The photocatalytic activity of a semiconductor‐based photocatalyst largely depends on the semiconductor’s intrinsic crystal and electronic properties.We have prepared two types of La and Cr co‐doped SrTiO3photocata...The photocatalytic activity of a semiconductor‐based photocatalyst largely depends on the semiconductor’s intrinsic crystal and electronic properties.We have prepared two types of La and Cr co‐doped SrTiO3photocatalysts(SrTiO3(La,Cr))using the polymerized complex method(PCM)and sol‐gel hydrothermal method(SHM).Under?>420‐nm visible light irradiation,only the Pt‐loaded SrTiO3(La,Cr)prepared by the SHM showed efficient photocatalytic activities for both H2evolution in the presence of an I?sacrificial reagent and for Z‐scheme overall water splitting when it was coupled with the Pt‐loaded WO3in the presence of I?and IO3?as the shuttle redox mediator.The superior photocatalytic activity of SrTiO3(La,Cr)prepared by the SHM has been ascribed to its more negative conduction‐band position,higher carrier concentration,and higher carrier mobility,demonstrating that the design and synthesis of an H2‐evolution photocatalyst with appropriate electronic properties is crucial for achieving Z‐scheme overall water splitting.展开更多
A two‐step photocatalytic water splitting system,termed a“Z‐scheme system”,was achieved using Zn‐doped g‐C3N4for H2evolution and BiVO4for O2evolution with Fe2+/Fe3+as a shuttle redox mediator.H2and O2were evalua...A two‐step photocatalytic water splitting system,termed a“Z‐scheme system”,was achieved using Zn‐doped g‐C3N4for H2evolution and BiVO4for O2evolution with Fe2+/Fe3+as a shuttle redox mediator.H2and O2were evaluated simultaneously when the doping amount of zinc was10%.Moreover,Zn‐doped(10%)g‐C3N4synthesized by an impregnation method showed superior active ability to form the Z‐scheme with BiVO4than by in‐situ synthesis.X‐ray diffraction,UV‐Vis spectroscopy,scanning electron microscopy,and X‐ray photoelectron spectroscopy were used to characterize the samples.It was determined that more Zn?N bonds could be formed on the surface of g‐C3N4by impregnation,which could facilitate charge transfer.展开更多
A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avo...A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.展开更多
Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by t...Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.展开更多
WT5,5”BX] A new class of numerical schemes is proposed to solve convection diffusion equations by combining the upwind technique and the method of operator splitting. For every time step, the multi dimensional approx...WT5,5”BX] A new class of numerical schemes is proposed to solve convection diffusion equations by combining the upwind technique and the method of operator splitting. For every time step, the multi dimensional approximation is performed in several independent directions alternatively, while the upwind technique is applied to treat the convection term in every individual direction. This scheme possesses maximum principle. Stability and convergence are analysed by energy method.[WT5,5”HZ]展开更多
Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly im...Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.展开更多
We propose a novel strategy numed basis-splitting scheme to split the intercepted quanta into several portions based on different bases, for eavesdropping in the process of quantum cryptography. Compared with intercep...We propose a novel strategy numed basis-splitting scheme to split the intercepted quanta into several portions based on different bases, for eavesdropping in the process of quantum cryptography. Compared with intercept- resend strategy, our simulation results of the basis-splitting scheme under the non-ideal condition show a greater performance, especially with the increase of the length of shifted bits. Consequently our scheme can aid eaves- dropper to gather much more useful information.展开更多
In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the...In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.展开更多
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting (MSS) method to solve the two-dimensional nonlinear Schrodinger equation (2D-NLSE) in this pap...Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting (MSS) method to solve the two-dimensional nonlinear Schrodinger equation (2D-NLSE) in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.展开更多
For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation r...For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.展开更多
In this work, a new numerical technique is proposed for the resolution of a fluid model based on three Boltzmann moments. The main purpose of this technique is to calculate electric and physical properties in the non-...In this work, a new numerical technique is proposed for the resolution of a fluid model based on three Boltzmann moments. The main purpose of this technique is to calculate electric and physical properties in the non-equilibrium electric discharge at low pressure. The transport and Poisson's equations form a self-consistent model. This equation system is written in cylindrical coordinates following the geometric shape of a plasma reactor. Our transport equation system is discretized using the finite volume approach and resolved by the N-BEE explicit scheme coupled to the time splitting method. This programming structure reduces computation time considerably. The 2D code is carried out and tested by comparing our results with those found in literature.展开更多
