Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution ...Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.展开更多
This paper proposes a novel Multivariate Quotient-Difference(MQD)method to obtain the approximate analytical solution for AC power flow equations.Therefore,in the online environment,the power flow solutions covering d...This paper proposes a novel Multivariate Quotient-Difference(MQD)method to obtain the approximate analytical solution for AC power flow equations.Therefore,in the online environment,the power flow solutions covering different operating conditions can be directly obtained by plugging values into multiple symbolic variables,such that the power injections and consumptions of selected buses or areas can be independently adjusted.This method first derives a power flow solution through a Multivariate Power Series(MPS).Next,the MQD method is applied to transform the obtained MPS to a Multivariate Pad´e Approximants(MPA)to expand the Radius of Convergence(ROC),so that the accuracy of the derived analytical solution can be significantly increased.In addition,the hypersurface of the voltage stability boundary can be identified by an analytical formula obtained from the coefficients of MPA.This direct method for power flow solutions and voltage stability boundaries is fast for many online applications,since such analytical solutions can be derived offline and evaluated online by only plugging values into the symbolic variables according to the actual operating conditions.The proposed method is validated in detail on New England 39-bus and IEEE 118-bus systems with independent load variations in multi-regions.展开更多
An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, clo...An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, cloud data de-noising optimization, construction, display and operation of three-dimensional model, model editing, profile generation, calculation of goaf volume and roof area, Boolean calculation among models and interaction with the third party soft ware. Concerning this system with a concise interface, plentiful data input/output interfaces, it is featured with high integration, simple and convenient operations of applications. According to practice, in addition to being well-adapted, this system is favorably reliable and stable.展开更多
Based on the potential flow theory, the vortex ring is introduced to simulate the toroidal bubble, and the boundary element method is applied to simulate the evo- lution of the bubble. Elastic-plasticity of structure ...Based on the potential flow theory, the vortex ring is introduced to simulate the toroidal bubble, and the boundary element method is applied to simulate the evo- lution of the bubble. Elastic-plasticity of structure being taken into account, the interaction between the bubble and the elastic-plastic structure is computed by combining the boundary element method (BEM) and the finite element method (FEM), and a corresponding 3D computing program is developed. This program is used to simulate the three-dimensional bubble dynamics in free field, near wall and near the elastic-plastic structure, and the numerical results are compared with the existing experimental results. The error is within 10%. The effects of different boundaries upon the bubble dynamics are presented by studying the bubble dy- namics near different boundaries.展开更多
The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy–Forchheimer porous medium. A bidirectional nonlinear stretching surface genera...The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy–Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method(OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.展开更多
This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluate...This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time intervals.The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting.It implies that a weak solution indeed satisfies the balance law.In fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.It should be emphasized that the weak solutions considered here need not be entropy solutions.Furthermore,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.展开更多
This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary eleme...This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.展开更多
In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe ...In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.展开更多
Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of press...Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of pressure gradient and the historical variation of eddy viscosity, so the model is with memory. Numerical calculation by solving boundary layer equations was carried out for the five pressure driven three dimensional turbulent boundary layers developed on flat plates, swept wing, and prolate spheroid in symmetrical plane. Comparing the computational results with the experimental data, it is obvious that the prediction will be more accurate if the proposed closure equations are used, especially for the turbulent shear stresses.展开更多
In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″...In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.展开更多
A Random Trajectory Model (RTM) for solid-liquid two-phase flow based on the Lagrangian Method is presented in this paper. The effects of water drag force, pressure gradient force, buoyancy and virtual mass force on t...A Random Trajectory Model (RTM) for solid-liquid two-phase flow based on the Lagrangian Method is presented in this paper. The effects of water drag force, pressure gradient force, buoyancy and virtual mass force on the particles were included and the turbulent dispersion was modeled by random method. Three-dimensional k-Ε model was used to calculate the flow field. A pumped-storage power station, with a natural lake as its upper pool, was taken as a case for the study. Averaged movement trajectories, velocities and the volume-concentration distributions for 5 groups of sediment particles, were predicted with RTM. The possible silted locations in the lake were also predicted.展开更多
Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in...Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE) after assimilation,the cost function may reach 1% or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.展开更多
Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock s...Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.展开更多
A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of tra...A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of transverse shear and nor-mal deformations,a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness.The conventional beam theories including the classical beam theory,the first-order beam theory,and the higher-order beam theory are regarded as the special cases of this model.The material proper-ties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme.The energy-based formulation is derived by a variational method integrated with the penalty function method,where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables.The formulation is validated by some comparative examples,and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.展开更多
基金Projects(51678547,41672296,51878634,51878185,41867034)supported by the National Natural Science Foundation of China。
文摘Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.
