The experimental tests of tensile for lead-flee solder Sn-3.5Ag were performed for the general work temperatures range from 11 to 90 ℃ and strain rate range from 5 × 10^-5 to 2 × 10^-2s^-1, and its stress--...The experimental tests of tensile for lead-flee solder Sn-3.5Ag were performed for the general work temperatures range from 11 to 90 ℃ and strain rate range from 5 × 10^-5 to 2 × 10^-2s^-1, and its stress--strain curves were compared to those of solder Sn-37Pb. The parameters in Anand model for solder Sn-3.5Ag were fitted based on experimental data and nonlinear fitting method, and its validity was checked by means of experimental data. Furthermore, the Anand model was used in the FEM analysis to evaluate solder joint thermal cycle reliability. The results show that solder Sn-3.5Ag has a better creep resistance than solder Sn-37Pb. The maximum stress is located at the upper right comer of the outmost solder joint from the symmetric center, and thermal fatigue life is predicted to be 3.796 × 10^4 cycles under the calculated conditions.展开更多
To investigate the validity of two dynamic modulus predictive models（ Witczak 1-37 A viscosity-based model and Witczak 1-40 D shear modulus-based model） in the context of Jiangsu, and evaluate the effect of differen...To investigate the validity of two dynamic modulus predictive models（ Witczak 1-37 A viscosity-based model and Witczak 1-40 D shear modulus-based model） in the context of Jiangsu, and evaluate the effect of different mixture design variables（ aggregate gradations, binder type, and volumetric properties） on dynamic modulus E＊, asphalt mixtures commonly used in the local surface layer, including Sup-13 and AC-13, are prepared in the laboratory and their dynamic modulus E＊values are predicted based on the above mentioned models. The corresponding asphalt tests, including viscosity and dynamic shear modulus tests, are also carried out to obtain the prediction model parameters. The test results showthat binder type and asphalt content have a significant impact on dynamic modulus.There is a good correlation between the E＊values based on above two predictive models and the measured E＊, while a relatively lower bias can be expected from Witczak 1-37 A model. The test results can be used for the calibration of dynamic modulus with higher accuracy.展开更多
In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reac...In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.展开更多
The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asym...The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asymptotic behaviour of the ruin probability.As a corollary,we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims.展开更多
In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the t...In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TV-PAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out.展开更多
Throughout the progress of epidemic scenarios,individuals in different health classes are expected to have different average daily contact behavior.This contact heterogeneity has been studied in recent adaptive models...Throughout the progress of epidemic scenarios,individuals in different health classes are expected to have different average daily contact behavior.This contact heterogeneity has been studied in recent adaptive models and allows us to capture the inherent differences across health statuses better.Diseases with reinfection bring out more complex scenarios and offer an important application to consider contact disaggregation.Therefore,we developed a nonlinear differential equation model to explore the dynamics of relapse phenomena and contact differences across health statuses.Our incidence rate function is formulated,taking inspiration from recent adaptive algorithms.It incorporates contact behavior for individuals in each health class.We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios.The relationship between the different contact rates heavily in-fluences these conditions.Numerical examples highlight the effect of temporarily recov-ered individuals and initial conditions on infected population persistence.展开更多
基金Project(50376076) supported by the National Natural Science Foundation of China
文摘The experimental tests of tensile for lead-flee solder Sn-3.5Ag were performed for the general work temperatures range from 11 to 90 ℃ and strain rate range from 5 × 10^-5 to 2 × 10^-2s^-1, and its stress--strain curves were compared to those of solder Sn-37Pb. The parameters in Anand model for solder Sn-3.5Ag were fitted based on experimental data and nonlinear fitting method, and its validity was checked by means of experimental data. Furthermore, the Anand model was used in the FEM analysis to evaluate solder joint thermal cycle reliability. The results show that solder Sn-3.5Ag has a better creep resistance than solder Sn-37Pb. The maximum stress is located at the upper right comer of the outmost solder joint from the symmetric center, and thermal fatigue life is predicted to be 3.796 × 10^4 cycles under the calculated conditions.
基金The Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20120092110053)
文摘To investigate the validity of two dynamic modulus predictive models（ Witczak 1-37 A viscosity-based model and Witczak 1-40 D shear modulus-based model） in the context of Jiangsu, and evaluate the effect of different mixture design variables（ aggregate gradations, binder type, and volumetric properties） on dynamic modulus E＊, asphalt mixtures commonly used in the local surface layer, including Sup-13 and AC-13, are prepared in the laboratory and their dynamic modulus E＊values are predicted based on the above mentioned models. The corresponding asphalt tests, including viscosity and dynamic shear modulus tests, are also carried out to obtain the prediction model parameters. The test results showthat binder type and asphalt content have a significant impact on dynamic modulus.There is a good correlation between the E＊values based on above two predictive models and the measured E＊, while a relatively lower bias can be expected from Witczak 1-37 A model. The test results can be used for the calibration of dynamic modulus with higher accuracy.
基金the National Natural Science Foundation of China (Grant Nos. 10801090, 10726016,10771032)the Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No.T200809)
文摘In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.
基金supported by National Natural Science Foundation of China (Grant Nos.10571167,70501028)the Beijing Sustentation Fund for Elitist (Grant No.20071D1600800421)+1 种基金the National Social Science Foundation of China (Grant No.05&ZD008)the Research Grant of Renmin University of China (Grant No.08XNA001)
文摘The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asymptotic behaviour of the ruin probability.As a corollary,we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims.
基金supported by the Doctoral Research Fund of the Ministry of Education, China (Grant No.20040285008)Grant-in-Aid for Scientific Research (B), the Ministry of Education, Science, Sports andCulture, Japan, 2005 (Grant No. 17300228)
文摘In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TV-PAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out.
基金support from the Research Center in Pure and Applied Mathematics and the Department of Mathematics at Universidad de Costa Rica.
文摘Throughout the progress of epidemic scenarios,individuals in different health classes are expected to have different average daily contact behavior.This contact heterogeneity has been studied in recent adaptive models and allows us to capture the inherent differences across health statuses better.Diseases with reinfection bring out more complex scenarios and offer an important application to consider contact disaggregation.Therefore,we developed a nonlinear differential equation model to explore the dynamics of relapse phenomena and contact differences across health statuses.Our incidence rate function is formulated,taking inspiration from recent adaptive algorithms.It incorporates contact behavior for individuals in each health class.We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios.The relationship between the different contact rates heavily in-fluences these conditions.Numerical examples highlight the effect of temporarily recov-ered individuals and initial conditions on infected population persistence.
