The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sw...The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.展开更多
It is intended to establish the recursive function theory on context free languages (CFLs). In this paper, the function class CFRF and its proper subclass CFPRF were defined on CFLs; it is quite straightforward to use...It is intended to establish the recursive function theory on context free languages (CFLs). In this paper, the function class CFRF and its proper subclass CFPRF were defined on CFLs; it is quite straightforward to use them for describing non-numerical algorithms. In fact, they are respectively the partial recursive functions and primitive recursive functions of context free languages. The structure induction method for proving CFPRF function properties was presented. A method for CFL sentence enumeration was given, the minimization operator was defined. Based on CFL sentence enumeration, the minimization operator evaluation method was given. Finally, the design and implementation principles of executable specification languages with the CFRF as theoretical basis were discussed.展开更多
In this paper, we investigate and analyze one-dimensional heat equation with appropriate initial and boundary condition using finite difference method. Finite difference method is a well-known numerical technique for ...In this paper, we investigate and analyze one-dimensional heat equation with appropriate initial and boundary condition using finite difference method. Finite difference method is a well-known numerical technique for obtaining the approximate solutions of an initial boundary value problem. We develop Forward Time Centered Space (FTCS) and Crank-Nicolson (CN) finite difference schemes for one-dimensional heat equation using the Taylor series. Later, we use these schemes to solve our governing equation. The stability criterion is discussed, and the stability conditions for both schemes are verified. We exhibit the results and then compare the results between the exact and approximate solutions. Finally, we estimate error between the exact and approximate solutions for a specific numerical problem to present the convergence of the numerical schemes, and demonstrate the resulting error in graphical representation.展开更多
The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and convergence.These challenges impose significant constraints on comput...The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and convergence.These challenges impose significant constraints on computational efficiency,particularly in the domain of engineering applications.To address these concerns,this paper proposes a robust implicit high-order discontinuous Galerkin(DG)method for solving compressible Navier-Stokes(NS)equations on arbitrary grids.The method achieves a favorable equilibrium between computational stability and efficiency.To solve the linear system,an exact Jacobian matrix solving strategy is employed for preconditioning and matrix-vector generation in the generalized minimal residual(GMRES)method.This approach mitigates numerical errors in Jacobian solution during implicit calculations and facilitates the implementation of an adaptive Courant-Friedrichs-Lewy(CFL)number increasing strategy,with the aim of improving convergence and robustness.To further enhance the applicability of the proposed method for intricate grid distortions,all simulations are performed in the reference domain.This practice significantly improves the reversibility of the mass matrix in implicit calculations.A comprehensive analysis of various parameters influencing computational stability and efficiency is conducted,including CFL number,Krylov subspace size,and GMRES convergence criteria.The computed results from a series of numerical test cases demonstrate the promising results achieved by combining the DG method,GMRES solver,exact Jacobian matrix,adaptive CFL number,and reference domain calculations in terms of robustness,convergence,and accuracy.These analysis results can serve as a reference for implicit computation in high-order calculations.展开更多
The selection of time step plays a crucial role in improving stability and efficiency in the Discontinuous Galerkin(DG)solution of hyperbolic conservation laws on adaptive moving meshes that typically employs explicit...The selection of time step plays a crucial role in improving stability and efficiency in the Discontinuous Galerkin(DG)solution of hyperbolic conservation laws on adaptive moving meshes that typically employs explicit stepping.A commonly used selection of time step is a direct extension based on Courant-Friedrichs-Levy(CFL)conditions established for fixed and uniform meshes.In this work,we provide a mathematical justification for those time step selection strategies used in practical adaptive DG computations.A stability analysis is presented for a moving mesh DG method for linear scalar conservation laws.Based on the analysis,a new selection strategy of the time step is proposed,which takes into consideration the coupling of theα-function(that is related to the eigenvalues of the Jacobian matrix of the flux and the mesh movement velocity)and the heights of the mesh elements.The analysis also suggests several stable combinations of the choices of theα-function in the numerical scheme and in the time step selection.Numerical results obtained with a moving mesh DG method for Burgers’and Euler equations are presented.For comparison purpose,numerical results obtained with an error-based time step-size selection strategy are also given。展开更多
