To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
Road traffic flow forecasting provides critical information for the operational management of road mobility challenges, and models are used to generate the forecast. This paper uses a random process to present a novel...Road traffic flow forecasting provides critical information for the operational management of road mobility challenges, and models are used to generate the forecast. This paper uses a random process to present a novel traffic modelling framework for aggregate traffic on urban roads. The main idea is that road traffic flow is random, even for the recurrent flow, such as rush hour traffic, which is predisposed to congestion. Therefore, the structure of the aggregate traffic flow model for urban roads should correlate well with the essential variables of the observed random dynamics of the traffic flow phenomena. The novelty of this paper is the developed framework, based on the Poisson process, the kinematics of urban road traffic flow, and the intermediate modelling approach, which were combined to formulate the model. Empirical data from an urban road in Ghana was used to explore the model’s fidelity. The results show that the distribution from the model correlates well with that of the empirical traffic, providing a strong validation of the new framework and instilling confidence in its potential for significantly improved forecasts and, hence, a more hopeful outlook for real-world traffic management.展开更多
To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=b.Variational quantum algorithms(VQAs)for the discretized Poisson equation have been studied before...To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=b.Variational quantum algorithms(VQAs)for the discretized Poisson equation have been studied before.We present a VQA based on the banded Toeplitz systems for solving the Poisson equation with respect to the structural features of matrix A.In detail,we decompose the matrices A and A^(2)into a linear combination of the corresponding banded Toeplitz matrix and sparse matrices with only a few non-zero elements.For the one-dimensional Poisson equation with different boundary conditions and the d-dimensional Poisson equation with Dirichlet boundary conditions,the number of decomposition terms is less than that reported in[Phys.Rev.A 2023108,032418].Based on the decomposition of the matrix,we design quantum circuits that efficiently evaluate the cost function.Additionally,numerical simulation verifies the feasibility of the proposed algorithm.Finally,the VQAs for linear systems of equations and matrix-vector multiplications with the K-banded Toeplitz matrix T_(n)^(K)are given,where T_(n)^(K)∈R^(n×n)and K∈O(ploylogn).展开更多
Earthquakes are caused directly by the motion of the stress field,therefore,observing the stress field is significant.Experiments on the relationships among wave velocity,stress factors,and faults show that the wave v...Earthquakes are caused directly by the motion of the stress field,therefore,observing the stress field is significant.Experiments on the relationships among wave velocity,stress factors,and faults show that the wave velocity of rock media under stable stress fields corresponds one-to-one with stress factors.Therefore,the wave velocity gradient can indicate the direction of stress vector,and the gradient divergence can indicate the strength of the stress field.To verify the results,considering the limitations of wave velocity measurement in solid crustal media,two quantities,namely the apparent wave velocity and Poisson ratios relating to wave velocity,were used to refl ect the stress field state.The seismic data of the Tangshan and Luzhou regions were studied separately.The calculated apparent wave velocity and Poisson ratios were interpolated to achieve regional data gridding.The gradients and the gradient divergences of the apparent wave velocity and Poisson ratio fields in the two regions were analyzed,and it was found that their spatial distribution in the same region was the same.They are believed to refl ect the vertical projection of the stress direction vector and strength on the surface in the stress field,consistent with the experimental results.Whether it can eff ectively refl ect the stress field requires further analysis of the specific situation of the local medium and the movement mode of the stress field.展开更多
In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a...In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a Lagrange multiplier.We obtain the critical point of the corresponding functional of the problem on mass constraint by the variational method and the Mountain pass lemma,and then find a normalized solution to this equation.展开更多
Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system a...Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system and a unipolar Navier-Stokes-Poisson system.Based on a delicate analysis of the corresponding Green function,L^(2) decay estimate of the solution is obtained.展开更多
In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)...In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)ϕ=u^(2),in R^(3),where s∈(3/4,1),t∈(0,1),q∈(1,2),p∈(4,2_(s)^(*)),2_(s)^(*):=6/3-2s is the fractional critical exponent in dimension 3,V_(λ)(x)=λV(x)+1 withλ>0.Under the case of steep potential well,we obtain the existence of the sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma.Furthermore,we prove that the energy of ground state sign-changing solution is strictly more than twice of the energy of the ground state solution.Our results improve the recent results in the literature.展开更多
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
文摘Road traffic flow forecasting provides critical information for the operational management of road mobility challenges, and models are used to generate the forecast. This paper uses a random process to present a novel traffic modelling framework for aggregate traffic on urban roads. The main idea is that road traffic flow is random, even for the recurrent flow, such as rush hour traffic, which is predisposed to congestion. Therefore, the structure of the aggregate traffic flow model for urban roads should correlate well with the essential variables of the observed random dynamics of the traffic flow phenomena. The novelty of this paper is the developed framework, based on the Poisson process, the kinematics of urban road traffic flow, and the intermediate modelling approach, which were combined to formulate the model. Empirical data from an urban road in Ghana was used to explore the model’s fidelity. The results show that the distribution from the model correlates well with that of the empirical traffic, providing a strong validation of the new framework and instilling confidence in its potential for significantly improved forecasts and, hence, a more hopeful outlook for real-world traffic management.
