The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real...The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.展开更多
In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochas...In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochastic differential equations (SDE), therefore the Fokker Planck Kolmogorov (FPK) equation is expressed in general form with no limitation on the degree of nonlinearity of the SDE, the type of δ correlated excitations, the existence of multiplicative excitations, and the dimension of SDE or FPK equation. Examples are given and numerical results are provided for comparing with known exact solution to show the effectiveness of the method.展开更多
With the discrete element method(DEM) ,employing the diameter distribution of natural sands sampled from the Tengger Desert,a mixed-size sand bed was produced and the particle-bed collision was simulated in the mixed-...With the discrete element method(DEM) ,employing the diameter distribution of natural sands sampled from the Tengger Desert,a mixed-size sand bed was produced and the particle-bed collision was simulated in the mixed-size wind sand movement. In the simulation,the shear wind velocity,particle diameter,incident velocity and incident angle of the impact sand particle were given the same values as the experimental results. After the particle-bed collision,we collected all the initial velocities of rising sand particles,including the liftoff angular velocities,liftoff linear velocities and their horizontal and vertical components. By the statistical analysis on the velocity sample for each velocity component,its probability density functions were obtained,and they are the functions of the shear wind velocity. The liftoff velocities and their horizontal and vertical components are distributed as an exponential density function,while the angular velocities are distributed as a normal density function.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11172233,11302169,11302170,and 11472212)the Fundamental Research Funds for the Central Universities(No.3102014JCQ01079)
文摘The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.
文摘In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochastic differential equations (SDE), therefore the Fokker Planck Kolmogorov (FPK) equation is expressed in general form with no limitation on the degree of nonlinearity of the SDE, the type of δ correlated excitations, the existence of multiplicative excitations, and the dimension of SDE or FPK equation. Examples are given and numerical results are provided for comparing with known exact solution to show the effectiveness of the method.
基金the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)
文摘With the discrete element method(DEM) ,employing the diameter distribution of natural sands sampled from the Tengger Desert,a mixed-size sand bed was produced and the particle-bed collision was simulated in the mixed-size wind sand movement. In the simulation,the shear wind velocity,particle diameter,incident velocity and incident angle of the impact sand particle were given the same values as the experimental results. After the particle-bed collision,we collected all the initial velocities of rising sand particles,including the liftoff angular velocities,liftoff linear velocities and their horizontal and vertical components. By the statistical analysis on the velocity sample for each velocity component,its probability density functions were obtained,and they are the functions of the shear wind velocity. The liftoff velocities and their horizontal and vertical components are distributed as an exponential density function,while the angular velocities are distributed as a normal density function.