To search new sources of lectin, an experiment on lectin distribution in humoral serum of crab Charybdis feriatus (in short, CFL) was conducted March, 2002. When adding solid ammonium sul-fate into the fluids up to 50...To search new sources of lectin, an experiment on lectin distribution in humoral serum of crab Charybdis feriatus (in short, CFL) was conducted March, 2002. When adding solid ammonium sul-fate into the fluids up to 50% saturation at 4℃, most CFL activity showed precipitates who were then continually extracted by ammonium sulfate of different concentrations. The supernatant, which was called primary CFL fluids, was given a 17.60-fold purification and 45.70% recovery of total activity. Finally, by using Sephadex G-100 column chromatography, the CFL in the primary CFL fluid was highly purified. Compared to the original humoral fluids, the last purified CFL got a 203.90-fold purification and 30.48% recovery of total activity, and demonstrated a single band on SDS-PAGE. In the same time, the purified CFL was detected for agglutination activity with 7 kinds of animal erythrocytes. Other characterization, such as sugar inhibition, and the effect of temperature on the agglutination activity of CFL were also studied. Our results indicate that agglutination activity of CFL was influenced by sugar and temperature.展开更多
This pilot study examined the effectiveness and students’perceptions of a multimedia module on intermediate Chinese-as-a-Foreign-Language(CFL)learners’understanding and use of the“shì...de”construction.The mo...This pilot study examined the effectiveness and students’perceptions of a multimedia module on intermediate Chinese-as-a-Foreign-Language(CFL)learners’understanding and use of the“shì...de”construction.The module was designed based on the First Principles of Instruction(Morrill,2002)and the Cognitive Theory of Multimedia Learning(Mayer,2009;2014).It provided a systematic and comprehensive approach to teaching the“shì...de”construction,one of the most challenging grammar points in CFL.Twenty-two CFL learners participated in this mixed-methods study.Data were collected using pre-and post-tests,a survey,think-alouds,and semi-structured interviews.Findings show that after using the module,students’understanding and use of the construction significantly improved,except for their understanding of the second usage.The students enjoyed using the module and appreciated how it was designed,the way it was presented,and its availability.The reasons for the effectiveness of the module were analyzed and led to suggested improvements to the design of the module.The detailed description of the design process and the research result contribute to the knowledge of designing grammar teaching modules with multimedia for online,blended,and flipped learning.展开更多
The application of prestressed carbon reinforced polymer （prestressed CFRP） in reinforced concrete （RC） members can improve the mechanical properties of strengthened structures and strengthening efficiency. This p...The application of prestressed carbon reinforced polymer （prestressed CFRP） in reinforced concrete （RC） members can improve the mechanical properties of strengthened structures and strengthening efficiency. This paper proposed a semi-empirical prediction fornmla of fatigue lives of the RC beams strengthened with prestressed CFRP under bending loads. The formula is established based on the fatigue life prediction method of RC beams and fatigue experimental data of non-prestressed CFRP reinforced beams done before. Fatigue effect coefficient of the formula was confirmed by the fatigue experiments of the RC beams strengthened with prestressed carbon fiber laminate （prestressed CFL） under cyclic bending loads. Fatigue lives of the strengthened beams predicted using the formula agreed well with the experimental data.展开更多
The recent trend in light emitting diode or LED lighting applications and their claimed energy saving capabilities together with their overall attractiveness has us all convinced that they really are a greener alterna...The recent trend in light emitting diode or LED lighting applications and their claimed energy saving capabilities together with their overall attractiveness has us all convinced that they really are a greener alternative to the compact fluorescent lights or CFL. As convincing as it seems, the actual energy saving capabilities of LEDs are yet to be proven scientifically or at the least, on an empirical level when compared to CFLs. This paper tackles the issue with the use of a solar cell by evaluating the photovoltaic current and voltage generated by the solar cell subjected to each lighting system. Graphical representations are drawn and a conclusion is then reached based on the amount of power generation in the solar cells in order to determine the energy saving capabilities of each lighting system and its efficiency. From the result, it has been found that an LED is 3.7 times more power efficient than a CFL based light source of equal wattage.展开更多
基金This work is partially supported by Sloan FoundationNSF DMS0513073+1 种基金ONR grant N00014-02-1-0090DARPA grant N00014-02-1-0603
文摘The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69873042) .
