We use the directional slacks-based measure of efficiency and inverse distance weighting method to analyze the spatial pattern evolution of the industrial green total factor productivity of 108 cities in the Yangtze R...We use the directional slacks-based measure of efficiency and inverse distance weighting method to analyze the spatial pattern evolution of the industrial green total factor productivity of 108 cities in the Yangtze River Economic Belt in 2003–2013.Results show that both the subprime mortgage crisis and ‘the new normal' had significant negative effects on productivity growth,leading to the different spatial patterns between 2003–2008 and 2009–2013.Before 2008,green poles had gathered around some capital cities and formed a tripartite pattern,which was a typical core-periphery pattern.Due to a combination of the polarization and the diffusion effects,capital cities became the growth poles and ‘core' regions,while surrounding areas became the ‘periphery'.This was mainly caused by the innate advantage of capital cities and ‘the rise of central China' strategy.After 2008,the tripartite pattern changed to a multi-poles pattern where green poles continuously and densely spread in the midstream and downstream areas.This is due to the regional difference in the leading effect of green poles.The leading effect of green poles in midstream and downstream areas has changed from polarization to diffusion,while the polarization effect still leads in the upstream area.展开更多
The fast and accurate design of terahertz devices for specific applications remains challenging,especially for tailoring metadevices,owing to the complex electromagnetic characteristics of these devices and their larg...The fast and accurate design of terahertz devices for specific applications remains challenging,especially for tailoring metadevices,owing to the complex electromagnetic characteristics of these devices and their large structural parameter space.The unique functionalities achieved by metadevices come at the cost of structural complexity,resulting in a time-consuming parameter sweep for conventional metadevice design.Here,we propose a general solution to achieve efficient inverse design for a terahertz metagrating via machine learning.Metagratings with different structural parameters were selected as illustrations to verify the effectiveness of this method.As proof-of-principle examples,the metagratings predicted via the inverse design model are numerically calculated and experimentally demonstrated.Initially,the physical modeling of a metagrating is performed via the finite element method(FEM).A spectrum dataset obtained from FEM simulation is prepared for the training of machine learning models.Then,trained machine learning models,including the Elman neural network(Elman),support vector machine(SVM),and general regression neutral network(GRNN),are used to predict probable structural parameters.The results of these models are compared and analyzed comprehensively,which verifies the effectiveness of the inverse design method.Compared with conventional methods,the inverse design method is much faster and can encompass a high degree of freedom to generate metadevice structures,which can ensure that the spectra of generated structures resemble the desired ones and can provide accurate data support for metadevice modeling.Furthermore,a metagrating tailored by an inverse design is used as a biological sensor to distinguish different microorganisms.The proposed data-driven inverse design method realizes fast and accurate design of the metagrating,which is expected to have great potential in metadevice design and tailoring for specific applications.展开更多
Block matrices associated with discrete Trigonometric transforms （DTT＇s） arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators ...Block matrices associated with discrete Trigonometric transforms （DTT＇s） arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators with the Method of Moments, the Boundary Element Method, and the Method of Auxiliary Sources. The DTT＇s are represented by the Fourier, Hartley, Cosine, and Sine matrices, which are unitary and offer simultaneous diagonalizations of specific matrix algebras. The main tool for the investigation of the aforementioned wave applications is the efficient inversion of such types of block matrices. To this direction, in this paper we develop an efficient algorithm for the inversion of matrices with U-diagonalizable blocks （U a fixed unitary matrix） by utilizing the U- diagonalization of each block and subsequently a similarity transformation procedure. We determine the developed method＇s computational complexity and point out its high efficiency compared to standard inversion techniques. An implementation of the algorithm in Matlab is given. Several numerical results are presented demonstrating the CPU-time efficiency and accuracy for ill-conditioned matrices of the method. The investigated matrices stem from real-world wave propagation applications.展开更多
基金Under the auspices of the post-funded project of National Social Science Foundation of China(No.16FJL009)
文摘We use the directional slacks-based measure of efficiency and inverse distance weighting method to analyze the spatial pattern evolution of the industrial green total factor productivity of 108 cities in the Yangtze River Economic Belt in 2003–2013.Results show that both the subprime mortgage crisis and ‘the new normal' had significant negative effects on productivity growth,leading to the different spatial patterns between 2003–2008 and 2009–2013.Before 2008,green poles had gathered around some capital cities and formed a tripartite pattern,which was a typical core-periphery pattern.Due to a combination of the polarization and the diffusion effects,capital cities became the growth poles and ‘core' regions,while surrounding areas became the ‘periphery'.This was mainly caused by the innate advantage of capital cities and ‘the rise of central China' strategy.After 2008,the tripartite pattern changed to a multi-poles pattern where green poles continuously and densely spread in the midstream and downstream areas.This is due to the regional difference in the leading effect of green poles.The leading effect of green poles in midstream and downstream areas has changed from polarization to diffusion,while the polarization effect still leads in the upstream area.
