A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equat...A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.展开更多
An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution...An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.展开更多
The Bi 2Ti 2O 7 thin films have been prepared on silicon by metalorganic deco mposition (MOD) technique using bismuth nitrate and titanium butoxide as source materials.The growth procedure of the Bi 2Ti 2O 7 thin film...The Bi 2Ti 2O 7 thin films have been prepared on silicon by metalorganic deco mposition (MOD) technique using bismuth nitrate and titanium butoxide as source materials.The growth procedure of the Bi 2Ti 2O 7 thin films was discussed.Th e surface morphology of the Bi 2Ti 2O 7 film was studied by the Electri c Force Microscope (EFM).The crystallization of the films was studied by X r ay diffraction (XRD).The Bi 2Ti 2O 7 thin film prepared on (100) silicon subs trate was proved with strong (111) orientation.The dielectric properties and the current voltage (I V) characteristics were measured.The dielectric constant o f the Bi 2Ti 2O 7 thin films vs.temperature and frequency in the interval 100 8 00℃ were studied.The dielectric constang is 118 and dielectric loss is 0.07 res pectively at 100KHz at room temperature.The resistivity of the Bi 2Ti 2O 7 th in film is higher than 1×10 12 (Ω·cm) under the applied voltage from -5V to 5V.For films 0.4μm thick annealed at 580℃ for 40 minutes,their leakage cu r r ent density is 4.06×10 -7 A/cm 2 at an applied voltage of 15V.This shows the films have very good insulating property. We observed the obviously ferroelectric phase transition and its Curie temperatu re in the Bi 2Ti 2O 7 ceramic.Capacitance vs.temperature was measured with 27 800℃ at 1kHz,10kHz,100kHz and 1MHz,respectively.展开更多
基金Supported by the National Natural Science Foundation of China(11271127)Science Research Projectof Guizhou Province Education Department(QJHKYZ[2013]207)
文摘A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.
基金This work was financially supported by the National Natural Science Foundation of China (No.50476083).
文摘An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.
文摘The Bi 2Ti 2O 7 thin films have been prepared on silicon by metalorganic deco mposition (MOD) technique using bismuth nitrate and titanium butoxide as source materials.The growth procedure of the Bi 2Ti 2O 7 thin films was discussed.Th e surface morphology of the Bi 2Ti 2O 7 film was studied by the Electri c Force Microscope (EFM).The crystallization of the films was studied by X r ay diffraction (XRD).The Bi 2Ti 2O 7 thin film prepared on (100) silicon subs trate was proved with strong (111) orientation.The dielectric properties and the current voltage (I V) characteristics were measured.The dielectric constant o f the Bi 2Ti 2O 7 thin films vs.temperature and frequency in the interval 100 8 00℃ were studied.The dielectric constang is 118 and dielectric loss is 0.07 res pectively at 100KHz at room temperature.The resistivity of the Bi 2Ti 2O 7 th in film is higher than 1×10 12 (Ω·cm) under the applied voltage from -5V to 5V.For films 0.4μm thick annealed at 580℃ for 40 minutes,their leakage cu r r ent density is 4.06×10 -7 A/cm 2 at an applied voltage of 15V.This shows the films have very good insulating property. We observed the obviously ferroelectric phase transition and its Curie temperatu re in the Bi 2Ti 2O 7 ceramic.Capacitance vs.temperature was measured with 27 800℃ at 1kHz,10kHz,100kHz and 1MHz,respectively.
