本文针对多重线性PageRank问题,结合松弛技术,提出了一般形式的张量分裂迭代算法,并给出了相应的收敛性分析。进一步,结合Anderson加速技术,提出了新的张量分裂算法。In this paper, combining relaxation techniques, a general form o...本文针对多重线性PageRank问题,结合松弛技术,提出了一般形式的张量分裂迭代算法,并给出了相应的收敛性分析。进一步,结合Anderson加速技术,提出了新的张量分裂算法。In this paper, combining relaxation techniques, a general form of tensor splitting iterative algorithm is proposed for the multilinear PageRank problem, and the corresponding convergence analysis is given. Furthermore, a new tensor splitting algorithm is proposed by incorporating Anderson acceleration techniques.展开更多
The aim of this study is to create a fast and stable iterative technique for numerical solution of a quasi-linear elliptic pressure equation. We developed a modified version of the Anderson acceleration(AA)algorithm t...The aim of this study is to create a fast and stable iterative technique for numerical solution of a quasi-linear elliptic pressure equation. We developed a modified version of the Anderson acceleration(AA)algorithm to fixed-point(FP) iteration method. It computes the approximation to the solutions at each iteration based on the history of vectors in extended space, which includes the vector of unknowns, the discrete form of the operator, and the equation's right-hand side. Several constraints are applied to AA algorithm, including a limitation of the time step variation during the iteration process, which allows switching to the base FP iterations to maintain convergence. Compared to the base FP algorithm, the improved version of the AA algorithm enables a reliable and rapid convergence of the iterative solution for the quasi-linear elliptic pressure equation describing the flow of particle-laden yield-stress fluids in a narrow channel during hydraulic fracturing, a key technology for stimulating hydrocarbon-bearing reservoirs. In particular, the proposed AA algorithm allows for faster computations and resolution of unyielding zones in hydraulic fractures that cannot be calculated using the FP algorithm. The quasi-linear elliptic pressure equation under consideration describes various physical processes, such as the displacement of fluids with viscoplastic rheology in a narrow cylindrical annulus during well cementing,the displacement of cross-linked gel in a proppant pack filling hydraulic fractures during the early stage of well production(fracture flowback), and multiphase filtration in a rock formation. We estimate computational complexity of the developed algorithm as compared to Jacobian-based algorithms and show that the performance of the former one is higher in modelling of flows of viscoplastic fluids. We believe that the developed algorithm is a useful numerical tool that can be implemented in commercial simulators to obtain fast and converged solutions to the non-linear problems described above.展开更多
Localization due to disorder has been one of the most intriguing theoretical concepts that evolved in condensed matter physics.Here,we expand the theory of localization by considering two types of disorders at the sam...Localization due to disorder has been one of the most intriguing theoretical concepts that evolved in condensed matter physics.Here,we expand the theory of localization by considering two types of disorders at the same time,namely,the original Anderson’s disorder and the structural defect disorder,which has been suggested to be a key component in recently discovered two-dimensional amorphous materials.While increasing the degree of both disorders could induce localization of wavefunction in real space,we find that a small degree of structural defect disorder can significantly enhance the localization.As the degree of structural defect disorder increases,localized states quickly appear within the extended phase to enter a broad crossover region with mixed phases.We establish two-dimensional diagrams for the wavefunction localization and conductivity to highlight the interplay between the two types of disorders.Our theoretical model provides a comprehensive understanding of localization in two-dimensional amorphous materials and highlights the promising tunability of their transport properties.展开更多
Using symmetrical rigid organic ligand 4,4'-dipyridy(4,4'-bipy),two new Anderson-based supramolecular compounds,namely,[H_(2)(4,4'-bipy)]_(3)·(TeMo_(6)O_(24))·(H_(2)Mo_(6)O_(19))(1)and{Cu_(2)[H(4...Using symmetrical rigid organic ligand 4,4'-dipyridy(4,4'-bipy),two new Anderson-based supramolecular compounds,namely,[H_(2)(4,4'-bipy)]_(3)·(TeMo_(6)O_(24))·(H_(2)Mo_(6)O_(19))(1)and{Cu_(2)[H(4,4'-bipy)]_(2)(H_(2)O)_(6)(TeMo_(6)O_(24))}·4H_(2)O(2),were synthesized in one-pot under hydrothermal conditions.The compounds 1 and 2 have been tested by IR spectra,elemental analyses and single-crystal X-ray diffraction.Compound 1 contains one discrete Anderson anion,one Lindqvist anion and three 4,4'-bipy organic ligands.The anions and 4,4'-bipy alternate with each other by hydrogen bonding,building a