We analysed the photooxidation reaction in the electro-(1O2) and nucleophilic (O2•−) reaction of 2-pyridone azo derivatives. First, we calculated the energy (enthalpies) of tautomers formation, which is a measure of d...We analysed the photooxidation reaction in the electro-(1O2) and nucleophilic (O2•−) reaction of 2-pyridone azo derivatives. First, we calculated the energy (enthalpies) of tautomers formation, which is a measure of durability and the probability of their formation. We performed the light fastness calculations of the monoazopyridone dyes. Using the semi-empirical methods of quantum chemistry AM1 and PM3, the reactivity indicators of superdelocalisability (SrE(N)) and the electron density distribution in ground state on the highest occupied HOMO orbital and the lowest unoccupied excited state LUMO in 2-pyridone phenylazo derivatives were calculated. Superdelocalisability coefficients enable the stability to oxidising agents of various chemical molecules depending on the tautomeric forms in which they may occur. The results of the electron density calculations at the HOMO and LUMO boundary orbitals allow to determine the tendency to electrophilic attack with singlet oxygen 1O2 or nucleophilic attack of the superoxide anion O2•−on a specific atom in the molecule. The structure of the dyes was optimised with MM+, MD and AM1 or PM3 until a constant energy value was achieved with a convergence criterion of 0.01 kcal/mol.展开更多
The N-1 criterion is a critical factor for ensuring the reliable and resilient operation of electric power distribution networks.However,the increasing complexity of distribution networks and the associated growth in ...The N-1 criterion is a critical factor for ensuring the reliable and resilient operation of electric power distribution networks.However,the increasing complexity of distribution networks and the associated growth in data size have created a significant challenge for distribution network planners.To address this issue,we propose a fast N-1 verification procedure for urban distribution networks that combines CIM file data analysis with MILP-based mathematical modeling.Our proposed method leverages the principles of CIM file analysis for distribution network N-1 analysis.We develop a mathematical model of distribution networks based on CIM data and transfer it into MILP.We also take into account the characteristics of medium voltage distribution networks after a line failure and select the feeder section at the exit of each substation with a high load rate to improve the efficiency of N-1 analysis.We validate our approach through a series of case studies and demonstrate its scalability and superiority over traditional N-1 analysis and heuristic optimization algorithms.By enabling online N-1 analysis,our approach significantly improves the work efficiency of distribution network planners.In summary,our proposed method provides a valuable tool for distribution network planners to enhance the accuracy and efficiency of their N-1 analyses.By leveraging the advantages of CIM file data analysis and MILP-based mathematical modeling,our approach contributes to the development of more resilient and reliable electric power distribution networks.展开更多
This paper aims to numerically study the generalized time-fractional Burgers equation in two spatial dimensions using the L1/LDG method. Here the L1 scheme is used to approximate the time-fractional derivative, i.e., ...This paper aims to numerically study the generalized time-fractional Burgers equation in two spatial dimensions using the L1/LDG method. Here the L1 scheme is used to approximate the time-fractional derivative, i.e., Caputo derivative, while the local discontinuous Galerkin (LDG) method is used to discretize the spatial derivative. If the solution has strong temporal regularity, i.e., its second derivative with respect to time being right continuous, then the L1 scheme on uniform meshes (uniform L1 scheme) is utilized. If the solution has weak temporal regularity, i.e., its first and/or second derivatives with respect to time blowing up at the starting time albeit the function itself being right continuous at the beginning time, then the L1 scheme on non-uniform meshes (non-uniform L1 scheme) is applied. Then both uniform L1/LDG and non-uniform L1/LDG schemes are constructed. They are both numerically stable and the \(L^2\) optimal error estimate for the velocity is obtained. Numerical examples support the theoretical analysis.展开更多
文摘We analysed the photooxidation reaction in the electro-(1O2) and nucleophilic (O2•−) reaction of 2-pyridone azo derivatives. First, we calculated the energy (enthalpies) of tautomers formation, which is a measure of durability and the probability of their formation. We performed the light fastness calculations of the monoazopyridone dyes. Using the semi-empirical methods of quantum chemistry AM1 and PM3, the reactivity indicators of superdelocalisability (SrE(N)) and the electron density distribution in ground state on the highest occupied HOMO orbital and the lowest unoccupied excited state LUMO in 2-pyridone phenylazo derivatives were calculated. Superdelocalisability coefficients enable the stability to oxidising agents of various chemical molecules depending on the tautomeric forms in which they may occur. The results of the electron density calculations at the HOMO and LUMO boundary orbitals allow to determine the tendency to electrophilic attack with singlet oxygen 1O2 or nucleophilic attack of the superoxide anion O2•−on a specific atom in the molecule. The structure of the dyes was optimised with MM+, MD and AM1 or PM3 until a constant energy value was achieved with a convergence criterion of 0.01 kcal/mol.
基金supported by the National Natural Science Foundation of China(52207105)。
文摘The N-1 criterion is a critical factor for ensuring the reliable and resilient operation of electric power distribution networks.However,the increasing complexity of distribution networks and the associated growth in data size have created a significant challenge for distribution network planners.To address this issue,we propose a fast N-1 verification procedure for urban distribution networks that combines CIM file data analysis with MILP-based mathematical modeling.Our proposed method leverages the principles of CIM file analysis for distribution network N-1 analysis.We develop a mathematical model of distribution networks based on CIM data and transfer it into MILP.We also take into account the characteristics of medium voltage distribution networks after a line failure and select the feeder section at the exit of each substation with a high load rate to improve the efficiency of N-1 analysis.We validate our approach through a series of case studies and demonstrate its scalability and superiority over traditional N-1 analysis and heuristic optimization algorithms.By enabling online N-1 analysis,our approach significantly improves the work efficiency of distribution network planners.In summary,our proposed method provides a valuable tool for distribution network planners to enhance the accuracy and efficiency of their N-1 analyses.By leveraging the advantages of CIM file data analysis and MILP-based mathematical modeling,our approach contributes to the development of more resilient and reliable electric power distribution networks.
基金the National Natural Science Foundation of China(Nos.11671251 and 12101266).
文摘This paper aims to numerically study the generalized time-fractional Burgers equation in two spatial dimensions using the L1/LDG method. Here the L1 scheme is used to approximate the time-fractional derivative, i.e., Caputo derivative, while the local discontinuous Galerkin (LDG) method is used to discretize the spatial derivative. If the solution has strong temporal regularity, i.e., its second derivative with respect to time being right continuous, then the L1 scheme on uniform meshes (uniform L1 scheme) is utilized. If the solution has weak temporal regularity, i.e., its first and/or second derivatives with respect to time blowing up at the starting time albeit the function itself being right continuous at the beginning time, then the L1 scheme on non-uniform meshes (non-uniform L1 scheme) is applied. Then both uniform L1/LDG and non-uniform L1/LDG schemes are constructed. They are both numerically stable and the \(L^2\) optimal error estimate for the velocity is obtained. Numerical examples support the theoretical analysis.
