For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, (bi)linear/(bi)linear and (bi)linear/constant element, is presented. The pressure projection stab...For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, (bi)linear/(bi)linear and (bi)linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r(Ω) norm and that of the pressure in the L r' (Ω) (1/r + 1/r' = 1). The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.展开更多
A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh si...A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O(H2), which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.展开更多
Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in o...Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.展开更多
In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cell...In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.展开更多
The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e.,...The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory(LST) for two-dimensional(2D) disturbance on one-dimensional(1D) basic flow, comparison with LST for three-dimensional(3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence(FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting(TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous' in secondary instability.展开更多
It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY iss...It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.展开更多
In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been...In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.展开更多
Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explaine...Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explained by analyzing the interface potential, the tangential energy flux, and the normal energy flux. A rigorous criterion for tip-splitting instability is established analytically, i.e., the ratio of the cellular tip radius to the cellular width α 〉3/2/π≈ 0.3899, which is in good agreement with simulation results. This study also reveals that the cellular tip splitting instability is attributable to weak Gibbs–Thomson energy acting on the interface.展开更多
The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper. Liquid sloshing dynamics was simplified as the spring-mass model, and flexible attachment was modeled as the li...The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper. Liquid sloshing dynamics was simplified as the spring-mass model, and flexible attachment was modeled as the linear shearing beam. The dynamic equations and Hamiltonian of the coupled spacecraft system were given by analyzing the rigid body, liquid fuel, and flexible appendage. Nonlinear stability conditions of the coupled spacecraft system were derived by computing the variation of Casimir function which was added to the Hamiltonian. The stable region of the parameter space was given and validated by numerical computation. Related results suggest that the change of inertia matrix, the length of flexible attachment, spacecraft spinning rate, and filled ratio of liquid fuel tank have strong influence on the stability of the spacecraft system.展开更多
In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the unif...In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining the centre deflection and the critical load, and the stability curve is also derived. This paper is a continuation of the author's previous paper[11]展开更多
In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid...Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.展开更多
Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems,the pressure close to the initial time produces large non-physical oscillations.In this paper,we propose a cl...Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems,the pressure close to the initial time produces large non-physical oscillations.In this paper,we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations.Optimal error estimates for the approximation of displacements and pressure at every time level are obtained,which are valid even close to the initial time.Numerical experiments illustrate and confirm our theoretical analysis.展开更多
This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability ...This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability method, we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions, and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers. Interestingly,for a certain class of coupling matrices across layers, it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger, intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers. Finally, numerical simulations further verify the theoretical results.展开更多
An evaluation method for the seismic stability of embankment slope was presented based on catastrophe theory. Seven control factors, including internal frictional angle, cohesion force, slope height, slope angle, surf...An evaluation method for the seismic stability of embankment slope was presented based on catastrophe theory. Seven control factors, including internal frictional angle, cohesion force, slope height, slope angle, surface gradients, peak acceleration, and distance to fault were selected for analysis of multi-level objective decomposition. According to the normalization formula and the fuzzy subject function produced by combination of catastrophe theory and fuzzy math, a recursive calculation was carried out to obtain a catastrophic affiliated functional value, which can be used to evaluate the seismic stability of embankment slope. Fifteen samples were used to verify the effectiveness of this method. The results show that compared with the traditional quantitative method, the catastrophe progression owns higher accuracy and good application potential in predicting the seismic stability of embankment slope.展开更多
Based on the low-order conforming finite element subspace (Vh, Mh) such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonl...Based on the low-order conforming finite element subspace (Vh, Mh) such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since (Vh, Mh) does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of (Vh, Mh) is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.展开更多
In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomi...In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions.The inf-sup condition for P_(1)-P_(0)triangular element(or Q_(1)-P_(0)quadrilateral element)is established.The optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.展开更多
