In order to explore the possible diffusion distance of carbon during proeutectoid ferrite transformation, a slow cooling test of low carbon steel was carried out under vacuum of the thermal simulator. The microstructu...In order to explore the possible diffusion distance of carbon during proeutectoid ferrite transformation, a slow cooling test of low carbon steel was carried out under vacuum of the thermal simulator. The microstructure and thermal expansion curve were discussed and the carbon concentration inside the sample was measured. The ferrite layer of about 450 μm thickness was obtained without pearlite on the surface of the sample in the microstructure. The thermal expansion curve shows that the ferrite layer without pearlite is formed during the local phase transformation, which is followed by the global transformation. The carbon concentration in the core of the sample (0.061%) is significantly higher than that of the bulk material (0.054%). All results show that carbon has long-range diffusion from the outer layer to the inner layer of the sample. The transformation is predominantly interface-controlled mode during local transformation, and the interface migration rate is about 2.25 μm/s.展开更多
New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave sol...New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.展开更多
Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebrai...Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.展开更多
A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. As an application of this method, we study the （2＋1）-dimensio...A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. As an application of this method, we study the （2＋1）-dimensional dispersive long wave equation. With the aid of computerized symbolic computation, a number of doubly periodic wave solutions expressed by various Jacobi elliptic functions are obtained. In the limit cases, the solitary wave solutions are derived as well.展开更多
In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transf...In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to （2＋1）-dimensionM dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these sohitions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations.展开更多
Reducing the module prices by increasing the efficiency of solar cells is one of the major challenges in today＇s photovoltaic research. The emitter formation by epitaxial growth offers a cost-efficient and faster alt...Reducing the module prices by increasing the efficiency of solar cells is one of the major challenges in today＇s photovoltaic research. The emitter formation by epitaxial growth offers a cost-efficient and faster alternative to the standard furnace diffusion process. The efficiency potential of epitaxial emitters 〉 22% has already been proven using a single wafer, low pressure, chemical vapour deposition tool. The purpose of this work is to show the potential of epitaxially grown emitters by APCVD （atmospheric pressure chemical vapour deposition） compared to diffused emitters. The APCVD formation of epitaxial emitters at 1,050 ~C can be realised as high throughput inline process and only takes 1-2 min, whereas the diffusion process using POCI3 takes up to 60 min. Simulations show an increase in voltage of AVoc = ＋10 mV and a reduction in saturation current ,1o of 30% for the epitaxial emitter. The lifetime experiments of solar cells with epitaxial emitter exhibit a diffusion length Leff〉 750μm and an emitter saturation current of Joe 〈 50 fA/cm2 on a planar 10 Ω2cm p-type FZ wafer. Another important aim of this work is to evaluate the limitations of epitaxial emitters due to high thermal budget, interface recombination and the change of reflective properties on textured wafers due to the deposition process. Solar cell efficiencies up to 18.4% on p-type and 20.0% on n-type wafers presented in this paper underline that the emitter epitaxy by APCVD is a competitive process for the emitter formation.展开更多
We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with rea...We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When 0 ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 〉 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.展开更多
基金Project(16PJ1430200)supported by Shanghai Pujiang Program,China
文摘In order to explore the possible diffusion distance of carbon during proeutectoid ferrite transformation, a slow cooling test of low carbon steel was carried out under vacuum of the thermal simulator. The microstructure and thermal expansion curve were discussed and the carbon concentration inside the sample was measured. The ferrite layer of about 450 μm thickness was obtained without pearlite on the surface of the sample in the microstructure. The thermal expansion curve shows that the ferrite layer without pearlite is formed during the local phase transformation, which is followed by the global transformation. The carbon concentration in the core of the sample (0.061%) is significantly higher than that of the bulk material (0.054%). All results show that carbon has long-range diffusion from the outer layer to the inner layer of the sample. The transformation is predominantly interface-controlled mode during local transformation, and the interface migration rate is about 2.25 μm/s.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx16
文摘New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.
基金The project supported by National Natural Science Foundation of China under Grant No.10072013the State Key Basic Research Development Program under Grant No.G1998030600
文摘Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10272071 and the Science Research Foundation of Huzhou University under Grant No. KX21025
文摘A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. As an application of this method, we study the （2＋1）-dimensional dispersive long wave equation. With the aid of computerized symbolic computation, a number of doubly periodic wave solutions expressed by various Jacobi elliptic functions are obtained. In the limit cases, the solitary wave solutions are derived as well.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004 CB 318000
文摘In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to （2＋1）-dimensionM dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these sohitions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations.
文摘Reducing the module prices by increasing the efficiency of solar cells is one of the major challenges in today＇s photovoltaic research. The emitter formation by epitaxial growth offers a cost-efficient and faster alternative to the standard furnace diffusion process. The efficiency potential of epitaxial emitters 〉 22% has already been proven using a single wafer, low pressure, chemical vapour deposition tool. The purpose of this work is to show the potential of epitaxially grown emitters by APCVD （atmospheric pressure chemical vapour deposition） compared to diffused emitters. The APCVD formation of epitaxial emitters at 1,050 ~C can be realised as high throughput inline process and only takes 1-2 min, whereas the diffusion process using POCI3 takes up to 60 min. Simulations show an increase in voltage of AVoc = ＋10 mV and a reduction in saturation current ,1o of 30% for the epitaxial emitter. The lifetime experiments of solar cells with epitaxial emitter exhibit a diffusion length Leff〉 750μm and an emitter saturation current of Joe 〈 50 fA/cm2 on a planar 10 Ω2cm p-type FZ wafer. Another important aim of this work is to evaluate the limitations of epitaxial emitters due to high thermal budget, interface recombination and the change of reflective properties on textured wafers due to the deposition process. Solar cell efficiencies up to 18.4% on p-type and 20.0% on n-type wafers presented in this paper underline that the emitter epitaxy by APCVD is a competitive process for the emitter formation.
基金supported by National Natural Science Foundation of China (Grant Nos. 91130003 and 11371157)the Scientific Research Innovation Team of the University “Aviation Industry Economy” (Grant No. 2016TD02)
文摘We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When 0 ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 〉 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.
