A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formu...A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.展开更多
Nuclear decay is investigated by the view of network science and the relationship of nuclear decay among different radionuclide can be mapped to a network topology directly.The network includes 1410 nodes and 1275 edg...Nuclear decay is investigated by the view of network science and the relationship of nuclear decay among different radionuclide can be mapped to a network topology directly.The network includes 1410 nodes and 1275 edges.The average degree of the network of nuclear decay is about 1.8,the cumulative degree distribution still meets the typical power-law distribution,and the corresponding exponent is about 4.1.Not considering their dynamic behavior,the fitting parameters of the nuclear decay network are obtained according to the LUHNM theory proposed by our group before.Their cumulated degree distributions of the nuclear decay network match well.The idea and method may provide a new way to study some other problems of nuclear physics.展开更多
文摘A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.
基金Supported by National Natural Science Foundation of China under Grant Nos. 60874087 and 61174151
文摘Nuclear decay is investigated by the view of network science and the relationship of nuclear decay among different radionuclide can be mapped to a network topology directly.The network includes 1410 nodes and 1275 edges.The average degree of the network of nuclear decay is about 1.8,the cumulative degree distribution still meets the typical power-law distribution,and the corresponding exponent is about 4.1.Not considering their dynamic behavior,the fitting parameters of the nuclear decay network are obtained according to the LUHNM theory proposed by our group before.Their cumulated degree distributions of the nuclear decay network match well.The idea and method may provide a new way to study some other problems of nuclear physics.