The performances of a well-known GHR car-following model was investigated by using numerical simulations in describing the acceleration and deceleration process induced by the motion of a leading car. It is shown that...The performances of a well-known GHR car-following model was investigated by using numerical simulations in describing the acceleration and deceleration process induced by the motion of a leading car. It is shown that in GHR model vehicle is allowed to run arbitrarily close together if their speed are identical,and it waves aside even though the separation is larger than its desired distance. Based on these investigations, a modified GHR model which features a new nonlinear term which attempts to adjust the inter-vehicle spacing to a certain desired value was proposed accordingly to overcome these deficiencies. In addition, the analysis of the additive nonlinear term and steady-state flow of the new model were studied to prove its rationality.展开更多
To analyze the physical structure of assembly process and assure product quality, the quality stability of multi-station assembly process was investigated. First, the assembly process was modeled as a one-dimensional ...To analyze the physical structure of assembly process and assure product quality, the quality stability of multi-station assembly process was investigated. First, the assembly process was modeled as a one-dimensional discrete variant system by state space equation based on variation stream. Then, the criterion to judge whether the process is stable or not and the index, stability degree, to show the level of stability were proposed by analyzing the bounded-input bounded-output (BIBO) stability of system. Finally, a simulated example of a sheet metal assembly process with three stations, was provided to verify the effectiveness of the proposed method.展开更多
In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), wit...In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), with Pm > 0, we establish some new sufficient conditions for an arbitrary solution N(t) to satisfy the initial conditions of the form N(0) = NO > 0 and N(-j) = N-j ≥ 0,j = 1, 2, ., m, to converge to the positive equilibrium N* as t →∞.展开更多
In this paper, a class of linear neutral differential system with distributed delay is considered. Sufficient conditions for the zero solution of the system to be uniformly stable as well as asymptotically stable are...In this paper, a class of linear neutral differential system with distributed delay is considered. Sufficient conditions for the zero solution of the system to be uniformly stable as well as asymptotically stable are obtained.展开更多
In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the n...In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.展开更多
Rain infiltration into a soil slope leads to propagation of the wetting front, transport of air in pores and deformation of the soils, in which coupled processes among the solid, liquid and gas phases are typically in...Rain infiltration into a soil slope leads to propagation of the wetting front, transport of air in pores and deformation of the soils, in which coupled processes among the solid, liquid and gas phases are typically involved. Most previous studies on the unsaturated flow and its influence on slope stability were based on the singlephase water flow model (i.e., the Richards Equation) or the waterair two-phase flow model. The effects of gas transport and soil deformation on the movement of groundwater and the evolution of slope stability were less examined with a coupled solid-water-air model. In this paper, a numerical model was established based on the principles of the continuum mechanics and the averaging approach of the mixture theory and implemented in an FEM code for analysis of the coupled deformation, water flow and gas transport in porous media. The proposed model and the computer code were validated by the Liakopoulos drainage test over a sand column, and the significant effect of the lateral air boundary condition on the draining process of water was discussed. On this basis, the coupled processes of groundwater flow, gas transport and soil deformation in a homogeneous soil slope under a long heavy rainfall were simulated with the proposed three-phase model, and the numerical results revealed the remarkable delaying effects of gas transport and soil deformation on the propagation of the wetting front and the evolution of the slope stability. The results may provide a helpful reference for hazard assessment and control of rainfall-induced landslides.展开更多
The theory of limit analysis is presented for a three-dimensional stability problem of excavation. In frictional soil, the failure surface has the shape of logarithm helicoid, with the outline profile defined by a log...The theory of limit analysis is presented for a three-dimensional stability problem of excavation. In frictional soil, the failure surface has the shape of logarithm helicoid, with the outline profile defined by a log- spiral curve. The internal dissipation rate of energy caused by soil cohesion and gravity power of the failure soil is obtained through theoretical derivation. By solving the energy balance equation, the stability factor for the excavation is obtained. Influence of the ratio of width to height, the slope angle, and the top angle on the stability is examined. Numerical results of the proposed algorithm are presented in the form of non dimensional graph. Examples illustrate the practical use of the results.展开更多
In the previous paper(see Li and Zhu(2014)), for a characteristic problem with not necessarily small initial data given on a complete null cone decaying like that in the work of the stability of Minkowski spacetime by...In the previous paper(see Li and Zhu(2014)), for a characteristic problem with not necessarily small initial data given on a complete null cone decaying like that in the work of the stability of Minkowski spacetime by Christodoulou and Klainerman(1993), we proved the local existence in retarded time, which means the solution to the vacuum Einstein equations exists in a uniform future neighborhood, while the global existence in retarded time is the weak cosmic censorship conjecture. In this paper, we prove that the local existence in retarded time still holds when the data is assumed to decay slower, like that in Bieri's work(2007)on the extension to the stability of Minkowski spacetime. Such decay guarantees the existence of the limit of the Hawking mass on the initial null cone, when approaching to infinity, in an optimal way.展开更多
基金Key Foundation Project of Shanghai (No.032912066)
文摘The performances of a well-known GHR car-following model was investigated by using numerical simulations in describing the acceleration and deceleration process induced by the motion of a leading car. It is shown that in GHR model vehicle is allowed to run arbitrarily close together if their speed are identical,and it waves aside even though the separation is larger than its desired distance. Based on these investigations, a modified GHR model which features a new nonlinear term which attempts to adjust the inter-vehicle spacing to a certain desired value was proposed accordingly to overcome these deficiencies. In addition, the analysis of the additive nonlinear term and steady-state flow of the new model were studied to prove its rationality.