supramolecular 1D chain.Adjacent 1D chains are interlinked through hydrogen bonding interactions to further connect a supramolecular 2D layer.Compounds containing both Anderson and Lindqvist polyanions are not common in the crystal structure of POMs.Compound 2 contains one Anderson anion and two metal-organic subunits{Cu_(2)[H(4,4'-bipy)]_(2)(H_(2)O)_(6)}^(6+)as modifiers.The Anderson anions and{Cu_(2)[H(4,4'-bipy)]_(2)(H_(2)O)_(6)}^(6+)subunits are organized into alternating through hydrogen bonding interactions to construct a supramolecular 1D chain.Additionally,the electrochemical properties of compounds 1 and 2 as well as photocatalytic properties are investigated.Results show that compounds 1 and 2 have photocatalytic activity,which can photocatalyze the degradation of organic dyes MB and AF.Also,compounds 1 and 2 have good electrochemical properties for amperometric detection of NO2-and Cr(Ⅵ).Furthermore,Compound 2 can be used as materials of supercapacitor.展开更多
Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AE...Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AEGD)[arXiv:2010.05109].The feasibility of our algorithm is ensured in light of the convergence theory for AEGD,though it is not a fixed-point iteration.We provide rigorous convergence rates of AA for gradient descent(GD)by an acceleration factor of the gain at each implementation of AA-GD.Our experimental results show that the proposed AA-AEGD algorithm requires little tuning of hyperparameters and exhibits superior fast convergence.展开更多
A new kind of Anderson type chromium molybdates containing the rare earth elements are synthesized, which have the general molecular formula of (NH4)6[CrMo5Ln(OH2)2O24H6]·xH2O (Ln=La,Ce,Pr,Nd,Sm,Gd and Yb). The c...A new kind of Anderson type chromium molybdates containing the rare earth elements are synthesized, which have the general molecular formula of (NH4)6[CrMo5Ln(OH2)2O24H6]·xH2O (Ln=La,Ce,Pr,Nd,Sm,Gd and Yb). The components of theseheteropoly complexes are determined by chemical elemental analysis, ICP and TG DTA. And IR, UV, ESR,XPS and 1H NMR are also applied to characterize the complexes as well. The results indicate that the structures of these complexes are Anderson B type and the rare earth elements are in the inner sphere of the heteropoly salts. The thermal stabilities of these complexes studied by TG DTA show that the range of pyrolysis temperature is between 490℃and 500℃.展开更多
文摘本文针对多重线性PageRank问题,结合松弛技术,提出了一般形式的张量分裂迭代算法,并给出了相应的收敛性分析。进一步,结合Anderson加速技术,提出了新的张量分裂算法。In this paper, combining relaxation techniques, a general form of tensor splitting iterative algorithm is proposed for the multilinear PageRank problem, and the corresponding convergence analysis is given. Furthermore, a new tensor splitting algorithm is proposed by incorporating Anderson acceleration techniques.
基金partial financial support from Gazpromneft Science and Technology Center。
文摘The aim of this study is to create a fast and stable iterative technique for numerical solution of a quasi-linear elliptic pressure equation. We developed a modified version of the Anderson acceleration(AA)algorithm to fixed-point(FP) iteration method. It computes the approximation to the solutions at each iteration based on the history of vectors in extended space, which includes the vector of unknowns, the discrete form of the operator, and the equation's right-hand side. Several constraints are applied to AA algorithm, including a limitation of the time step variation during the iteration process, which allows switching to the base FP iterations to maintain convergence. Compared to the base FP algorithm, the improved version of the AA algorithm enables a reliable and rapid convergence of the iterative solution for the quasi-linear elliptic pressure equation describing the flow of particle-laden yield-stress fluids in a narrow channel during hydraulic fracturing, a key technology for stimulating hydrocarbon-bearing reservoirs. In particular, the proposed AA algorithm allows for faster computations and resolution of unyielding zones in hydraulic fractures that cannot be calculated using the FP algorithm. The quasi-linear elliptic pressure equation under consideration describes various physical processes, such as the displacement of fluids with viscoplastic rheology in a narrow cylindrical annulus during well cementing,the displacement of cross-linked gel in a proppant pack filling hydraulic fractures during the early stage of well production(fracture flowback), and multiphase filtration in a rock formation. We estimate computational complexity of the developed algorithm as compared to Jacobian-based algorithms and show that the performance of the former one is higher in modelling of flows of viscoplastic fluids. We believe that the developed algorithm is a useful numerical tool that can be implemented in commercial simulators to obtain fast and converged solutions to the non-linear problems described above.