文摘It is intended to establish the recursive function theory on context free languages (CFLs). In this paper, the function class CFRF and its proper subclass CFPRF were defined on CFLs; it is quite straightforward to use them for describing non-numerical algorithms. In fact, they are respectively the partial recursive functions and primitive recursive functions of context free languages. The structure induction method for proving CFPRF function properties was presented. A method for CFL sentence enumeration was given, the minimization operator was defined. Based on CFL sentence enumeration, the minimization operator evaluation method was given. Finally, the design and implementation principles of executable specification languages with the CFRF as theoretical basis were discussed.
文摘In this paper, we investigate and analyze one-dimensional heat equation with appropriate initial and boundary condition using finite difference method. Finite difference method is a well-known numerical technique for obtaining the approximate solutions of an initial boundary value problem. We develop Forward Time Centered Space (FTCS) and Crank-Nicolson (CN) finite difference schemes for one-dimensional heat equation using the Taylor series. Later, we use these schemes to solve our governing equation. The stability criterion is discussed, and the stability conditions for both schemes are verified. We exhibit the results and then compare the results between the exact and approximate solutions. Finally, we estimate error between the exact and approximate solutions for a specific numerical problem to present the convergence of the numerical schemes, and demonstrate the resulting error in graphical representation.
基金supported by the National Natural Science Foundation of China(Grant No.12102247)the Technology Development Program(Grant No.JCKY2022110C119).
文摘The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and convergence.These challenges impose significant constraints on computational efficiency,particularly in the domain of engineering applications.To address these concerns,this paper proposes a robust implicit high-order discontinuous Galerkin(DG)method for solving compressible Navier-Stokes(NS)equations on arbitrary grids.The method achieves a favorable equilibrium between computational stability and efficiency.To solve the linear system,an exact Jacobian matrix solving strategy is employed for preconditioning and matrix-vector generation in the generalized minimal residual(GMRES)method.This approach mitigates numerical errors in Jacobian solution during implicit calculations and facilitates the implementation of an adaptive Courant-Friedrichs-Lewy(CFL)number increasing strategy,with the aim of improving convergence and robustness.To further enhance the applicability of the proposed method for intricate grid distortions,all simulations are performed in the reference domain.This practice significantly improves the reversibility of the mass matrix in implicit calculations.A comprehensive analysis of various parameters influencing computational stability and efficiency is conducted,including CFL number,Krylov subspace size,and GMRES convergence criteria.The computed results from a series of numerical test cases demonstrate the promising results achieved by combining the DG method,GMRES solver,exact Jacobian matrix,adaptive CFL number,and reference domain calculations in terms of robustness,convergence,and accuracy.These analysis results can serve as a reference for implicit computation in high-order calculations.
基金M.Zhang was partially supported by the Postdoctoral Science Foundation of China(Grant 2022M710229)J.Qiu was partially supported by National Natural Science Foundation of China(Grant 12071392).