基金National Natural Science Foundation of China(82272428,61905177)Foundation of National Key Laboratory of Shock Wave and Detonation Physics(JCKYS2022212001)+2 种基金Natural Science Foundation of Tianjin Municipality(23JCYBJC00300)Key Research and Development Program of Tianjin City(23YFZCSN00090)Natural Science Foundation of Chongqing Municipality(CSTB2024NSCQ-MSX0057)。
文摘The fast and accurate design of terahertz devices for specific applications remains challenging,especially for tailoring metadevices,owing to the complex electromagnetic characteristics of these devices and their large structural parameter space.The unique functionalities achieved by metadevices come at the cost of structural complexity,resulting in a time-consuming parameter sweep for conventional metadevice design.Here,we propose a general solution to achieve efficient inverse design for a terahertz metagrating via machine learning.Metagratings with different structural parameters were selected as illustrations to verify the effectiveness of this method.As proof-of-principle examples,the metagratings predicted via the inverse design model are numerically calculated and experimentally demonstrated.Initially,the physical modeling of a metagrating is performed via the finite element method(FEM).A spectrum dataset obtained from FEM simulation is prepared for the training of machine learning models.Then,trained machine learning models,including the Elman neural network(Elman),support vector machine(SVM),and general regression neutral network(GRNN),are used to predict probable structural parameters.The results of these models are compared and analyzed comprehensively,which verifies the effectiveness of the inverse design method.Compared with conventional methods,the inverse design method is much faster and can encompass a high degree of freedom to generate metadevice structures,which can ensure that the spectra of generated structures resemble the desired ones and can provide accurate data support for metadevice modeling.Furthermore,a metagrating tailored by an inverse design is used as a biological sensor to distinguish different microorganisms.The proposed data-driven inverse design method realizes fast and accurate design of the metagrating,which is expected to have great potential in metadevice design and tailoring for specific applications.
文摘Block matrices associated with discrete Trigonometric transforms （DTT＇s） arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators with the Method of Moments, the Boundary Element Method, and the Method of Auxiliary Sources. The DTT＇s are represented by the Fourier, Hartley, Cosine, and Sine matrices, which are unitary and offer simultaneous diagonalizations of specific matrix algebras. The main tool for the investigation of the aforementioned wave applications is the efficient inversion of such types of block matrices. To this direction, in this paper we develop an efficient algorithm for the inversion of matrices with U-diagonalizable blocks （U a fixed unitary matrix） by utilizing the U- diagonalization of each block and subsequently a similarity transformation procedure. We determine the developed method＇s computational complexity and point out its high efficiency compared to standard inversion techniques. An implementation of the algorithm in Matlab is given. Several numerical results are presented demonstrating the CPU-time efficiency and accuracy for ill-conditioned matrices of the method. The investigated matrices stem from real-world wave propagation applications.