基金supported by the National Natural Science Foundation of China(Grant No.92165101)the National Key R&D Program of China(Grant No.2021YFA1400500)+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB33000000)the Beijing Natural Science Foundation(Grant No.JQ22001).We are grateful for computational resources supported by High-performance Computing Platform of Peking University.
文摘Localization due to disorder has been one of the most intriguing theoretical concepts that evolved in condensed matter physics.Here,we expand the theory of localization by considering two types of disorders at the same time,namely,the original Anderson’s disorder and the structural defect disorder,which has been suggested to be a key component in recently discovered two-dimensional amorphous materials.While increasing the degree of both disorders could induce localization of wavefunction in real space,we find that a small degree of structural defect disorder can significantly enhance the localization.As the degree of structural defect disorder increases,localized states quickly appear within the extended phase to enter a broad crossover region with mixed phases.We establish two-dimensional diagrams for the wavefunction localization and conductivity to highlight the interplay between the two types of disorders.Our theoretical model provides a comprehensive understanding of localization in two-dimensional amorphous materials and highlights the promising tunability of their transport properties.
基金supported by the National Natural Science Foundation of China(21571023)
文摘Using symmetrical rigid organic ligand 4,4'-dipyridy(4,4'-bipy),two new Anderson-based supramolecular compounds,namely,[H_(2)(4,4'-bipy)]_(3)·(TeMo_(6)O_(24))·(H_(2)Mo_(6)O_(19))(1)and{Cu_(2)[H(4,4'-bipy)]_(2)(H_(2)O)_(6)(TeMo_(6)O_(24))}·4H_(2)O(2),were synthesized in one-pot under hydrothermal conditions.The compounds 1 and 2 have been tested by IR spectra,elemental analyses and single-crystal X-ray diffraction.Compound 1 contains one discrete Anderson anion,one Lindqvist anion and three 4,4'-bipy organic ligands.The anions and 4,4'-bipy alternate with each other by hydrogen bonding,building a supramolecular 1D chain.Adjacent 1D chains are interlinked through hydrogen bonding interactions to further connect a supramolecular 2D layer.Compounds containing both Anderson and Lindqvist polyanions are not common in the crystal structure of POMs.Compound 2 contains one Anderson anion and two metal-organic subunits{Cu_(2)[H(4,4'-bipy)]_(2)(H_(2)O)_(6)}^(6+)as modifiers.The Anderson anions and{Cu_(2)[H(4,4'-bipy)]_(2)(H_(2)O)_(6)}^(6+)subunits are organized into alternating through hydrogen bonding interactions to construct a supramolecular 1D chain.Additionally,the electrochemical properties of compounds 1 and 2 as well as photocatalytic properties are investigated.Results show that compounds 1 and 2 have photocatalytic activity,which can photocatalyze the degradation of organic dyes MB and AF.Also,compounds 1 and 2 have good electrochemical properties for amperometric detection of NO2-and Cr(Ⅵ).Furthermore,Compound 2 can be used as materials of supercapacitor.
基金partially supported by the National Science Foundation under(Grant DMS No.1812666)。
文摘Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AEGD)[arXiv:2010.05109].The feasibility of our algorithm is ensured in light of the convergence theory for AEGD,though it is not a fixed-point iteration.We provide rigorous convergence rates of AA for gradient descent(GD)by an acceleration factor of the gain at each implementation of AA-GD.Our experimental results show that the proposed AA-AEGD algorithm requires little tuning of hyperparameters and exhibits superior fast convergence.
文摘A new kind of Anderson type chromium molybdates containing the rare earth elements are synthesized, which have the general molecular formula of (NH4)6[CrMo5Ln(OH2)2O24H6]·xH2O (Ln=La,Ce,Pr,Nd,Sm,Gd and Yb). The components of theseheteropoly complexes are determined by chemical elemental analysis, ICP and TG DTA. And IR, UV, ESR,XPS and 1H NMR are also applied to characterize the complexes as well. The results indicate that the structures of these complexes are Anderson B type and the rare earth elements are in the inner sphere of the heteropoly salts. The thermal stabilities of these complexes studied by TG DTA show that the range of pyrolysis temperature is between 490℃and 500℃.
