Aiming at increasing the calculation efficiency of the pseudospectral methods, a multiple- interval Radau pseudospectral method (RPM) is presented to generate a reusable launch vehicle (RLV) 's optimal re-entry t...Aiming at increasing the calculation efficiency of the pseudospectral methods, a multiple- interval Radau pseudospectral method (RPM) is presented to generate a reusable launch vehicle (RLV) 's optimal re-entry trajectory. After dividing the optimal control problem into many intervals, the state and control variables are approximated using many fixed- and low-degree Lagrange polyno- mials in each interval. Convergence of the numerical discretization is then achieved by increasing the number of intervals. With the application of the proposed method, the normal nonlinear program- ming (NLP) problem transcribed from the optimal control problem can avoid being dense because of the low-degree approximation polynomials in each interval. Thus, the NLP solver can easily compute a solution. Finally, simulation results show that the optimized re-entry trajectories satisfy the path constraints and the boundary constraints successfully. Compared with the single interval RPM, the multiple-interval RPM is significantly faster and has higher calculation efficiency. The results indicate that the multiple-interval RPM can be applied for real-time trajectory generation due to its high effi- ciency and high precision.展开更多
The shear failure of rocks under both a static triaxial stress and a dynamic disturbance is common in deep underground engineering and it is therefore essential for the design of underground engineering to quantitivel...The shear failure of rocks under both a static triaxial stress and a dynamic disturbance is common in deep underground engineering and it is therefore essential for the design of underground engineering to quantitively estimate the dynamic ModeⅡfracture toughness KⅡCof rocks under a triaxial stress state.However,the method for determining the dynamic KⅡCof rocks under a triaxial stress has not been developed yet.With an optimal sample preparation,the short core in compression(SCC)method was designed and verified in this study to measure the dynamic KⅡCof Fangshan marble(FM)subjected to different hydrostatic pressures through a triaxial dynamic testing system.The formula for calculating the dynamic KⅡCof the rock SCC specimen under hydrostatic pressures was obtained by using the finite element method in combination with secondary cracks.The experimental results indicate that the failure mode of the rock SCC specimen under a hydrostatic pressure is the shear fracture and the KⅡCof FM increases as the loading rate.In addition,at a given loading rate the dynamic rock KⅡCis barely affected by hydrostatic pressures.Another important observation is that the dynamic fracture energy of FM enhances with loading rates and hydrostatic pressures.展开更多
A highly sensitive and selective catalytic kinetic spectrophotometric method for the determination of Cu(Ⅱ) is proposed. It is based on the catalytic effect of Cu(Ⅱ) on the oxidation of glutathione(GSH) by potassium...A highly sensitive and selective catalytic kinetic spectrophotometric method for the determination of Cu(Ⅱ) is proposed. It is based on the catalytic effect of Cu(Ⅱ) on the oxidation of glutathione(GSH) by potassium hexacyanoferrate(Ⅲ) in acidic medium at 25.0℃. The reaction is monitored spectrophotometrically by measuring the decrease in absorbance of oxidant at 420 nm using the fix-time method. Under the optimum conditions, the proposed method allows the determination of Cu(Ⅱ) in a range of 0-35.0 ng m L^(-1) with good precision and accuracy and the limit of detection is down to 0.04 ng m L^(-1). The relative standard deviation(RSD) is 1.02%. The reaction orders with respect to each reagent are found to be 1, 1/2, and 1/2 for potassium hexacyanoferrate(Ⅲ), glutathione and Cu(Ⅱ) respectively. On the basis of these values, the rate equation is obtained and the possible mechanism is established. Moreover, few anions and cations can interfere with the determination of Cu(Ⅱ). The new proposed method can be successfully used to the determination of Cu(Ⅱ) in fresh water samples and seawater samples. It is found that the proposed method has fairly good selectivity, high sensitivity, good repeatability, simplicity and rapidity.展开更多
A novel and facile wet-chemical method for synthesis of silver microwires was developed.The well-defined particles were prepared by adding an iron(Ⅱ) sulfate heptahydrate solution into a silver nitrate solution con...A novel and facile wet-chemical method for synthesis of silver microwires was developed.The well-defined particles were prepared by adding an iron(Ⅱ) sulfate heptahydrate solution into a silver nitrate solution containing citric acid drop by drop at 50 °C.The resulting products were characterized by scanning electron microscopy and X-ray diffraction.It was found that the particles consisted of numerous silver microwires.The reaction temperature greatly affected the morphologies of the as-prepared particles.Both of the mean length and width of the silver microwires increased with the decrease of the concentration of silver nitrate.And the lower concentration was unfavorable for the formation of more silver microwires.Similar findings were also observed when the concentration of iron(Ⅱ) sulfate was decreased.The amount of citric acid also greatly affected the shape of the as-prepared particles.It was concluded that citric acid was the key role in the formation of silver microwires via the Oswald ripening mechanism.展开更多
