We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable mo...We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson （G J） hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra E of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell （KN） hierarchy which, consisting of two arbitrary parameters a and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations.展开更多
Increasing complexity of distributed hydrological model （DHM） has lowered the efficiency of convergence.In this study,global sensitivity analysis （SA） was introduced by combining multiobjective （MO） optimization...Increasing complexity of distributed hydrological model （DHM） has lowered the efficiency of convergence.In this study,global sensitivity analysis （SA） was introduced by combining multiobjective （MO） optimization for DHM calibration.Latin Hypercube-once at a time （LH-OAT） was adopted in global parameter SA to obtain relative sensitivity of model parameter,which can be categorized into different sensitivity levels.Two comparative study cases were conducted to present the efficiency and feasibility by combining SA with MO（SA-MO）.WetSpa model with non-dominated sorting genetic algorithm-Ⅱ （NSGA-Ⅱ） algorithm and EasyDHM model with multi-objective sequential complex evolutionary metropolis-uncertainty analysis （MOSCEM-UA）algorithm were adopted to demonstrate the general feasibility of combining SA in optimization.Results showed that the LH-OAT was globally effective in selecting high sensitivity parameters.It proves that using parameter from high sensitivity groups results in higher convergence efficiency.Study case Ⅰ showed a better Pareto front distribution and convergence compared with model calibration without SA.Study case Ⅱ indicated a more efficient convergence of parameters in sequential evolution of MOSCEM-UA under the same iteration.It indicates that SA-MO is feasible and efficient for high dimensional DHM calibration.展开更多
基金Supported by a Research Grant from the CityU Strategic Research under Grant No. 7002564
文摘We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson （G J） hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra E of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell （KN） hierarchy which, consisting of two arbitrary parameters a and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations.
基金National Basic Research Program(973)of China(No.2010CB951102)Innovative Research Groups of the National Natural Science Foundation,China(No.51021006)National Natural Science Foundation of China(No.51079028)
文摘Increasing complexity of distributed hydrological model （DHM） has lowered the efficiency of convergence.In this study,global sensitivity analysis （SA） was introduced by combining multiobjective （MO） optimization for DHM calibration.Latin Hypercube-once at a time （LH-OAT） was adopted in global parameter SA to obtain relative sensitivity of model parameter,which can be categorized into different sensitivity levels.Two comparative study cases were conducted to present the efficiency and feasibility by combining SA with MO（SA-MO）.WetSpa model with non-dominated sorting genetic algorithm-Ⅱ （NSGA-Ⅱ） algorithm and EasyDHM model with multi-objective sequential complex evolutionary metropolis-uncertainty analysis （MOSCEM-UA）algorithm were adopted to demonstrate the general feasibility of combining SA in optimization.Results showed that the LH-OAT was globally effective in selecting high sensitivity parameters.It proves that using parameter from high sensitivity groups results in higher convergence efficiency.Study case Ⅰ showed a better Pareto front distribution and convergence compared with model calibration without SA.Study case Ⅱ indicated a more efficient convergence of parameters in sequential evolution of MOSCEM-UA under the same iteration.It indicates that SA-MO is feasible and efficient for high dimensional DHM calibration.