文摘The selection of time step plays a crucial role in improving stability and efficiency in the Discontinuous Galerkin(DG)solution of hyperbolic conservation laws on adaptive moving meshes that typically employs explicit stepping.A commonly used selection of time step is a direct extension based on Courant-Friedrichs-Levy(CFL)conditions established for fixed and uniform meshes.In this work,we provide a mathematical justification for those time step selection strategies used in practical adaptive DG computations.A stability analysis is presented for a moving mesh DG method for linear scalar conservation laws.Based on the analysis,a new selection strategy of the time step is proposed,which takes into consideration the coupling of theα-function(that is related to the eigenvalues of the Jacobian matrix of the flux and the mesh movement velocity)and the heights of the mesh elements.The analysis also suggests several stable combinations of the choices of theα-function in the numerical scheme and in the time step selection.Numerical results obtained with a moving mesh DG method for Burgers’and Euler equations are presented.For comparison purpose,numerical results obtained with an error-based time step-size selection strategy are also given。
基金Supported by Project of Technology Bureau of Quanzhou of Fujian Province(Z200239) , and by the Fujian Natural Science Foundation (B0410027)
文摘To search new sources of lectin, an experiment on lectin distribution in humoral serum of crab Charybdis feriatus (in short, CFL) was conducted March, 2002. When adding solid ammonium sul-fate into the fluids up to 50% saturation at 4℃, most CFL activity showed precipitates who were then continually extracted by ammonium sulfate of different concentrations. The supernatant, which was called primary CFL fluids, was given a 17.60-fold purification and 45.70% recovery of total activity. Finally, by using Sephadex G-100 column chromatography, the CFL in the primary CFL fluid was highly purified. Compared to the original humoral fluids, the last purified CFL got a 203.90-fold purification and 30.48% recovery of total activity, and demonstrated a single band on SDS-PAGE. In the same time, the purified CFL was detected for agglutination activity with 7 kinds of animal erythrocytes. Other characterization, such as sugar inhibition, and the effect of temperature on the agglutination activity of CFL were also studied. Our results indicate that agglutination activity of CFL was influenced by sugar and temperature.
文摘This pilot study examined the effectiveness and students’perceptions of a multimedia module on intermediate Chinese-as-a-Foreign-Language(CFL)learners’understanding and use of the“shì...de”construction.The module was designed based on the First Principles of Instruction(Morrill,2002)and the Cognitive Theory of Multimedia Learning(Mayer,2009;2014).It provided a systematic and comprehensive approach to teaching the“shì...de”construction,one of the most challenging grammar points in CFL.Twenty-two CFL learners participated in this mixed-methods study.Data were collected using pre-and post-tests,a survey,think-alouds,and semi-structured interviews.Findings show that after using the module,students’understanding and use of the construction significantly improved,except for their understanding of the second usage.The students enjoyed using the module and appreciated how it was designed,the way it was presented,and its availability.The reasons for the effectiveness of the module were analyzed and led to suggested improvements to the design of the module.The detailed description of the design process and the research result contribute to the knowledge of designing grammar teaching modules with multimedia for online,blended,and flipped learning.
基金Project supported by the National Natural Science Foundation of China (Nos. 11132004 and 51078145)the Guangdong Province Natural Science Foundation of China (No. 9251064101000016)
文摘The application of prestressed carbon reinforced polymer （prestressed CFRP） in reinforced concrete （RC） members can improve the mechanical properties of strengthened structures and strengthening efficiency. This paper proposed a semi-empirical prediction fornmla of fatigue lives of the RC beams strengthened with prestressed CFRP under bending loads. The formula is established based on the fatigue life prediction method of RC beams and fatigue experimental data of non-prestressed CFRP reinforced beams done before. Fatigue effect coefficient of the formula was confirmed by the fatigue experiments of the RC beams strengthened with prestressed carbon fiber laminate （prestressed CFL） under cyclic bending loads. Fatigue lives of the strengthened beams predicted using the formula agreed well with the experimental data.
文摘The recent trend in light emitting diode or LED lighting applications and their claimed energy saving capabilities together with their overall attractiveness has us all convinced that they really are a greener alternative to the compact fluorescent lights or CFL. As convincing as it seems, the actual energy saving capabilities of LEDs are yet to be proven scientifically or at the least, on an empirical level when compared to CFLs. This paper tackles the issue with the use of a solar cell by evaluating the photovoltaic current and voltage generated by the solar cell subjected to each lighting system. Graphical representations are drawn and a conclusion is then reached based on the amount of power generation in the solar cells in order to determine the energy saving capabilities of each lighting system and its efficiency. From the result, it has been found that an LED is 3.7 times more power efficient than a CFL based light source of equal wattage.