基金supported by the Shandong Provincial Natural Science Foundation for Quantum Science under Grant No.ZR2021LLZ002the Fundamental Research Funds for the Central Universities under Grant No.22CX03005A。
文摘To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=b.Variational quantum algorithms(VQAs)for the discretized Poisson equation have been studied before.We present a VQA based on the banded Toeplitz systems for solving the Poisson equation with respect to the structural features of matrix A.In detail,we decompose the matrices A and A^(2)into a linear combination of the corresponding banded Toeplitz matrix and sparse matrices with only a few non-zero elements.For the one-dimensional Poisson equation with different boundary conditions and the d-dimensional Poisson equation with Dirichlet boundary conditions,the number of decomposition terms is less than that reported in[Phys.Rev.A 2023108,032418].Based on the decomposition of the matrix,we design quantum circuits that efficiently evaluate the cost function.Additionally,numerical simulation verifies the feasibility of the proposed algorithm.Finally,the VQAs for linear systems of equations and matrix-vector multiplications with the K-banded Toeplitz matrix T_(n)^(K)are given,where T_(n)^(K)∈R^(n×n)and K∈O(ploylogn).
文摘Earthquakes are caused directly by the motion of the stress field,therefore,observing the stress field is significant.Experiments on the relationships among wave velocity,stress factors,and faults show that the wave velocity of rock media under stable stress fields corresponds one-to-one with stress factors.Therefore,the wave velocity gradient can indicate the direction of stress vector,and the gradient divergence can indicate the strength of the stress field.To verify the results,considering the limitations of wave velocity measurement in solid crustal media,two quantities,namely the apparent wave velocity and Poisson ratios relating to wave velocity,were used to refl ect the stress field state.The seismic data of the Tangshan and Luzhou regions were studied separately.The calculated apparent wave velocity and Poisson ratios were interpolated to achieve regional data gridding.The gradients and the gradient divergences of the apparent wave velocity and Poisson ratio fields in the two regions were analyzed,and it was found that their spatial distribution in the same region was the same.They are believed to refl ect the vertical projection of the stress direction vector and strength on the surface in the stress field,consistent with the experimental results.Whether it can eff ectively refl ect the stress field requires further analysis of the specific situation of the local medium and the movement mode of the stress field.
基金supported by the National Natural Science Foundation of China(No.12461024)the Natural Science Research Project of Department of Education of Guizhou Province(Nos.QJJ2023012,QJJ2023061,QJJ2023062)the Natural Science Research Project of Guizhou Minzu University(No.GZMUZK[2022]YB06)。
文摘In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a Lagrange multiplier.We obtain the critical point of the corresponding functional of the problem on mass constraint by the variational method and the Mountain pass lemma,and then find a normalized solution to this equation.
基金Supported by the National Natural Science Foundation of China (12271141)。
文摘Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system and a unipolar Navier-Stokes-Poisson system.Based on a delicate analysis of the corresponding Green function,L^(2) decay estimate of the solution is obtained.
基金supported by the Natural Science Foundation of Sichuan(No.2023NSFSC0073)。
文摘In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)ϕ=u^(2),in R^(3),where s∈(3/4,1),t∈(0,1),q∈(1,2),p∈(4,2_(s)^(*)),2_(s)^(*):=6/3-2s is the fractional critical exponent in dimension 3,V_(λ)(x)=λV(x)+1 withλ>0.Under the case of steep potential well,we obtain the existence of the sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma.Furthermore,we prove that the energy of ground state sign-changing solution is strictly more than twice of the energy of the ground state solution.Our results improve the recent results in the literature.
