To reveal the dynamic mechanical characteristics of deep rocks,a series of impact tests under triaxial static stress states corresponding to depths of 300-2400 m were conducted.The results showed that both the strain ...To reveal the dynamic mechanical characteristics of deep rocks,a series of impact tests under triaxial static stress states corresponding to depths of 300-2400 m were conducted.The results showed that both the strain rates and the stress environments in depth significantly affect the mechanical characteristics of rocks.The sensitivity of strain rate to the dynamic strength and deformation modulus shows a negative correlation with depth,indicating that producing penetrative cracks in deep environments is more difficult when damage occurs.The dynamic strength shows a tendency to decrease and then increase slightly,but decreases sharply finally.Transmissivity demonstrates a similar trend as that of strength,whereas reflectivity indicates the opposite trend.Furthermore,two critical depths with high dynamically induced hazard possibilities based on the China Jinping Underground Laboratory(CJPL)were proposed for deep engineering.The first critical depth is 600-900 m,beyond which the sensitivity of rock dynamic characteristics to the strain rate and restraint of circumferential stress decrease,causing instability of surrounding rocks under axial stress condition.The second one lies at 1500-1800 m,where the wave impedance and dynamic strength of deep surrounding rocks drop sharply,and the dissipation energy presents a negative value.It suggests that the dynamic instability of deep surrounding rocks can be divided into dynamic load dominant and dynamic load induced types,depending on the second critical depth.展开更多
The model of nuclear reactor dynamics is an initial-boundary value problems of a cou- pled nonlinear integrodifferential equation system of one ordinary differential equation and one par-- tial differential equation. ...The model of nuclear reactor dynamics is an initial-boundary value problems of a cou- pled nonlinear integrodifferential equation system of one ordinary differential equation and one par-- tial differential equation. In this this,paper,a linearized difference scheme is derived by the method of reduction of order.It is proved that the scheme is uniquely solvable and unconditionally convergent with the convergence rate of order two both in discrete H1norm and in discrete maxinum narm,and one needs only to solve a tridiagonal system of linear algebraic equations at each time lev- el.The method of reduction of order is an indirect constructing-difference-scheme method,which aim is for the analysis of solvablity and convergence of the constructed difference scheme.展开更多
When acquaintances of a model are little or the model is too complicate to build by using traditional time series methods, it is convenient for us to take advantage of genetic programming (GP) to build the model. Cons...When acquaintances of a model are little or the model is too complicate to build by using traditional time series methods, it is convenient for us to take advantage of genetic programming (GP) to build the model. Considering the complexity of nonlinear dynamic systems, this paper proposes modeling dynamic systems by using the nonlinear difference e-quation based on GP technique. First it gives the method, criteria and evaluation of modeling. Then it describes the modeling algorithm using GP. Finally two typical examples of time series are used to perform the numerical experiments. The result shows that this algorithm can successfully establish the difference equation model of dynamic systems and its predictive result is also satisfactory.展开更多
In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solu...In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.展开更多
We used simulated data to investigate both the small and large sample properties of the within-groups (WG) estimator and the first difference generalized method of moments (FD-GMM) estimator of a dynamic panel data (D...We used simulated data to investigate both the small and large sample properties of the within-groups (WG) estimator and the first difference generalized method of moments (FD-GMM) estimator of a dynamic panel data (DPD) model. The magnitude of WG and FD-GMM estimates are almost the same for square panels. WG estimator performs best for long panels such as those with time dimension as large as 50. The advantage of FD-GMM estimator however, is observed on panels that are long and wide, say with time dimension at least 25 and cross-section dimension size of at least 30. For small-sized panels, the two methods failed since their optimality was established in the context of asymptotic theory. We developed parametric bootstrap versions of WG and FD-GMM estimators. Simulation study indicates the advantages of the bootstrap methods under small sample cases on the assumption that variances of the individual effects and the disturbances are of similar magnitude. The boostrapped WG and FD-GMM estimators are optimal for small samples.展开更多
欧美发达国家债务危机的频繁发生引起国际社会的广泛关注与思考,对其内在原因的深入探讨迅速成为学术界的研究焦点。文章从国防支出的角度出发,通过构建政府债务的动态面板模型,考察国防支出与政府债务之间的关系。以1991—2013年15个...欧美发达国家债务危机的频繁发生引起国际社会的广泛关注与思考,对其内在原因的深入探讨迅速成为学术界的研究焦点。文章从国防支出的角度出发,通过构建政府债务的动态面板模型,考察国防支出与政府债务之间的关系。以1991—2013年15个经济合作与发展组织(organization for economic co-operation and development,OECD)国家为样本,利用两步法系统广义矩估计(generalized method of moments,GMM)进行面板估计,从而得到比之前研究更稳健的估计量。结果表明,经济状况对政府债务规模有显著的消极影响,相反国防支出对其则有显著的积极影响,且作用力度是经济发展状况的4倍多。发达国家可通过适度削减国防开支、大力推动经济发展等措施达到控制债务规模、化解债务危机的目的。展开更多
基金supported by the National Natural Science Foundation of China(No.U1965203).