The underground water-sealed storage technique is critically important and generally accepted for the national energy strategy in China. Although several small underground water-sealed oil storage caverns have been bu...The underground water-sealed storage technique is critically important and generally accepted for the national energy strategy in China. Although several small underground water-sealed oil storage caverns have been built in China since the 1970s, there is still a lack of experience for large-volume underground storage in complicated geological conditions. The current design concept of water curtain system and the technical instruction for system operation have limitations in maintaining the stability of surrounding rock mass during the construction of the main storage caverns, as well as the long-term stability. Although several large-scale underground oil storage projects are under construction at present in China, the design concepts and construction methods, especially for the water curtain system, are mainly based on the ideal porosity medium flow theory and the experiences gained from the similar projects overseas. The storage projects currently constructed in China have the specific features such as huge scale, large depth, multiple-level arrangement, high seepage pressure, complicated geological conditions, and high in situ stresses, which are the challenging issues for the stability of the storage caverns. Based on years’ experiences obtained from the first large-scale (millions of cubic meters) underground water-sealed oil storage project in China, some design and operation problems related to water curtain system during project construction are discussed. The drawbacks and merits of the water curtain system are also presented. As an example, the conventional concept of “filling joints with water” is widely used in many cases, as a basic concept for the design of the water curtain system, but it is immature. In this paper, the advantages and disadvantages of the conventional concept are pointed out, with respect to the long-term stability as well as the safety of construction of storage caverns. Finally, new concepts and principles for design and construction of the underground water-sealed oil storage caverns are proposed.展开更多
For lower dimensional Fermi–Pasta–Ulam(FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of th...For lower dimensional Fermi–Pasta–Ulam(FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α(t) and β(t) with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions.展开更多
A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this ...A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.展开更多
基金Project supported by the Key Technology Research and Development Program of Sichuan Province of China(No.05GG006-006-2)
文摘For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, (bi)linear/(bi)linear and (bi)linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r(Ω) norm and that of the pressure in the L r' (Ω) (1/r + 1/r' = 1). The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.
基金Project supported by the National Natural Science Foundation of China(Nos.10901131,10971166, and 10961024)the National High Technology Research and Development Program of China (No.2009AA01A135)the Natural Science Foundation of Xinjiang Uygur Autonomous Region (No.2010211B04)
文摘A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O(H2), which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.
基金the support received from the Laoshan Laboratory(No.LSKJ202202000)the National Natural Science Foundation of China(Grant Nos.12032002,U22A20256,and 12302253)the Natural Science Foundation of Beijing(No.L212023)for partially funding this work.
文摘Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61105130 and 61175124)
文摘In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.1120214711332007+2 种基金11172203and 91216111)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120032120007)
文摘The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory(LST) for two-dimensional(2D) disturbance on one-dimensional(1D) basic flow, comparison with LST for three-dimensional(3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence(FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting(TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous' in secondary instability.
基金the National Natural Science Foundation of China(No.10590353)theNatural Science Foundation of Shaanxi Province of China(No.2005A16)
文摘It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.
文摘In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.
基金Project supported by the National Basic Research Program of China(Grant No.2011CB610401)the National Natural Science Foundation of China(Grant No.51371151)the Free Research Fund of State Key Laboratory of Solidification Processing,China(Grant No.100-QP-2014)
文摘Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explained by analyzing the interface potential, the tangential energy flux, and the normal energy flux. A rigorous criterion for tip-splitting instability is established analytically, i.e., the ratio of the cellular tip radius to the cellular width α 〉3/2/π≈ 0.3899, which is in good agreement with simulation results. This study also reveals that the cellular tip splitting instability is attributable to weak Gibbs–Thomson energy acting on the interface.
基金supported by the National Natural Science Foundation of China (11472041, 11532002)the Innovation Fund Designated for Graduate Students of Beijing Institute of Technology (2015CX10003)the Research Fund for the Doctoral Program of Higher Education of China (20131101110002)
文摘The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper. Liquid sloshing dynamics was simplified as the spring-mass model, and flexible attachment was modeled as the linear shearing beam. The dynamic equations and Hamiltonian of the coupled spacecraft system were given by analyzing the rigid body, liquid fuel, and flexible appendage. Nonlinear stability conditions of the coupled spacecraft system were derived by computing the variation of Casimir function which was added to the Hamiltonian. The stable region of the parameter space was given and validated by numerical computation. Related results suggest that the change of inertia matrix, the length of flexible attachment, spacecraft spinning rate, and filled ratio of liquid fuel tank have strong influence on the stability of the spacecraft system.
文摘In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining the centre deflection and the critical load, and the stability curve is also derived. This paper is a continuation of the author's previous paper[11]
文摘In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
文摘Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.
基金The computations in Section 4.4 were done by Free Fem++[21]This research was supported by the Natural Science Foundation of China(No.11271273).
