This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation.Their Hamiltonian formulations are furnished by the trace identity,which ...This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation.Their Hamiltonian formulations are furnished by the trace identity,which guarantee the commuting property of infinitely many symmetries and conserved Hamiltonian functionals.Illustrative examples of the resulting integrable equations of second and third orders are explicitly computed.展开更多
Porous organic molecular materials(POMMs)are an emergent class of molecular-based materials characterized by the formation of extended porous frameworks,mainly held by non-covalent interactions.POMMs represent a varie...Porous organic molecular materials(POMMs)are an emergent class of molecular-based materials characterized by the formation of extended porous frameworks,mainly held by non-covalent interactions.POMMs represent a variety of chemical families,such as hydrogen-bonded organic frameworks,porous organic salts,porous organic cages,C-H···πmicroporous crystals,supramolecular organic frameworks,π-organic frameworks,halogen-bonded organic framework,and intrinsically porous molecular materials.In some porous materials such as zeolites and metal organic frameworks,the integration of multiscale has been adopted to build materials with multifunctionality and optimized properties.Therefore,considering the significant role of hierarchy in porous materials and the growing importance of POMMs in the realm of synthetic porous materials,we consider it appropriate to dedicate for the first time a critical review covering both topics.Herein,we will provide a summary of literature examples showcasing hierarchical POMMs,with a focus on their main synthetic approaches,applications,and the advantages brought forth by introducing hierarchy.展开更多
For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functio...For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.展开更多
This paper builds a binary tree for the target based on the bounding volume hierarchy technology,thereby achieving strict acceleration of the shadow judgment process and reducing the computational complexity from the ...This paper builds a binary tree for the target based on the bounding volume hierarchy technology,thereby achieving strict acceleration of the shadow judgment process and reducing the computational complexity from the original O(N^(3))to O(N^(2)logN).Numerical results show that the proposed method is more efficient than the traditional method.It is verified in multiple examples that the proposed method can complete the convergence of the current.Moreover,the proposed method avoids the error of judging the lit-shadow relationship based on the normal vector,which is beneficial to current iteration and convergence.Compared with the brute force method,the current method can improve the simulation efficiency by 2 orders of magnitude.The proposed method is more suitable for scattering problems in electrically large cavities and complex scenarios.展开更多
基金supported in part by the NSFC(12271488,11975145,11972291)the Ministry of Science and Technology of China(G2021016032L,G2023016011L)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17 KJB 110020)。
文摘This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation.Their Hamiltonian formulations are furnished by the trace identity,which guarantee the commuting property of infinitely many symmetries and conserved Hamiltonian functionals.Illustrative examples of the resulting integrable equations of second and third orders are explicitly computed.
基金the MICINN (Spain)(Projects PID2019-104778GB-I00, PID2020-115100GB-I00Excellence Unit “Maria de Maeztu” CEX2019-000919-M)+5 种基金the Royal Society of Chemistryfunded by Generalitat Valenciana(PROMETEU/2021/054 and SEJI/2020/034)the “Ramón y Cajal” program (RYC2019-027940-I)the Royal Society (RGSR1221390)Royal Society of Chemistry (R21-5119312833) for the funding.
文摘Porous organic molecular materials(POMMs)are an emergent class of molecular-based materials characterized by the formation of extended porous frameworks,mainly held by non-covalent interactions.POMMs represent a variety of chemical families,such as hydrogen-bonded organic frameworks,porous organic salts,porous organic cages,C-H···πmicroporous crystals,supramolecular organic frameworks,π-organic frameworks,halogen-bonded organic framework,and intrinsically porous molecular materials.In some porous materials such as zeolites and metal organic frameworks,the integration of multiscale has been adopted to build materials with multifunctionality and optimized properties.Therefore,considering the significant role of hierarchy in porous materials and the growing importance of POMMs in the realm of synthetic porous materials,we consider it appropriate to dedicate for the first time a critical review covering both topics.Herein,we will provide a summary of literature examples showcasing hierarchical POMMs,with a focus on their main synthetic approaches,applications,and the advantages brought forth by introducing hierarchy.
基金supported by the National Key R and D Program of China(2020YFA0713100).
文摘For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.
基金the National Natural Science Foundation of China under Grants No.62231021 and No.92373201.
文摘This paper builds a binary tree for the target based on the bounding volume hierarchy technology,thereby achieving strict acceleration of the shadow judgment process and reducing the computational complexity from the original O(N^(3))to O(N^(2)logN).Numerical results show that the proposed method is more efficient than the traditional method.It is verified in multiple examples that the proposed method can complete the convergence of the current.Moreover,the proposed method avoids the error of judging the lit-shadow relationship based on the normal vector,which is beneficial to current iteration and convergence.Compared with the brute force method,the current method can improve the simulation efficiency by 2 orders of magnitude.The proposed method is more suitable for scattering problems in electrically large cavities and complex scenarios.
