Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
Fujian cuisine is a distinctive Chinese cuisine.Today,there are many faults and mistakes in the translation of the dish names,which leads to the failure and inconvenience of cross-cultural communication.The paper is a...Fujian cuisine is a distinctive Chinese cuisine.Today,there are many faults and mistakes in the translation of the dish names,which leads to the failure and inconvenience of cross-cultural communication.The paper is an attempt to probe into the appropriate translation of Fujian dish names by the employment of explicitation.展开更多
In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solut...In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solution method(abbreviated as mI-nE-MTS method).The TTS system is divided into train-track subsystem and substruc-ture subsystem.Considering that the root cause of low effi-ciency of obtaining TTS solution lies in solving the alge-braic equation of the substructures,the high-efficient Zhai method,an explicit integration scheme,can be introduced to avoid matrix inversion process.The train-track system is solved by implicitly Park method.Moreover,it is known that the requirement of time step size differs for different sub-systems,integration methods and structural frequency response characteristics.A multi-time-step solution is pro-posed,in which time step size for the train-track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand,namely the time spent for m implicit integral steps is equal to n explicit integral steps,i.e.,mI=nE as mentioned above.The numeri-cal examples show the accuracy,efficiency,and engineering practicality of the proposed method.展开更多
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on ex...We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge–Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om extended phase space symplectic-like methods with the midpoint permutation.展开更多
This study aimed to identify the effectiveness of explicit vocabulary instruction on productive vocabulary learning in writing among intermediate school learners in Saudi Arabia,verify the existence of any statistical...This study aimed to identify the effectiveness of explicit vocabulary instruction on productive vocabulary learning in writing among intermediate school learners in Saudi Arabia,verify the existence of any statistically significant differences at the significance level of 0.01 between the mean scores of the post-test of the control group and the experimental group in the vocabulary test,and verify the existence of any statistically significant differences at the significance level of 0.01 between the mean scores of the pre-and post-test of the experimental group in the vocabulary test in favor of the post-test.The study community consisted of all intermediate school students in the Kingdom of Saudi Arabia,while the study sample included 30 students.The experimental method was adopted to identify the effectiveness of explicit vocabulary instruction on productive vocabulary learning in writing and the achievement test was used as the study tool.The study reached many results including there were no statistically significant differences at the significance level of 0.01 between the mean scores of the post-test of the control group and the experimental group in the vocabulary test and there were no statistically significant differences at the significance level of 0.01 between the mean scores of the pre-and post-test of the experimental group in the vocabulary test in favor of the post-test.According to these results,some recommendations and proposals were made including training English teachers at the intermediate school level in the Kingdom of Saudi Arabia,on explicit vocabulary instruction and conducting future researches on the trends of English teachers at the intermediate school level,in the Kingdom of Saudi Arabia,regarding the adoption of explicit vocabulary instruction while teaching the English language.展开更多
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
文摘Fujian cuisine is a distinctive Chinese cuisine.Today,there are many faults and mistakes in the translation of the dish names,which leads to the failure and inconvenience of cross-cultural communication.The paper is an attempt to probe into the appropriate translation of Fujian dish names by the employment of explicitation.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.52008404,U1934217 and 11790283)Science and Technology Research and Development Program Project of China Railway Group Limited(Major Special Project,No.2020-Special-02)the National Natural Science Foundation of Hunan Province(Grant No.2021JJ30850).
文摘In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solution method(abbreviated as mI-nE-MTS method).The TTS system is divided into train-track subsystem and substruc-ture subsystem.Considering that the root cause of low effi-ciency of obtaining TTS solution lies in solving the alge-braic equation of the substructures,the high-efficient Zhai method,an explicit integration scheme,can be introduced to avoid matrix inversion process.The train-track system is solved by implicitly Park method.Moreover,it is known that the requirement of time step size differs for different sub-systems,integration methods and structural frequency response characteristics.A multi-time-step solution is pro-posed,in which time step size for the train-track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand,namely the time spent for m implicit integral steps is equal to n explicit integral steps,i.e.,mI=nE as mentioned above.The numeri-cal examples show the accuracy,efficiency,and engineering practicality of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11901564 and 12171466)。
文摘We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge–Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om extended phase space symplectic-like methods with the midpoint permutation.
文摘This study aimed to identify the effectiveness of explicit vocabulary instruction on productive vocabulary learning in writing among intermediate school learners in Saudi Arabia,verify the existence of any statistically significant differences at the significance level of 0.01 between the mean scores of the post-test of the control group and the experimental group in the vocabulary test,and verify the existence of any statistically significant differences at the significance level of 0.01 between the mean scores of the pre-and post-test of the experimental group in the vocabulary test in favor of the post-test.The study community consisted of all intermediate school students in the Kingdom of Saudi Arabia,while the study sample included 30 students.The experimental method was adopted to identify the effectiveness of explicit vocabulary instruction on productive vocabulary learning in writing and the achievement test was used as the study tool.The study reached many results including there were no statistically significant differences at the significance level of 0.01 between the mean scores of the post-test of the control group and the experimental group in the vocabulary test and there were no statistically significant differences at the significance level of 0.01 between the mean scores of the pre-and post-test of the experimental group in the vocabulary test in favor of the post-test.According to these results,some recommendations and proposals were made including training English teachers at the intermediate school level in the Kingdom of Saudi Arabia,on explicit vocabulary instruction and conducting future researches on the trends of English teachers at the intermediate school level,in the Kingdom of Saudi Arabia,regarding the adoption of explicit vocabulary instruction while teaching the English language.
