The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values o...The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^＋ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered.展开更多
After introducing dark parameters into the traditional physical models, some types of new phenomena may be found. An important difficult problem is how to directly observe this kind of physical phenomena. An alternati...After introducing dark parameters into the traditional physical models, some types of new phenomena may be found. An important difficult problem is how to directly observe this kind of physical phenomena. An alternative treatment is to introduce equivalent multiple partner fields. If use this ideal to integrable systems, one may obtain infinitely many new coupled integrable systems constituted by the original usuM field and partner fields. The idea is illustrated via the celebrate KdV equation. From the procedure, some byproducts can be obtained： A new method to find exact solutions of some types of coupled nonlinear physical problems, say, the perturbation KdV systems, is provided; Some new localized modes such as the staggered modes can be found and some new interaction phenomena like the ghost interaction are discovered.展开更多
Conversion of SrSO4 to acidic strontium oxalate hydrate(H[Sr(C2O4)1.5(H2O)]) in aqueous H2C2O4 solutions proceeds as a consecutive reaction. In the first step of the consecutive reaction, SrSO4 reacts with H2C2O4 and ...Conversion of SrSO4 to acidic strontium oxalate hydrate(H[Sr(C2O4)1.5(H2O)]) in aqueous H2C2O4 solutions proceeds as a consecutive reaction. In the first step of the consecutive reaction, SrSO4 reacts with H2C2O4 and pseudomorphic conversion to SrC2 O4·H2O occurs. In the second step, SrC2 O4·H2O reacts with H2C2O4 to form H[Sr(C2 O4)1.5(H2O)]. Sr(HC2 O4)(C2 O4)0.5·H2 O crystallizes during cooling of the reaction mixture to room temperature if the solution reaches the saturation concentration of (H[Sr(C2O4)1.5(H2O)]. The aims of this study are the derivation of reaction rate equations and the determination of the kinetic parameters such as pre-exponential factor, apparent activation energy and order of H2C2O4 concentration for each reaction step.Fractional conversions of SrSO4 were calculated using the quantitative amounts of dissolved S and Sr. It was determined that the reaction rate increased at the initial time of reaction by increasing the temperature using solutions with approximately same H2C2O4 concentrations. The reaction extends very slowly after a certain time in solutions with low H2C2O4 concentration and ends by the formation of a protective layer of SrC2O4-H2O around the surfaces of solid particles. Fractional conversion of SrSO4 is increased by increasing concentration of H2C2O4 at constant temperature. Kinetic model equations were derived using shrinking core model for each step.展开更多
Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been w...Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been widely used. An approach that combines differential evolution （DE） algorithm and control vector parameteri- zation （CVP） is proposed in this paper. In the proposed CVP, control variables are approximated with polynomials based on state variables and time in the entire time interval. Region reduction strategy is used in DE to reduce the width of the search region, which improves the computing efficiency. The results of the case studies demonstrate the feasibility and efficiency of the oroposed methods.展开更多
To obtain flow behavior and workability of 7055 aluminium alloy during hot deformation,hot compression tests at different temperatures and strain rates are conducted.True stress?strain curves of 7055 aluminium alloy u...To obtain flow behavior and workability of 7055 aluminium alloy during hot deformation,hot compression tests at different temperatures and strain rates are conducted.True stress?strain curves of 7055 aluminium alloy under different conditions are obtained and the flow stress increases with ascending strain rate and descending temperature.For Arrhenius constitutive equation,each material parameter is set as a constant,which will bring forth large error for predicting flow behavior.In this work,material parameters are fitted as a function of temperature or strain rate based on experimental results and a modified constitutive equation is established for more accurate prediction of flow behavior of 7055 aluminium alloy.The effects of temperature and strain rate on power dissipation and instability are analyzed to establish a processing map of 7055 aluminium alloy.The dominant deformation mechanism for microstructure evolution at different deformation conditions can be determined and high efficiency of power dissipation may be achieved from power dissipation map.Meanwhile,proper processing parameters to avoid flow instability can be easily acquired in instability map.According to the processing map,optimized processing parameters of 7055 aluminium alloy are temperature of 673?723 K and strain rate of 0.01?0.4 s^?1,during which its efficiency of power dissipation is over 30%.Finite element method(FEM)is used to obtain optimized parameter in hot rolling process on the basis of processing map.展开更多
