In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the...In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.展开更多
This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of construc...This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of constructive and destructive chemical reactions are reported. Convergent solutions of the resulting differential systems are presented in series forms. Characteristics of various sundry parameters on the velocity, concentration, skin friction and local Sherwood number are analyzed and discussed.展开更多
In order to describe the interrelation forces among different regions during the economic growth, this paper introduces and analyzes the dynamical system model with the theory of differential systems dynamics. A pract...In order to describe the interrelation forces among different regions during the economic growth, this paper introduces and analyzes the dynamical system model with the theory of differential systems dynamics. A practical example based on a simplified model is given to analyze the dynamical process of Sichuan economy growth.展开更多
A sufficient condition is obtained for a two-agent opinion dynamical system with pro-cessing delay to experience unconditional consensus. To this end, the dynamics proposed is transformed into a general class of delay...A sufficient condition is obtained for a two-agent opinion dynamical system with pro-cessing delay to experience unconditional consensus. To this end, the dynamics proposed is transformed into a general class of delay differential equation and asymptotic stability of the origin is then analyzed. It is also shown that increasing delay can prolong the time needed for the system to realize consensus and even induce a Hopf bifurcation.展开更多
This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string...This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations (SPDEs). We show that the mean field limit as N -+ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.展开更多
A stochastic celhflar automaton (CA) model for activated sludge system (ASS) is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary diff...A stochastic celhflar automaton (CA) model for activated sludge system (ASS) is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations (ODEs) of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, com- plexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.展开更多
基金Project(2006AA04Z405) supported by the National High Technology Research and Development Program of ChinaProject(3102019) supported by Beijing Municipal Natural Science Foundation,China
文摘In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.
文摘This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of constructive and destructive chemical reactions are reported. Convergent solutions of the resulting differential systems are presented in series forms. Characteristics of various sundry parameters on the velocity, concentration, skin friction and local Sherwood number are analyzed and discussed.
基金This research is supported by the National Natural Science Foundation of China(No.70171021)
文摘In order to describe the interrelation forces among different regions during the economic growth, this paper introduces and analyzes the dynamical system model with the theory of differential systems dynamics. A practical example based on a simplified model is given to analyze the dynamical process of Sichuan economy growth.
基金This work was jointly supported by National Natural Science Foundation of China (11401577) and Youth Top-notch Talent Support Program of NUDT (2014-2017).
文摘A sufficient condition is obtained for a two-agent opinion dynamical system with pro-cessing delay to experience unconditional consensus. To this end, the dynamics proposed is transformed into a general class of delay differential equation and asymptotic stability of the origin is then analyzed. It is also shown that increasing delay can prolong the time needed for the system to realize consensus and even induce a Hopf bifurcation.
基金supported by National Natural Science Foundation of China(Grant No.91130005)the US Army Research Office(Grant No.W911NF-11-1-0101)
文摘This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations (SPDEs). We show that the mean field limit as N -+ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.
基金This research was supported by the National Natural Science Foundation of China (No. 30870397) and the State Key Laboratory of Vegetation and Environmental Change.
文摘A stochastic celhflar automaton (CA) model for activated sludge system (ASS) is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations (ODEs) of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, com- plexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.