HYDRODYNAMICAL INSTABILITY OF NEWTONIAN FLOW BEFORE AN AXISYMMETRIC SUDDEN CONTRACTION

The sizes of the vortex region before the axisymmetric sudden contraction of the circular pipe at the Newtonian flow have been investigated. Area ratios 0.250 and 0.500 were considered. The sizes of the vortex region have the extreme dependence with a maximum at the transition of the laminar flow into a turbulent flow one. When the Reynolds number at the laminar flow increase, these sizes also increase, and they decrease at the turbulent flow. In both cases, the sizes of the vortex region are proportional to the Reynolds number. A transition region between laminar flow and turbulent flow lies in the range of the Reynolds number from 3000 to 5300 and 750…1300, determined by the diameter of a bigger pipe of sudden expansion and a step height correspondingly

Extreme Dependence in International Stock Markets

Extreme Dependence in International Stock Markets

Extreme Dependence in International Stock Markets

Extreme Dependence in International Stock Markets

The haze extreme co-movements in Beijing–Tianjin–Hebei region and its extreme dependence pattern recognitions

Extreme haze was often observed at many locations in Beijing–Tianjin–Hebei region within several hours when they occurred, which is referred to as extreme co-movements and extreme dependence in statistics. This article applies tail quotient correlation coefficient to explore the temporal and spatial extreme dependence patterns of haze in this region. Hourly PM2.5 station-level data during 2014–2018 are used, and the results show that the tail quotient correlation coefficient between stations increases with month. Specifically, the simultaneous extreme dependence was strong in the fourth season, while the haze was severe. In the first season, while the haze was also severe, the extreme hazes only show strong co-movements with a time difference. These observations lead to the study of two special scenarios, that is, the concurrence/extreme dependence of the worst extreme haze and its lag effects. City clusters suffering simultaneous extreme haze or with certain time difference as well as the most frequently co-movement cities are identified. The extreme co-movements of these cities and the reasons for their occurrences have strong implications for improving the PM2.5 joint prevention and control in the Beijing–Tianjin–Hebei region. The importance of lag effects is also reflected in the precedence order of the extreme haze’s appearance. It is especially useful when setting the mechanism of the early warning system which can be triggered by the first appearance of extreme haze. The precedence orders also avail in investigating the transmission path of the haze, based on which more precise meteorological models can be made to benefit the haze forecasting of the region.