The joint optimization of detection threshold and waveform parameters for target tracking which comes from the idea of cognitive radar is investigated for the modified probabilistic data association(MPDA)filter.The tr...The joint optimization of detection threshold and waveform parameters for target tracking which comes from the idea of cognitive radar is investigated for the modified probabilistic data association(MPDA)filter.The transmitted waveforms and detection threshold are adaptively selected to enhance the tracking performance.The modified Riccati equation is adopted to predict the error covariance which is used as the criterion function,while the optimization problem is solved through the genetic algorithm(GA).The detection probability,false alarm probability and measurement noise covariance are all considered together,which significantly improves the tracking performance of the joint detection and tracking system.Simulation results show that the proposed adaptive waveform-detection threshold joint optimization method outperforms the adaptive threshold method and the fixed parameters method,which will reduce the tracking error.The average reduction of range error between the adaptive joint method and the fixed parameters method is about 0.6 m,while that between the adaptive joint method and the adaptive threshold only method is about 0.3 m.Similar error reduction occurs for the velocity error and acceleration error.展开更多
Enhancing the ability of the WRF model in simulating a large area covering the West Pacific Ocean, China's Mainland, and the East Indian Ocean is very important to improve prediction of the East Asian monsoon clim...Enhancing the ability of the WRF model in simulating a large area covering the West Pacific Ocean, China's Mainland, and the East Indian Ocean is very important to improve prediction of the East Asian monsoon climate. The objective of this study is to identify a reasonable configuration of physical parameterization schemes to simulate the precipitation and temperature in this large area. The Mellor-Yamada-Janjic （MYJ） and Yonsei University （YSU） PBL schemes, the WSM3 and WSM5 microphysics schemes, and the Betts-Miller-Janjic （BMJ） and Tiedtke cumulus schemes are compared through simulation of the regional climate of summer 2008. All cases exhibit a similar spatial distribution of temperature as observed, and the spatial correlation coefficients are all higher than 0.95. The cases combining MY J, WSM3/WSM5, and BMJ have the smallest biases of temperature. The choice of PBL scheme has a significant effect on precipitation in such a large area. The cases with MYJ reproduce a better distribution of rain belts, while YSU strongly overestimates the precipitation intensity. The precipitation simulated using WSM3 is similar to that using WSM5. The BMJ cumulus scheme combined with the MYJ PBL scheme has a smaller bias of precipitation. However, the Tiedtke scheme reproduces the precipitation pattern better, especially over the ITCZ.展开更多
基金The project supported in part by the Natural Science Foundation of Education Department of Henan Province of China under Grant No. 2006110002 and the Science Foundations of Henan University of Science and Technology under Grant Nos. 2004ZD002 and 2006ZY001
文摘The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^＋ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered.
基金Sponsored by the National Natural Science Foundation of China under Grang No.10735030the National Basic Research Programs of China(973 Programs 2007CB814800 and 2005CB422301)K.C.Wong Magna Fund in Ningbo University
文摘After introducing dark parameters into the traditional physical models, some types of new phenomena may be found. An important difficult problem is how to directly observe this kind of physical phenomena. An alternative treatment is to introduce equivalent multiple partner fields. If use this ideal to integrable systems, one may obtain infinitely many new coupled integrable systems constituted by the original usuM field and partner fields. The idea is illustrated via the celebrate KdV equation. From the procedure, some byproducts can be obtained： A new method to find exact solutions of some types of coupled nonlinear physical problems, say, the perturbation KdV systems, is provided; Some new localized modes such as the staggered modes can be found and some new interaction phenomena like the ghost interaction are discovered.
基金the financial support of the Scientific Research Projects Coordination Unit of Istanbul University (Project number: 17344 and 31088)
文摘Conversion of SrSO4 to acidic strontium oxalate hydrate(H[Sr(C2O4)1.5(H2O)]) in aqueous H2C2O4 solutions proceeds as a consecutive reaction. In the first step of the consecutive reaction, SrSO4 reacts with H2C2O4 and pseudomorphic conversion to SrC2 O4·H2O occurs. In the second step, SrC2 O4·H2O reacts with H2C2O4 to form H[Sr(C2 O4)1.5(H2O)]. Sr(HC2 O4)(C2 O4)0.5·H2 O crystallizes during cooling of the reaction mixture to room temperature if the solution reaches the saturation concentration of (H[Sr(C2O4)1.5(H2O)]. The aims of this study are the derivation of reaction rate equations and the determination of the kinetic parameters such as pre-exponential factor, apparent activation energy and order of H2C2O4 concentration for each reaction step.Fractional conversions of SrSO4 were calculated using the quantitative amounts of dissolved S and Sr. It was determined that the reaction rate increased at the initial time of reaction by increasing the temperature using solutions with approximately same H2C2O4 concentrations. The reaction extends very slowly after a certain time in solutions with low H2C2O4 concentration and ends by the formation of a protective layer of SrC2O4-H2O around the surfaces of solid particles. Fractional conversion of SrSO4 is increased by increasing concentration of H2C2O4 at constant temperature. Kinetic model equations were derived using shrinking core model for each step.