基金supported by the National Natural Science Foundation of China under Project 52007133 and U22B20100。
文摘This paper proposes a novel Multivariate Quotient-Difference(MQD)method to obtain the approximate analytical solution for AC power flow equations.Therefore,in the online environment,the power flow solutions covering different operating conditions can be directly obtained by plugging values into multiple symbolic variables,such that the power injections and consumptions of selected buses or areas can be independently adjusted.This method first derives a power flow solution through a Multivariate Power Series(MPS).Next,the MQD method is applied to transform the obtained MPS to a Multivariate Pad´e Approximants(MPA)to expand the Radius of Convergence(ROC),so that the accuracy of the derived analytical solution can be significantly increased.In addition,the hypersurface of the voltage stability boundary can be identified by an analytical formula obtained from the coefficients of MPA.This direct method for power flow solutions and voltage stability boundaries is fast for many online applications,since such analytical solutions can be derived offline and evaluated online by only plugging values into the symbolic variables according to the actual operating conditions.The proposed method is validated in detail on New England 39-bus and IEEE 118-bus systems with independent load variations in multi-regions.
基金Project(51274250)supported by the National Natural Science Foundation of ChinaProject(2012BAK09B02-05)supported by the National Key Technology R&D Program during the 12th Five-year Plan of China
文摘An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, cloud data de-noising optimization, construction, display and operation of three-dimensional model, model editing, profile generation, calculation of goaf volume and roof area, Boolean calculation among models and interaction with the third party soft ware. Concerning this system with a concise interface, plentiful data input/output interfaces, it is featured with high integration, simple and convenient operations of applications. According to practice, in addition to being well-adapted, this system is favorably reliable and stable.
基金the National Natural Science Foundation of China (Grant No. 50779007)the National Science Foundation for Young Scientists of China (Grant No. 50809018)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070217074)the Defense Advanced Research Program of Science and Technology of Ship Industry (Grant No. 07J1.1.6)Harbin Engineering University Foundation (Grant No. HEUFT07069)
文摘Based on the potential flow theory, the vortex ring is introduced to simulate the toroidal bubble, and the boundary element method is applied to simulate the evo- lution of the bubble. Elastic-plasticity of structure being taken into account, the interaction between the bubble and the elastic-plastic structure is computed by combining the boundary element method (BEM) and the finite element method (FEM), and a corresponding 3D computing program is developed. This program is used to simulate the three-dimensional bubble dynamics in free field, near wall and near the elastic-plastic structure, and the numerical results are compared with the existing experimental results. The error is within 10%. The effects of different boundaries upon the bubble dynamics are presented by studying the bubble dy- namics near different boundaries.
文摘The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy–Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method(OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.
基金the Institute of Applied Physics and Computational Mathematics,Beijing,for the hospitality and support.The second author is supported by the NSFC(Nos.11771054,12072042,91852207)the Sino-German Research Group Project(No.GZ1465)the National Key Project GJXM92579.
文摘This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time intervals.The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting.It implies that a weak solution indeed satisfies the balance law.In fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.It should be emphasized that the weak solutions considered here need not be entropy solutions.Furthermore,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.
文摘This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.
基金Supported by National Natural Science Foundation of China under Grant No.10801027Fok Ying Tong Education Foundation under Grant No.121003
文摘In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.
基金National Natural Science F oundation of China !( No.91880 10 )National Defense Science Foundation!( 95 J13 A .1.2 )
文摘Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of pressure gradient and the historical variation of eddy viscosity, so the model is with memory. Numerical calculation by solving boundary layer equations was carried out for the five pressure driven three dimensional turbulent boundary layers developed on flat plates, swept wing, and prolate spheroid in symmetrical plane. Comparing the computational results with the experimental data, it is obvious that the prediction will be more accurate if the proposed closure equations are used, especially for the turbulent shear stresses.
基金supported by the National Natural Science Foundation of China(No.12071491)。
文摘In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.
文摘A Random Trajectory Model (RTM) for solid-liquid two-phase flow based on the Lagrangian Method is presented in this paper. The effects of water drag force, pressure gradient force, buoyancy and virtual mass force on the particles were included and the turbulent dispersion was modeled by random method. Three-dimensional k-Ε model was used to calculate the flow field. A pumped-storage power station, with a natural lake as its upper pool, was taken as a case for the study. Averaged movement trajectories, velocities and the volume-concentration distributions for 5 groups of sediment particles, were predicted with RTM. The possible silted locations in the lake were also predicted.
基金Supported by the State Ministry of Science and Technology of China (Nos.2007AA09Z118,2008AA09A402)the National Natural Science Foundation of China(No.41076006)the Ministry of Education's 111 Project(No.B07036)
文摘Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE) after assimilation,the cost function may reach 1% or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.
基金This work was supported in part by National Nature Science Foundation of China(11371141 and 11871218)by Science and Technology Commission of Shanghai Municipality(18dz2271000).
文摘Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.
基金Project supported by the National Natural Science Foundation of China(Nos.51805250 and 11602145)the Natural Science Foundation of Jiangsu Province of China(No.BK20180429)+1 种基金the China Postdoctoral Science Foundation(No.2019M660114)the Jiangsu Planned Projects for Postdoctoral Research Funds of China(No.2019K054)。
文摘A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of transverse shear and nor-mal deformations,a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness.The conventional beam theories including the classical beam theory,the first-order beam theory,and the higher-order beam theory are regarded as the special cases of this model.The material proper-ties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme.The energy-based formulation is derived by a variational method integrated with the penalty function method,where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables.The formulation is validated by some comparative examples,and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.