The paper is devised to combine the approximated semi-Lagrange weighted essentially non-oscillatory scheme and flux vector splitting. The approximated finite volume semi-Lagrange that is weighted essentially non-oscil...The paper is devised to combine the approximated semi-Lagrange weighted essentially non-oscillatory scheme and flux vector splitting. The approximated finite volume semi-Lagrange that is weighted essentially non-oscillatory scheme with Roe flux had been proposed. The methods using Roe speed to construct the flux probably generates entropy-violating solutions. More seriously, the methods maybe perform numerical instability in two-dimensional cases. A robust and simply remedy is to use a global flux splitting to substitute Roe flux. The combination is tested by several numerical examples. In addition, the comparisons of computing time and resolution between the classical weighted essentially non-oscillatory scheme (WENOJS-LF) and the semi-Lagrange weighted essentially non-oscillatory scheme (WENOEL-LF) which is presented (both combining with the flux vector splitting).展开更多
In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the targe...In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.展开更多
In flexible job-shop batch scheduling problem, the optimal lot-size of different process is not always the same because of different processing time and set-up time. Even for the same process of the same workpiece, th...In flexible job-shop batch scheduling problem, the optimal lot-size of different process is not always the same because of different processing time and set-up time. Even for the same process of the same workpiece, the choice of machine also affects the optimal lot-size. In addition, different choices of lot-size between the constrained processes will impact the manufacture efficiency. Considering that each process has its own appropriate lot-size, we put forward the concept of scheduling with lot-splitting based on process and set up the scheduling model of lot-splitting to critical path process as the core. The model could update the set of batch process and machine selection strategy dynamically to determine processing route and arrange proper lot-size for different processes, to achieve the purpose of optimizing the makespan and reducing the processing batches effectively. The experiment results show that, comparing with lot-splitting scheduling scheme based on workpiece, this model optimizes the makespan and improves the utilization efficiency of the machine. It also greatly decreases the machined batches (42%) and reduces the complexity of shop scheduling production management.展开更多
An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics (MHD) equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method (...An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics (MHD) equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method (AUSM) scheme, and a 5-stage explicit Runge-Kutta scheme is adopted in the time integration. To avoid the influence of the magnetic field divergence created during the simulation, the hyperbolic divergence cleaning method is introduced. The shock-capturing properties of the method are verified by solving the MHD shock-tube problem. Then the 2-D nozzle flow with the magnetic field is numerically simulated on the unstructured mesh. Computational results demonstrate the effects of the magnetic field and agree well with those from references.展开更多
In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe...In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.展开更多
基金supported by the National Natural Science Foundation of China (21763013, 21473189)the National Key Research and Development Program of China (2017YFA0204804)~~
文摘The photocatalytic activity of a semiconductor‐based photocatalyst largely depends on the semiconductor’s intrinsic crystal and electronic properties.We have prepared two types of La and Cr co‐doped SrTiO3photocatalysts(SrTiO3(La,Cr))using the polymerized complex method(PCM)and sol‐gel hydrothermal method(SHM).Under?>420‐nm visible light irradiation,only the Pt‐loaded SrTiO3(La,Cr)prepared by the SHM showed efficient photocatalytic activities for both H2evolution in the presence of an I?sacrificial reagent and for Z‐scheme overall water splitting when it was coupled with the Pt‐loaded WO3in the presence of I?and IO3?as the shuttle redox mediator.The superior photocatalytic activity of SrTiO3(La,Cr)prepared by the SHM has been ascribed to its more negative conduction‐band position,higher carrier concentration,and higher carrier mobility,demonstrating that the design and synthesis of an H2‐evolution photocatalyst with appropriate electronic properties is crucial for achieving Z‐scheme overall water splitting.
基金supported by the National Natural Science Foundation of China (21773153)~~
文摘A two‐step photocatalytic water splitting system,termed a“Z‐scheme system”,was achieved using Zn‐doped g‐C3N4for H2evolution and BiVO4for O2evolution with Fe2+/Fe3+as a shuttle redox mediator.H2and O2were evaluated simultaneously when the doping amount of zinc was10%.Moreover,Zn‐doped(10%)g‐C3N4synthesized by an impregnation method showed superior active ability to form the Z‐scheme with BiVO4than by in‐situ synthesis.X‐ray diffraction,UV‐Vis spectroscopy,scanning electron microscopy,and X‐ray photoelectron spectroscopy were used to characterize the samples.It was determined that more Zn?N bonds could be formed on the surface of g‐C3N4by impregnation,which could facilitate charge transfer.
基金Supported by the National Basic Research Program of China(2012CB825601)the National Natural Science Foundationof China(41031066,41231068,41274192,41074121,41204127)+1 种基金the Knowledge Innovation Program of the ChineseAcademy of Sciences(KZZD-EW-01-4)the Specialized Research Fund for State Key Laboratories
文摘A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.
