The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely ana...The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V（r） =α1r^8 ＋α2r^3 ＋ α3r^2 ＋β3r^-1 ＋β2r^-3 ＋β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials＇ superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.展开更多
In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence ...In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.展开更多
This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the li...This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.展开更多
Access to electricity is poor in the Economic Community of West African States (ECOWAS). Concentrating Solar Power (CSP) presents better opportunities for increasing access to electricity and for diversifying sources ...Access to electricity is poor in the Economic Community of West African States (ECOWAS). Concentrating Solar Power (CSP) presents better opportunities for increasing access to electricity and for diversifying sources of energy in the ECOWAS region;however, to date, except for Burkina Faso, no site evaluation pertaining to the region has ever been performed for CSP. This study provides potential assessment and site ranking for large-scale CSP projects in the ECOWAS region. It computes the nominal potential power and gives the corresponding energy yield with many scenarios. By considering only 1% of the suitable land area with daily DNI greater or equal to 5 kWh/m2, a land slope less or equal to 5% and distance to transmission line not more than 100 km, the study showed, for example, that West Africa has a potential nominal capacity of 21.3 GW for parabolic trough technology.展开更多
Corrosion of reinforcing steel is a major cause for degradation of concrete structures,especially when exposed to chloride ions.Thus,the Silver/Nano-silver Chloride (SNSC) electrodes as sensors of chloride concentrati...Corrosion of reinforcing steel is a major cause for degradation of concrete structures,especially when exposed to chloride ions.Thus,the Silver/Nano-silver Chloride (SNSC) electrodes as sensors of chloride concentration were prepared and encapsulated carefully.The properties of the electrode were studied by emerging them in a series of concrete pore solutions with different admixed KCl contents.These SNSC sensors show that good stability in concrete pore solutions at room temperature.Polarization disposal can shorten the stabilized period of the sensors.The electrochemical tests indicate the SNSC sensors with desirable linearity and reproducibility.The response time of SNSC sensors is short enough for monitoring the chloride ions concentration in concrete structures.The good performance of SNSC sensors indicate that they could be embedded in the concrete structures in the future.展开更多
Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechani...Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechanical behavior of these solids.In this work,a perturbation finite element(FE)formulation is developed to analyze chemo-elastic boundary value problems(BVPs)under chemical equilibrium.The perturbation method is applied to the FE equations because of the nonlinearity in the chemical potential expression as a function of solute concentration.The compositional expansion coefficient is used as the perturbation parameter.After the perturbation expansion,a system of partial differential equations for the displacement and dimensionless solute concentration functions is obtained and solved in consecutive steps.The presence of a numerical solution enables modeling 3D chemo-elastic solids,such as battery electrodes or ionic gels,of any geometric shape with defects of different shapes.The proposed method is tested in several numerical examples such as plates with circular or elliptical holes,and cracks.The numerical examples showed how the shape of the defect can change the distribution of solute concentration around the defect.Cracks in chemo-elastic solids create sharp peaks in solute concentration around crack tips,and the intensity of these peaks increases as the far field solute concentration decreases.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10575140the Basic Research of Chongqing Education Committee under Grant No.KJ060813
文摘The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V（r） =α1r^8 ＋α2r^3 ＋ α3r^2 ＋β3r^-1 ＋β2r^-3 ＋β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials＇ superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.
基金supported by National Natural Science Foundation of China(11971393)。
文摘In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.
基金Supported by National Science Foundation of China (11071177)Excellent Youth Foundation of Sichuan Province (2012JQ0011)
文摘This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.
文摘Access to electricity is poor in the Economic Community of West African States (ECOWAS). Concentrating Solar Power (CSP) presents better opportunities for increasing access to electricity and for diversifying sources of energy in the ECOWAS region;however, to date, except for Burkina Faso, no site evaluation pertaining to the region has ever been performed for CSP. This study provides potential assessment and site ranking for large-scale CSP projects in the ECOWAS region. It computes the nominal potential power and gives the corresponding energy yield with many scenarios. By considering only 1% of the suitable land area with daily DNI greater or equal to 5 kWh/m2, a land slope less or equal to 5% and distance to transmission line not more than 100 km, the study showed, for example, that West Africa has a potential nominal capacity of 21.3 GW for parabolic trough technology.
基金Funded by the National Natural Science Foundation of China (No.50678053)
文摘Corrosion of reinforcing steel is a major cause for degradation of concrete structures,especially when exposed to chloride ions.Thus,the Silver/Nano-silver Chloride (SNSC) electrodes as sensors of chloride concentration were prepared and encapsulated carefully.The properties of the electrode were studied by emerging them in a series of concrete pore solutions with different admixed KCl contents.These SNSC sensors show that good stability in concrete pore solutions at room temperature.Polarization disposal can shorten the stabilized period of the sensors.The electrochemical tests indicate the SNSC sensors with desirable linearity and reproducibility.The response time of SNSC sensors is short enough for monitoring the chloride ions concentration in concrete structures.The good performance of SNSC sensors indicate that they could be embedded in the concrete structures in the future.
文摘Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechanical behavior of these solids.In this work,a perturbation finite element(FE)formulation is developed to analyze chemo-elastic boundary value problems(BVPs)under chemical equilibrium.The perturbation method is applied to the FE equations because of the nonlinearity in the chemical potential expression as a function of solute concentration.The compositional expansion coefficient is used as the perturbation parameter.After the perturbation expansion,a system of partial differential equations for the displacement and dimensionless solute concentration functions is obtained and solved in consecutive steps.The presence of a numerical solution enables modeling 3D chemo-elastic solids,such as battery electrodes or ionic gels,of any geometric shape with defects of different shapes.The proposed method is tested in several numerical examples such as plates with circular or elliptical holes,and cracks.The numerical examples showed how the shape of the defect can change the distribution of solute concentration around the defect.Cracks in chemo-elastic solids create sharp peaks in solute concentration around crack tips,and the intensity of these peaks increases as the far field solute concentration decreases.