基金Supported by the Major State Basic Research Development Program of China(2012CB720500)the National Natural Science Foundation of China(Key Program:U1162202)+2 种基金the National Science Fund for Outstanding Young Scholars(61222303)the National Natural Science Foundation of China(61174118,21206037)Shanghai Leading Academic Discipline Project(B504)
文摘Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been widely used. An approach that combines differential evolution （DE） algorithm and control vector parameteri- zation （CVP） is proposed in this paper. In the proposed CVP, control variables are approximated with polynomials based on state variables and time in the entire time interval. Region reduction strategy is used in DE to reduce the width of the search region, which improves the computing efficiency. The results of the case studies demonstrate the feasibility and efficiency of the oroposed methods.
基金Project(51175257)supported by National Natural Science Foundation of ChinaProject(BK20170785)supported by the Natural Science Foundation of Jiangsu Province,China+1 种基金Project(BE2016179)supported by Science and Technology Planning Project of Jiangsu Province,ChinaProject(Kfkt2017-08)supported by Open Research Fund of State Key Laboratory for High Performance Complex Manufacturing,Central South University,China
文摘To obtain flow behavior and workability of 7055 aluminium alloy during hot deformation,hot compression tests at different temperatures and strain rates are conducted.True stress?strain curves of 7055 aluminium alloy under different conditions are obtained and the flow stress increases with ascending strain rate and descending temperature.For Arrhenius constitutive equation,each material parameter is set as a constant,which will bring forth large error for predicting flow behavior.In this work,material parameters are fitted as a function of temperature or strain rate based on experimental results and a modified constitutive equation is established for more accurate prediction of flow behavior of 7055 aluminium alloy.The effects of temperature and strain rate on power dissipation and instability are analyzed to establish a processing map of 7055 aluminium alloy.The dominant deformation mechanism for microstructure evolution at different deformation conditions can be determined and high efficiency of power dissipation may be achieved from power dissipation map.Meanwhile,proper processing parameters to avoid flow instability can be easily acquired in instability map.According to the processing map,optimized processing parameters of 7055 aluminium alloy are temperature of 673?723 K and strain rate of 0.01?0.4 s^?1,during which its efficiency of power dissipation is over 30%.Finite element method(FEM)is used to obtain optimized parameter in hot rolling process on the basis of processing map.
基金Project(61171133) supported by the National Natural Science Foundation of ChinaProject(11JJ1010) supported by the Natural Science Fund for Distinguished Young Scholars of Hunan Province,China
文摘The joint optimization of detection threshold and waveform parameters for target tracking which comes from the idea of cognitive radar is investigated for the modified probabilistic data association(MPDA)filter.The transmitted waveforms and detection threshold are adaptively selected to enhance the tracking performance.The modified Riccati equation is adopted to predict the error covariance which is used as the criterion function,while the optimization problem is solved through the genetic algorithm(GA).The detection probability,false alarm probability and measurement noise covariance are all considered together,which significantly improves the tracking performance of the joint detection and tracking system.Simulation results show that the proposed adaptive waveform-detection threshold joint optimization method outperforms the adaptive threshold method and the fixed parameters method,which will reduce the tracking error.The average reduction of range error between the adaptive joint method and the fixed parameters method is about 0.6 m,while that between the adaptive joint method and the adaptive threshold only method is about 0.3 m.Similar error reduction occurs for the velocity error and acceleration error.
基金funded by the National Natural Science Foundation of China[General Project,grant number 41275108]the Strategic Priority Research Program of the Chinese Academy of Sciences[grant number XDA11010404]
文摘Enhancing the ability of the WRF model in simulating a large area covering the West Pacific Ocean, China's Mainland, and the East Indian Ocean is very important to improve prediction of the East Asian monsoon climate. The objective of this study is to identify a reasonable configuration of physical parameterization schemes to simulate the precipitation and temperature in this large area. The Mellor-Yamada-Janjic （MYJ） and Yonsei University （YSU） PBL schemes, the WSM3 and WSM5 microphysics schemes, and the Betts-Miller-Janjic （BMJ） and Tiedtke cumulus schemes are compared through simulation of the regional climate of summer 2008. All cases exhibit a similar spatial distribution of temperature as observed, and the spatial correlation coefficients are all higher than 0.95. The cases combining MY J, WSM3/WSM5, and BMJ have the smallest biases of temperature. The choice of PBL scheme has a significant effect on precipitation in such a large area. The cases with MYJ reproduce a better distribution of rain belts, while YSU strongly overestimates the precipitation intensity. The precipitation simulated using WSM3 is similar to that using WSM5. The BMJ cumulus scheme combined with the MYJ PBL scheme has a smaller bias of precipitation. However, the Tiedtke scheme reproduces the precipitation pattern better, especially over the ITCZ.