文摘Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.
文摘WT5,5”BX] A new class of numerical schemes is proposed to solve convection diffusion equations by combining the upwind technique and the method of operator splitting. For every time step, the multi dimensional approximation is performed in several independent directions alternatively, while the upwind technique is applied to treat the convection term in every individual direction. This scheme possesses maximum principle. Stability and convergence are analysed by energy method.[WT5,5”HZ]
文摘Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61301171 and 61372076the Fundamental Research Funds for the Central Universities of China under Grant No K5051301018the National 111 Project of Higher Education of China under Grant No B8038
文摘We propose a novel strategy numed basis-splitting scheme to split the intercepted quanta into several portions based on different bases, for eavesdropping in the process of quantum cryptography. Compared with intercept- resend strategy, our simulation results of the basis-splitting scheme under the non-ideal condition show a greater performance, especially with the increase of the length of shifted bits. Consequently our scheme can aid eaves- dropper to gather much more useful information.
基金Partly supported by the State Major Key Project for Basic Researches
文摘In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.
基金Supported by the Natural Science Foundation of China under Grant No.0971226the 973 Project of China under Grant No.2009CB723802+1 种基金the Research Innovation Fund of Hunan Province under Grant No.CX2011B011the Innovation Fund of NUDT under Grant No.B110205
文摘Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting (MSS) method to solve the two-dimensional nonlinear Schrodinger equation (2D-NLSE) in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
基金the Major State Basic Research Program of China(19990328)NNSF of China(19871051,19972039) the Doctorate Foundation of the State Education Commission
文摘For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.
文摘In this work, a new numerical technique is proposed for the resolution of a fluid model based on three Boltzmann moments. The main purpose of this technique is to calculate electric and physical properties in the non-equilibrium electric discharge at low pressure. The transport and Poisson's equations form a self-consistent model. This equation system is written in cylindrical coordinates following the geometric shape of a plasma reactor. Our transport equation system is discretized using the finite volume approach and resolved by the N-BEE explicit scheme coupled to the time splitting method. This programming structure reduces computation time considerably. The 2D code is carried out and tested by comparing our results with those found in literature.
文摘The paper is devised to combine the approximated semi-Lagrange weighted essentially non-oscillatory scheme and flux vector splitting. The approximated finite volume semi-Lagrange that is weighted essentially non-oscillatory scheme with Roe flux had been proposed. The methods using Roe speed to construct the flux probably generates entropy-violating solutions. More seriously, the methods maybe perform numerical instability in two-dimensional cases. A robust and simply remedy is to use a global flux splitting to substitute Roe flux. The combination is tested by several numerical examples. In addition, the comparisons of computing time and resolution between the classical weighted essentially non-oscillatory scheme (WENOJS-LF) and the semi-Lagrange weighted essentially non-oscillatory scheme (WENOEL-LF) which is presented (both combining with the flux vector splitting).
基金AFOSR and NSF for their support of this work under grants FA9550-19-1-0281 and FA9550-17-1-0394 and NSF grant DMS 191218。
文摘In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.
基金Supported by National Key Technology R&D Program(No.2013BAJ06B)
文摘In flexible job-shop batch scheduling problem, the optimal lot-size of different process is not always the same because of different processing time and set-up time. Even for the same process of the same workpiece, the choice of machine also affects the optimal lot-size. In addition, different choices of lot-size between the constrained processes will impact the manufacture efficiency. Considering that each process has its own appropriate lot-size, we put forward the concept of scheduling with lot-splitting based on process and set up the scheduling model of lot-splitting to critical path process as the core. The model could update the set of batch process and machine selection strategy dynamically to determine processing route and arrange proper lot-size for different processes, to achieve the purpose of optimizing the makespan and reducing the processing batches effectively. The experiment results show that, comparing with lot-splitting scheduling scheme based on workpiece, this model optimizes the makespan and improves the utilization efficiency of the machine. It also greatly decreases the machined batches (42%) and reduces the complexity of shop scheduling production management.
文摘An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics (MHD) equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method (AUSM) scheme, and a 5-stage explicit Runge-Kutta scheme is adopted in the time integration. To avoid the influence of the magnetic field divergence created during the simulation, the hyperbolic divergence cleaning method is introduced. The shock-capturing properties of the method are verified by solving the MHD shock-tube problem. Then the 2-D nozzle flow with the magnetic field is numerically simulated on the unstructured mesh. Computational results demonstrate the effects of the magnetic field and agree well with those from references.
文摘In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.