文摘To reveal the dynamic mechanical characteristics of deep rocks,a series of impact tests under triaxial static stress states corresponding to depths of 300-2400 m were conducted.The results showed that both the strain rates and the stress environments in depth significantly affect the mechanical characteristics of rocks.The sensitivity of strain rate to the dynamic strength and deformation modulus shows a negative correlation with depth,indicating that producing penetrative cracks in deep environments is more difficult when damage occurs.The dynamic strength shows a tendency to decrease and then increase slightly,but decreases sharply finally.Transmissivity demonstrates a similar trend as that of strength,whereas reflectivity indicates the opposite trend.Furthermore,two critical depths with high dynamically induced hazard possibilities based on the China Jinping Underground Laboratory(CJPL)were proposed for deep engineering.The first critical depth is 600-900 m,beyond which the sensitivity of rock dynamic characteristics to the strain rate and restraint of circumferential stress decrease,causing instability of surrounding rocks under axial stress condition.The second one lies at 1500-1800 m,where the wave impedance and dynamic strength of deep surrounding rocks drop sharply,and the dissipation energy presents a negative value.It suggests that the dynamic instability of deep surrounding rocks can be divided into dynamic load dominant and dynamic load induced types,depending on the second critical depth.
基金NSF of Jiangsu Province (BK97004) and NSF of China (19801007)
文摘The model of nuclear reactor dynamics is an initial-boundary value problems of a cou- pled nonlinear integrodifferential equation system of one ordinary differential equation and one par-- tial differential equation. In this this,paper,a linearized difference scheme is derived by the method of reduction of order.It is proved that the scheme is uniquely solvable and unconditionally convergent with the convergence rate of order two both in discrete H1norm and in discrete maxinum narm,and one needs only to solve a tridiagonal system of linear algebraic equations at each time lev- el.The method of reduction of order is an indirect constructing-difference-scheme method,which aim is for the analysis of solvablity and convergence of the constructed difference scheme.
基金Supported by Foundation for University Key Teacher by the Ministry of Education of China
文摘When acquaintances of a model are little or the model is too complicate to build by using traditional time series methods, it is convenient for us to take advantage of genetic programming (GP) to build the model. Considering the complexity of nonlinear dynamic systems, this paper proposes modeling dynamic systems by using the nonlinear difference e-quation based on GP technique. First it gives the method, criteria and evaluation of modeling. Then it describes the modeling algorithm using GP. Finally two typical examples of time series are used to perform the numerical experiments. The result shows that this algorithm can successfully establish the difference equation model of dynamic systems and its predictive result is also satisfactory.
文摘In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.
文摘We used simulated data to investigate both the small and large sample properties of the within-groups (WG) estimator and the first difference generalized method of moments (FD-GMM) estimator of a dynamic panel data (DPD) model. The magnitude of WG and FD-GMM estimates are almost the same for square panels. WG estimator performs best for long panels such as those with time dimension as large as 50. The advantage of FD-GMM estimator however, is observed on panels that are long and wide, say with time dimension at least 25 and cross-section dimension size of at least 30. For small-sized panels, the two methods failed since their optimality was established in the context of asymptotic theory. We developed parametric bootstrap versions of WG and FD-GMM estimators. Simulation study indicates the advantages of the bootstrap methods under small sample cases on the assumption that variances of the individual effects and the disturbances are of similar magnitude. The boostrapped WG and FD-GMM estimators are optimal for small samples.
文摘欧美发达国家债务危机的频繁发生引起国际社会的广泛关注与思考,对其内在原因的深入探讨迅速成为学术界的研究焦点。文章从国防支出的角度出发,通过构建政府债务的动态面板模型,考察国防支出与政府债务之间的关系。以1991—2013年15个经济合作与发展组织(organization for economic co-operation and development,OECD)国家为样本,利用两步法系统广义矩估计(generalized method of moments,GMM)进行面板估计,从而得到比之前研究更稳健的估计量。结果表明,经济状况对政府债务规模有显著的消极影响,相反国防支出对其则有显著的积极影响,且作用力度是经济发展状况的4倍多。发达国家可通过适度削减国防开支、大力推动经济发展等措施达到控制债务规模、化解债务危机的目的。