文摘Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems,the pressure close to the initial time produces large non-physical oscillations.In this paper,we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations.Optimal error estimates for the approximation of displacements and pressure at every time level are obtained,which are valid even close to the initial time.Numerical experiments illustrate and confirm our theoretical analysis.
基金Project supported in part by the National Natural Science Foundation of China(Grant Nos.61573004 and 11501221)the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(Grant No.ZQN-YX301)+1 种基金the Program for New Century Excellent Talents in Fujian Province University in 2016the Project of Education and Scientific Research for Middle and Young Teachers in Fujian Province,China(Grant Nos.JAT170027 and JA15030)
文摘This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability method, we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions, and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers. Interestingly,for a certain class of coupling matrices across layers, it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger, intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers. Finally, numerical simulations further verify the theoretical results.
基金financially supported by the open research fund of Key Laboratory of Highway Engineering of Sichuan Province, Southwest Jiaotong University (No. LHTE009201109)
文摘An evaluation method for the seismic stability of embankment slope was presented based on catastrophe theory. Seven control factors, including internal frictional angle, cohesion force, slope height, slope angle, surface gradients, peak acceleration, and distance to fault were selected for analysis of multi-level objective decomposition. According to the normalization formula and the fuzzy subject function produced by combination of catastrophe theory and fuzzy math, a recursive calculation was carried out to obtain a catastrophic affiliated functional value, which can be used to evaluate the seismic stability of embankment slope. Fifteen samples were used to verify the effectiveness of this method. The results show that compared with the traditional quantitative method, the catastrophe progression owns higher accuracy and good application potential in predicting the seismic stability of embankment slope.
基金supported by the National Natural Science Foundation of China(10901122)Zhejiang Provincial Natural Science Foundation (Y6090108)supported by the National Natural Science Foundation of China(10971165)
文摘Based on the low-order conforming finite element subspace (Vh, Mh) such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since (Vh, Mh) does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of (Vh, Mh) is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.
基金the support of the Natural Science Foundation of China(No.10671154)the National Basic Research Program(No.2005CB321703)。
文摘In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions.The inf-sup condition for P_(1)-P_(0)triangular element(or Q_(1)-P_(0)quadrilateral element)is established.The optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.
文摘The underground water-sealed storage technique is critically important and generally accepted for the national energy strategy in China. Although several small underground water-sealed oil storage caverns have been built in China since the 1970s, there is still a lack of experience for large-volume underground storage in complicated geological conditions. The current design concept of water curtain system and the technical instruction for system operation have limitations in maintaining the stability of surrounding rock mass during the construction of the main storage caverns, as well as the long-term stability. Although several large-scale underground oil storage projects are under construction at present in China, the design concepts and construction methods, especially for the water curtain system, are mainly based on the ideal porosity medium flow theory and the experiences gained from the similar projects overseas. The storage projects currently constructed in China have the specific features such as huge scale, large depth, multiple-level arrangement, high seepage pressure, complicated geological conditions, and high in situ stresses, which are the challenging issues for the stability of the storage caverns. Based on years’ experiences obtained from the first large-scale (millions of cubic meters) underground water-sealed oil storage project in China, some design and operation problems related to water curtain system during project construction are discussed. The drawbacks and merits of the water curtain system are also presented. As an example, the conventional concept of “filling joints with water” is widely used in many cases, as a basic concept for the design of the water curtain system, but it is immature. In this paper, the advantages and disadvantages of the conventional concept are pointed out, with respect to the long-term stability as well as the safety of construction of storage caverns. Finally, new concepts and principles for design and construction of the underground water-sealed oil storage caverns are proposed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.1130110611201288+6 种基金and 11261013)the Natural Science Foundation of Guangxi Zhuang Autonomous RegionChina(Grant No.2014GXNSFBA118017)the Innovation Project of Graduate Education of Guangxi Zhuang Autonomous RegionChina(Grant No.YCSZ2014143)the Guangxi Experiment Center of Information Science(Grant No.YB1410)
文摘For lower dimensional Fermi–Pasta–Ulam(FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α(t) and β(t) with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions.
基金supported by the National Key Basic Research Program of China(973 Program)(2012CB725402)the National High-Tech R&D Program of China(863 Program)(SS2014AA110303)the Science Foundation for Post-doctoral Scientists of Jiangsu Province(1301011A)
文摘A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.