obtained by applying the binormial-residue representation （BRR） method, whose ttamiltonian structure is derived from the trace identity for deducing （2＋1）-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the （2＋1 ）-dimensionai AKNS hierarchy, the second-type reduction reveals an integrable coupling of the （2＋1）-dimensional AKNS equation （also called the Davey-Stewartson hierarchy）, a kind of （2＋1）-dimensionai Sehr6dinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new （2＋1）-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the （2＋1）-dimensional integrable coupling, which is further reduced to the standard （2＋1）-dimensionaJ diffusion equation along with a parameter. In addition, the well-known （1＋1）-dimensional AKNS hierarchy, the （1＋1）-dimensional nonlinear Schr6dinger equation are all special cases of the （2＋1）-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the yon Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the （2＋1）-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated.展开更多
Based on the analysis of tin penetration mechanism in the float glass process, the oxidation model of stannous ion is constructed considering the oxygen activity and the redox reaction in the glass surface layer. The ...Based on the analysis of tin penetration mechanism in the float glass process, the oxidation model of stannous ion is constructed considering the oxygen activity and the redox reaction in the glass surface layer. The calculation of stannous ion's oxidation rate makes it possible to predict both stannous and stannic ion's concentrations independently. And it is also the necessary precondition for the numerical verification of tin penetration mechanism. Coupled diffusion simulation method is established to simulate the penetration process of both stannous and stannic ions simultaneously. The result shows that when the green glass is formed in the reducing atmosphere in tin bath, the stannic ion is accumulated at the position where oxygen activity changes sharply. Satellite peak (internal local concentration maximum) occurs in the tin concentration profile of green glass, which is quite different from that in low iron glass. Compared with gradually cooling temperature regulation, the tin penetrated shifts to greater depth and the depth and magnitude of the satellite peak also increase when reheating temperature regulation is applied. In order to reduce the amount of penetrated tin, the residual time in the high temperature region should be shortened.展开更多
基金Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology(2014)the National Natural Science Foundation of China under Grant No.11371361+1 种基金the Fundamental Research Funds for the Central Universities(2013XK03)the Natural Science Foundation of Shandong Province under Grant No.ZR2013AL016
文摘With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding （2＋1）-dimensional integrable hierarchy is obtained by applying the binormial-residue representation （BRR） method, whose ttamiltonian structure is derived from the trace identity for deducing （2＋1）-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the （2＋1 ）-dimensionai AKNS hierarchy, the second-type reduction reveals an integrable coupling of the （2＋1）-dimensional AKNS equation （also called the Davey-Stewartson hierarchy）, a kind of （2＋1）-dimensionai Sehr6dinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new （2＋1）-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the （2＋1）-dimensional integrable coupling, which is further reduced to the standard （2＋1）-dimensionaJ diffusion equation along with a parameter. In addition, the well-known （1＋1）-dimensional AKNS hierarchy, the （1＋1）-dimensional nonlinear Schr6dinger equation are all special cases of the （2＋1）-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the yon Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the （2＋1）-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated.
基金supported by the National Basic Research Program of China ("973" Project) (Grant No. 2007CB206901)the Key Projects in the National Science & Technology Pillar Program during the Eleventh Five-Year Plan Period (Grant No. 2006BAF02A27)
文摘Based on the analysis of tin penetration mechanism in the float glass process, the oxidation model of stannous ion is constructed considering the oxygen activity and the redox reaction in the glass surface layer. The calculation of stannous ion's oxidation rate makes it possible to predict both stannous and stannic ion's concentrations independently. And it is also the necessary precondition for the numerical verification of tin penetration mechanism. Coupled diffusion simulation method is established to simulate the penetration process of both stannous and stannic ions simultaneously. The result shows that when the green glass is formed in the reducing atmosphere in tin bath, the stannic ion is accumulated at the position where oxygen activity changes sharply. Satellite peak (internal local concentration maximum) occurs in the tin concentration profile of green glass, which is quite different from that in low iron glass. Compared with gradually cooling temperature regulation, the tin penetrated shifts to greater depth and the depth and magnitude of the satellite peak also increase when reheating temperature regulation is applied. In order to reduce the amount of penetrated tin, the residual time in the high temperature region should be shortened.
