On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict ...On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination,different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters(injection pressure,ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.展开更多
The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals ...The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coefficients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For regime-switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent regime-switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.展开更多
There is an explicit and implicit assumption in multimodal traffic equilibrium models, that is, if the equilibrium exists, then it will also occur. The assumption is very idealized; in fact, it may be shown that the q...There is an explicit and implicit assumption in multimodal traffic equilibrium models, that is, if the equilibrium exists, then it will also occur. The assumption is very idealized; in fact, it may be shown that the quite contrary could happen, because in multimodal traffic network, especially in mixed traffic conditions the interaction among traffic modes is asymmetric and the asymmetric interaction may result in the instability of traffic system. In this paper, to study the stability of multimodal traffic system, we respectively present the travel cost function in mixed traffic conditions and in traffic network with dedicated bus lanes. Based on a day-to-day dynamical model, we study the evolution of daily route choice of travelers in multimodal traffic network using 10000 random initial values for different cases. From the results of simulation, it can be concluded that the asymmetric interaction between the cars and buses in mixed traffic conditions can lead the traffic system to instability when traffic demand is larger. We also study the effect of travelers' perception error on the stability of multimodal traffic network. Although the larger perception error can alleviate the effect of interaction between cars and buses and improve the stability of traffic system in mixed traffic conditions, the traffic system also become instable when the traffic demand is larger than a number. For all cases simulated in this study, with the same parameters, traffic system with dedicated bus lane has better stability for traffic demand than that in mixed traffic conditions. We also find that the network with dedicated bus lane has higher portion of travelers by bus than it of mixed traffic network. So it can be concluded that building dedicated bus lane can improve the stability of traffic system and attract more travelers to choose bus reducing the traffic congestion.展开更多
基金Supported by the National Natural Science Foundation of China(11172205,11372219,51176137)
文摘On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination,different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters(injection pressure,ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.
基金supported by National Natural Science Foundation of China (Grant Nos. 11301030, 11401169 and 11431014)Key Scientific Research Projects of Henan Province (Grant No. 16A110010)
文摘The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coefficients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For regime-switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent regime-switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.
基金Supported by the National Basic Research Development Program of China under Grant No. 2012CB725401, Fundamental Research Funds for the Central Universities under Grant No. 2012JBZ 005, Funds for International Cooperation and Exchange of the National Natural Science Foundation of China under Grant No. 71210001, National Natural Science Foundation of China under Grant No. 71271023, Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant No. 201170, and Beijing Nova Program under Grant No. 2009A15
文摘There is an explicit and implicit assumption in multimodal traffic equilibrium models, that is, if the equilibrium exists, then it will also occur. The assumption is very idealized; in fact, it may be shown that the quite contrary could happen, because in multimodal traffic network, especially in mixed traffic conditions the interaction among traffic modes is asymmetric and the asymmetric interaction may result in the instability of traffic system. In this paper, to study the stability of multimodal traffic system, we respectively present the travel cost function in mixed traffic conditions and in traffic network with dedicated bus lanes. Based on a day-to-day dynamical model, we study the evolution of daily route choice of travelers in multimodal traffic network using 10000 random initial values for different cases. From the results of simulation, it can be concluded that the asymmetric interaction between the cars and buses in mixed traffic conditions can lead the traffic system to instability when traffic demand is larger. We also study the effect of travelers' perception error on the stability of multimodal traffic network. Although the larger perception error can alleviate the effect of interaction between cars and buses and improve the stability of traffic system in mixed traffic conditions, the traffic system also become instable when the traffic demand is larger than a number. For all cases simulated in this study, with the same parameters, traffic system with dedicated bus lane has better stability for traffic demand than that in mixed traffic conditions. We also find that the network with dedicated bus lane has higher portion of travelers by bus than it of mixed traffic network. So it can be concluded that building dedicated bus lane can improve the stability of traffic system and attract more travelers to choose bus reducing the traffic congestion.
