Based on their Euler poles, we calculated the relative velocities between every two plates in the typical global plate motion models, respectively, and estimated the area change along these boundaries. In our calculat...Based on their Euler poles, we calculated the relative velocities between every two plates in the typical global plate motion models, respectively, and estimated the area change along these boundaries. In our calculations, plates on both sides accommodated area changes depending on the boundary types： extensional, convergent or transform, so we can estimate area change of each plate and then globally. Our preliminary results show that the area of the southern hemisphere increased while that of the northern hemisphere decreased over the past I million years, and global area has increased by 26,000km^2 to 36,000km^2, which corresponds to the 160m - 250m increment on the Earth＇s radius if all these area increments are attributed to Earth＇s expansion. Taking the NUVEL-1 model as an example, of the 14 plates in this model, 11 are decreasing, but the global area has increased because of the larger increment amount from Africa, North America and Antarctica. Finally, we also discussed factors affecting the global area change such as subduction zone retreating and back-arc spreading.展开更多
A transient three-dimensional（3 D） model was established to understand the bubble motion in an industrial electrolytic process. An anode with a new design was tested. It incorporates two slots that allow an efficien...A transient three-dimensional（3 D） model was established to understand the bubble motion in an industrial electrolytic process. An anode with a new design was tested. It incorporates two slots that allow an efficient removal of gas bubbles. The electromagnetic fields were described by solving Maxwell＇s equations. The bubble movement was studied with two-way coupling Euler-Lagrange approach. The interplay of current density and bubble nucleation rate was included. The collision and coalescence of bubbles were considered. Random walk module was invoked for involving the chaotic effect of the turbulence. The numerical results were validated by experimental measurements. The results indicate that the current distribution and the bubble nucleation periodically change. Due to the slot, the bubble elimination heavily increases. The contribution of the slot to the bubble removal exceeds 50% in the case of three currents, and the promotion of the slot decays with increasing the current.展开更多
The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type...The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.展开更多
The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this pa...The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this paper.In a paper(Comm.Pure Appl.Math.,46,1993,621-665) by Z.P.Xin,the author constructed a sequence of solutions to one-dimensional Navier-Stokes isentropic equations converging to the rarefaction wave as the viscosity tends to zero.Furthermore,he obtained that the convergence rate is ε 1/4 | ln ε|.In this paper,Xin's convergence rate is improved to ε1/3|lnε|2 by different scaling arguments.The new scaling has various applications in related problems.展开更多
In this paper, a one-dimensional bipolar Euler-Poisson system （a hydrodynamic model） from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric f...In this paper, a one-dimensional bipolar Euler-Poisson system （a hydrodynamic model） from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy＇s law time asymp- totically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the cor- responding one-dimensional compressible Euler equations with damping exponentially fast as t → ＋∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.展开更多
基金sponsored by the National Natural Science Foundation (40574047),China
文摘Based on their Euler poles, we calculated the relative velocities between every two plates in the typical global plate motion models, respectively, and estimated the area change along these boundaries. In our calculations, plates on both sides accommodated area changes depending on the boundary types： extensional, convergent or transform, so we can estimate area change of each plate and then globally. Our preliminary results show that the area of the southern hemisphere increased while that of the northern hemisphere decreased over the past I million years, and global area has increased by 26,000km^2 to 36,000km^2, which corresponds to the 160m - 250m increment on the Earth＇s radius if all these area increments are attributed to Earth＇s expansion. Taking the NUVEL-1 model as an example, of the 14 plates in this model, 11 are decreasing, but the global area has increased because of the larger increment amount from Africa, North America and Antarctica. Finally, we also discussed factors affecting the global area change such as subduction zone retreating and back-arc spreading.
基金Project(51434005) supported by the National Natural Science Foundation of China
文摘A transient three-dimensional（3 D） model was established to understand the bubble motion in an industrial electrolytic process. An anode with a new design was tested. It incorporates two slots that allow an efficient removal of gas bubbles. The electromagnetic fields were described by solving Maxwell＇s equations. The bubble movement was studied with two-way coupling Euler-Lagrange approach. The interplay of current density and bubble nucleation rate was included. The collision and coalescence of bubbles were considered. Random walk module was invoked for involving the chaotic effect of the turbulence. The numerical results were validated by experimental measurements. The results indicate that the current distribution and the bubble nucleation periodically change. Due to the slot, the bubble elimination heavily increases. The contribution of the slot to the bubble removal exceeds 50% in the case of three currents, and the promotion of the slot decays with increasing the current.
基金Supported by the National Fundations of Natural sciences. Supported by the Henan Fundations of Scientific Committee.
文摘The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.
基金supported by the National Natural Science Foundation of China for Outstanding Young Scholars(No. 10825102)the National Basic Research Program of China (973 Program) (No. 2011CB808002)
文摘The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this paper.In a paper(Comm.Pure Appl.Math.,46,1993,621-665) by Z.P.Xin,the author constructed a sequence of solutions to one-dimensional Navier-Stokes isentropic equations converging to the rarefaction wave as the viscosity tends to zero.Furthermore,he obtained that the convergence rate is ε 1/4 | ln ε|.In this paper,Xin's convergence rate is improved to ε1/3|lnε|2 by different scaling arguments.The new scaling has various applications in related problems.
基金supported by the National Natural Science Foundation of China(No.11171223)the Innovation Program of Shanghai Municipal Education Commission(No.13ZZ109)
文摘In this paper, a one-dimensional bipolar Euler-Poisson system （a hydrodynamic model） from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy＇s law time asymp- totically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the cor- responding one-dimensional compressible Euler equations with damping exponentially fast as t → ＋∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.