文摘Aiming at increasing the calculation efficiency of the pseudospectral methods, a multiple- interval Radau pseudospectral method (RPM) is presented to generate a reusable launch vehicle (RLV) 's optimal re-entry trajectory. After dividing the optimal control problem into many intervals, the state and control variables are approximated using many fixed- and low-degree Lagrange polyno- mials in each interval. Convergence of the numerical discretization is then achieved by increasing the number of intervals. With the application of the proposed method, the normal nonlinear program- ming (NLP) problem transcribed from the optimal control problem can avoid being dense because of the low-degree approximation polynomials in each interval. Thus, the NLP solver can easily compute a solution. Finally, simulation results show that the optimized re-entry trajectories satisfy the path constraints and the boundary constraints successfully. Compared with the single interval RPM, the multiple-interval RPM is significantly faster and has higher calculation efficiency. The results indicate that the multiple-interval RPM can be applied for real-time trajectory generation due to its high effi- ciency and high precision.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)(No.72031326)the National Natural Science Foundation of China(No.52079091)+2 种基金supported by Academy of Finland under Grant No.322518supported by the opening project of State Key Laboratory of Explosion Science and Technology(Beijing Institute of Technology)The opening project number is KFJJ20-01M。
文摘The shear failure of rocks under both a static triaxial stress and a dynamic disturbance is common in deep underground engineering and it is therefore essential for the design of underground engineering to quantitively estimate the dynamic ModeⅡfracture toughness KⅡCof rocks under a triaxial stress state.However,the method for determining the dynamic KⅡCof rocks under a triaxial stress has not been developed yet.With an optimal sample preparation,the short core in compression(SCC)method was designed and verified in this study to measure the dynamic KⅡCof Fangshan marble(FM)subjected to different hydrostatic pressures through a triaxial dynamic testing system.The formula for calculating the dynamic KⅡCof the rock SCC specimen under hydrostatic pressures was obtained by using the finite element method in combination with secondary cracks.The experimental results indicate that the failure mode of the rock SCC specimen under a hydrostatic pressure is the shear fracture and the KⅡCof FM increases as the loading rate.In addition,at a given loading rate the dynamic rock KⅡCis barely affected by hydrostatic pressures.Another important observation is that the dynamic fracture energy of FM enhances with loading rates and hydrostatic pressures.
文摘A highly sensitive and selective catalytic kinetic spectrophotometric method for the determination of Cu(Ⅱ) is proposed. It is based on the catalytic effect of Cu(Ⅱ) on the oxidation of glutathione(GSH) by potassium hexacyanoferrate(Ⅲ) in acidic medium at 25.0℃. The reaction is monitored spectrophotometrically by measuring the decrease in absorbance of oxidant at 420 nm using the fix-time method. Under the optimum conditions, the proposed method allows the determination of Cu(Ⅱ) in a range of 0-35.0 ng m L^(-1) with good precision and accuracy and the limit of detection is down to 0.04 ng m L^(-1). The relative standard deviation(RSD) is 1.02%. The reaction orders with respect to each reagent are found to be 1, 1/2, and 1/2 for potassium hexacyanoferrate(Ⅲ), glutathione and Cu(Ⅱ) respectively. On the basis of these values, the rate equation is obtained and the possible mechanism is established. Moreover, few anions and cations can interfere with the determination of Cu(Ⅱ). The new proposed method can be successfully used to the determination of Cu(Ⅱ) in fresh water samples and seawater samples. It is found that the proposed method has fairly good selectivity, high sensitivity, good repeatability, simplicity and rapidity.
基金Project (2011CDC114) supported by the Hubei Provincial Natural Science Foundation of China
文摘A novel and facile wet-chemical method for synthesis of silver microwires was developed.The well-defined particles were prepared by adding an iron(Ⅱ) sulfate heptahydrate solution into a silver nitrate solution containing citric acid drop by drop at 50 °C.The resulting products were characterized by scanning electron microscopy and X-ray diffraction.It was found that the particles consisted of numerous silver microwires.The reaction temperature greatly affected the morphologies of the as-prepared particles.Both of the mean length and width of the silver microwires increased with the decrease of the concentration of silver nitrate.And the lower concentration was unfavorable for the formation of more silver microwires.Similar findings were also observed when the concentration of iron(Ⅱ) sulfate was decreased.The amount of citric acid also greatly affected the shape of the as-prepared particles.It was concluded that citric acid was the key role in the formation of silver microwires via the Oswald ripening mechanism.