This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a gen...This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.展开更多
Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation al...Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.展开更多
The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with...The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling.展开更多
In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the br...In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.展开更多
We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry.Destructive interference generates...We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry.Destructive interference generates a flat spectrum at the exceptional point,where the Creutz ladder maintains coalesced and degenerate eigenvalues with compact localized states distributed in a single plaquette.All excitations are completely confined within the localization area,unaffected by gain and loss.Single-site excitations exhibit nonunitary dynamics with intensities increasing due to level coalescence,while multiple-site excitations may display oscillating or constant intensities at the exceptional point.These results provide insights into the fascinating dynamics of non-Hermitian localization,where level coalescence and degeneracy coexist at the exceptional point.展开更多
We propose an ansatz without adjustable parameters for the calculation of a dynamical structure factor.The ansatz combines the quasi-particle Green’s function,especially the contribution from the renormalization fact...We propose an ansatz without adjustable parameters for the calculation of a dynamical structure factor.The ansatz combines the quasi-particle Green’s function,especially the contribution from the renormalization factor,and the exchange-correlation kernel from time-dependent density functional theory together,verified for typical metals and semiconductors from a plasmon excitation regime to the Compton scattering regime.It has the capability to reconcile both small-angle and large-angle inelastic x-ray scattering(IXS)signals with muchimproved accuracy,which can be used as the theoretical base model,in inversely inferring electronic structures of condensed matter from IXS experimental signals directly.It may also be used to diagnose thermal parameters,such as temperature and density,of dense plasmas in x-ray Thomson scattering experiments.展开更多
基金Project supported by the National Research Foundation of Korea(Nos.NRF-2020R1C1C1011970 and NRF-2018R1A5A7023490)。
文摘This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12235007, 11975131, and 12275144)the K. C. Wong Magna Fund in Ningbo Universitythe Natural Science Foundation of Zhejiang Province of China (Grant No. LQ20A010009)
文摘Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.
文摘The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12274046,11874094,and 12147102)Chongqing Natural Science Foundation(Grant No.CSTB2022NSCQ-JQX0018)Fundamental Research Funds for the Central Universities(Grant No.2021CDJZYJH-003).
文摘In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.
基金supported by the National Natural Science Foundation of China(Grant Nos.12222504 and 11975128).
文摘We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry.Destructive interference generates a flat spectrum at the exceptional point,where the Creutz ladder maintains coalesced and degenerate eigenvalues with compact localized states distributed in a single plaquette.All excitations are completely confined within the localization area,unaffected by gain and loss.Single-site excitations exhibit nonunitary dynamics with intensities increasing due to level coalescence,while multiple-site excitations may display oscillating or constant intensities at the exceptional point.These results provide insights into the fascinating dynamics of non-Hermitian localization,where level coalescence and degeneracy coexist at the exceptional point.
基金supported by the National Natural Science Foundation of China(Grant Nos.12375234,12005012,and U1930402)the Laboratory Youth Fund of Institute of Applied Physics and Computational Mathematics(Grant No.6142A05QN21005)。
文摘We propose an ansatz without adjustable parameters for the calculation of a dynamical structure factor.The ansatz combines the quasi-particle Green’s function,especially the contribution from the renormalization factor,and the exchange-correlation kernel from time-dependent density functional theory together,verified for typical metals and semiconductors from a plasmon excitation regime to the Compton scattering regime.It has the capability to reconcile both small-angle and large-angle inelastic x-ray scattering(IXS)signals with muchimproved accuracy,which can be used as the theoretical base model,in inversely inferring electronic structures of condensed matter from IXS experimental signals directly.It may also be used to diagnose thermal parameters,such as temperature and density,of dense plasmas in x-ray Thomson scattering experiments.