基金Supported bythe National High-Tech Research and Development Plan (National"863"Plan) (No2006AA04Z115)Tianjin Science andTechnology Key Project (No05YFGDGX08700)
文摘To analyze the physical structure of assembly process and assure product quality, the quality stability of multi-station assembly process was investigated. First, the assembly process was modeled as a one-dimensional discrete variant system by state space equation based on variation stream. Then, the criterion to judge whether the process is stable or not and the index, stability degree, to show the level of stability were proposed by analyzing the bounded-input bounded-output (BIBO) stability of system. Finally, a simulated example of a sheet metal assembly process with three stations, was provided to verify the effectiveness of the proposed method.
基金Supported by the Science Foundation of Hunan Educational Commites (99C12)
文摘In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), with Pm > 0, we establish some new sufficient conditions for an arbitrary solution N(t) to satisfy the initial conditions of the form N(0) = NO > 0 and N(-j) = N-j ≥ 0,j = 1, 2, ., m, to converge to the positive equilibrium N* as t →∞.
基金Supported by the Natural Science Foundation of inner Mongolia (97118) and InnerMongolia Higher Education Science Research Prog
文摘In this paper, a class of linear neutral differential system with distributed delay is considered. Sufficient conditions for the zero solution of the system to be uniformly stable as well as asymptotically stable are obtained.
基金supported by the Hong Kong General Research Fund (Grant Nos. 202112, 15302214 and 509213)National Natural Science Foundation of China/Research Grants Council Joint Research Scheme (Grant Nos. N HKBU204/12 and 11261160486)+1 种基金National Natural Science Foundation of China (Grant No. 11471046)the Ministry of Education Program for New Century Excellent Talents Project (Grant No. NCET-12-0053)
文摘In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50839004, 51079107) the Program for New Centu-ry Excellent Talents in University (Grant No. NCET-09-0610)
文摘Rain infiltration into a soil slope leads to propagation of the wetting front, transport of air in pores and deformation of the soils, in which coupled processes among the solid, liquid and gas phases are typically involved. Most previous studies on the unsaturated flow and its influence on slope stability were based on the singlephase water flow model (i.e., the Richards Equation) or the waterair two-phase flow model. The effects of gas transport and soil deformation on the movement of groundwater and the evolution of slope stability were less examined with a coupled solid-water-air model. In this paper, a numerical model was established based on the principles of the continuum mechanics and the averaging approach of the mixture theory and implemented in an FEM code for analysis of the coupled deformation, water flow and gas transport in porous media. The proposed model and the computer code were validated by the Liakopoulos drainage test over a sand column, and the significant effect of the lateral air boundary condition on the draining process of water was discussed. On this basis, the coupled processes of groundwater flow, gas transport and soil deformation in a homogeneous soil slope under a long heavy rainfall were simulated with the proposed three-phase model, and the numerical results revealed the remarkable delaying effects of gas transport and soil deformation on the propagation of the wetting front and the evolution of the slope stability. The results may provide a helpful reference for hazard assessment and control of rainfall-induced landslides.
基金the National Natural Science Foundation of China(Nos.41002095,41172251 and 41272317)
文摘The theory of limit analysis is presented for a three-dimensional stability problem of excavation. In frictional soil, the failure surface has the shape of logarithm helicoid, with the outline profile defined by a log- spiral curve. The internal dissipation rate of energy caused by soil cohesion and gravity power of the failure soil is obtained through theoretical derivation. By solving the energy balance equation, the stability factor for the excavation is obtained. Influence of the ratio of width to height, the slope angle, and the top angle on the stability is examined. Numerical results of the proposed algorithm are presented in the form of non dimensional graph. Examples illustrate the practical use of the results.
基金supported by National Natural Science Foundation of China(Grant No.11271377)the Fundamental Research Funds for the Central Universities
文摘In the previous paper(see Li and Zhu(2014)), for a characteristic problem with not necessarily small initial data given on a complete null cone decaying like that in the work of the stability of Minkowski spacetime by Christodoulou and Klainerman(1993), we proved the local existence in retarded time, which means the solution to the vacuum Einstein equations exists in a uniform future neighborhood, while the global existence in retarded time is the weak cosmic censorship conjecture. In this paper, we prove that the local existence in retarded time still holds when the data is assumed to decay slower, like that in Bieri's work(2007)on the extension to the stability of Minkowski spacetime. Such decay guarantees the existence of the limit of the Hawking mass on the initial null cone, when approaching to infinity, in an optimal way.
