This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's t...This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.展开更多
The vortex pump is suitable for salt solution transportation. But the salt-out flow mechanism in the pump has not been understood fully. Salt-out layer formation and growth rate are closely related to crystal particle...The vortex pump is suitable for salt solution transportation. But the salt-out flow mechanism in the pump has not been understood fully. Salt-out layer formation and growth rate are closely related to crystal particle motion and concentration distribution. Study on the particle hydrodynamic characteristics in the pump volute becomes a key problem, because the crystal particles are mainly distributing in this zone after they enter the pump. Phase Doppler particle analyzer（PDPA） is used to measure the two-phase flow field in a model pump volute to get more understanding about the salt-out phenomenon. The crystal particle velocities are obtained in all three peripheral, radial and axial directions. Particle size and particle number density（PND） measurements are also performed in the experiment. Results are presented and discussed along the radial direction under different pump operating conditions, as well as various axial measurement positions. It is found that particle velocity gradient of peripheral component varies with the pump discharge. There is a turning point of relation between peripheral velocity component and discharge. Radial flow velocity curves look like a saddle shape and velocity magnitudes are changing greatly with the discharge. The non-equilibrium velocity feature between liquid and solid phase on this direction is also remarkable. Particles flow into the impeller at radial position R〈I, and the axial velocity component increases in this region. The particle size curve shows an open-up parabola distribution. The largest particles are distributing near the casing peripheral wall. As flow rate increases, accordingly PND increases. It also grows up in the axial-outward direction towards the suction cover. Crystal particle aggregation phenomenon can be revealed from the analysis of particle size and PND distribution, and the aggregation region is determined as well. Research results are helpful for optimal design of this kind of pump preventing salt-out.展开更多
The precipitation during landfall of typhoon Haitang （2005） showed asymmetric structures （left side/right side of the track）. Analysis of Weather Research and Forecasting model simulation data showed that rainfall...The precipitation during landfall of typhoon Haitang （2005） showed asymmetric structures （left side/right side of the track）. Analysis of Weather Research and Forecasting model simulation data showed that rainfall on the right side was more than 15 times stronger than on the left side. The causes were analyzed by focusing on comparing the water vapor flux, stability and upward motion between the two sides. The major results were as follows： （1） Relative humidity on both sides was over 80%, whereas the convergence of water vapor flux in the lower troposphere was about 10 times larger on the right side than on the left side. （2） Both sides featured conditional symmetric instability [MPV （moist potential vorticity） 〈0], but the right side was more unstable than the left side. （3） Strong （weak） upward motion occurred throughout the troposphere on the right （left） side. The Q vector diagnosis suggested that large-scale and mesoscale forcing accounted for the difference in vertical velocity. Orographic lift and surface friction forced the development of the asymmetric precipitation pattern. On the right side, strong upward motion from the forcing of different scale weather systems and topography caused a substantial release of unstable energy and the transportation of water vapor from the lower to the upper troposphere, which produced torrential rainfall. However, the above conditions on the left side were all much weaker, which led to weaker rainfall. This may have been the cause of the asymmetric distribution of rainfall during the landfall of typhoon Haitang.展开更多
Particle-fluid transport and placement mechanism in tortuous fracture played a crucial role in uncon-ventional reservoirs.Currently,most studies focused on mono-size proppant with fluid transport pro-cesses in tortuou...Particle-fluid transport and placement mechanism in tortuous fracture played a crucial role in uncon-ventional reservoirs.Currently,most studies focused on mono-size proppant with fluid transport pro-cesses in tortuous fractures.However,the mixture-size proppant with fluid movement mechanism in tortuous fracture was still uncommon.Therefore,this study designed and applied a series of experiments with a physical analog model of a tortuous fracture with 120°and 90°-angled bends and combined high-speed camera-based equipment.This experimental system was used to track different-mixture-sized proppant particle motion trajectories for a series of proppant injection schemes;The following conclu-sions were drawn from this study:1.The pile-up processes mechanism in all investigated schemes were similar and could be reduced to four main stages.2.The packing structure at both sides of the fracture wall had different variation rates,which were controlled by the mix ratio(change from 1∶1-1∶5)of proppant size.3.Some new packing patterns,such as Zebra Stripe,had occurred,controlled by the different proppant injection sequences.4.Small-sized mono-proppant(30/50 mesh)had the highest transport efficiency in the tortuous fracture,followed by the mixed-sized multi-proppant(10/20 mesh:30/50 mesh),large-sized proppant(10/20 mesh)was the worst.5.An optimized alternating in-jection mode was recommended as injecting small-sized proppant first(30/50 mesh)and followed by mixed-sized multi-proppant(10/20 mesh:30/50 mesh),which could contribute to obtaining the optimal both proppant packing height and travel distance in tortuous fracture.6.Two correlations were devel-oped for predicting the proppant packing height and transportation distance.展开更多
基金supported by National Basic Research Program of China (Grant No.2007CB814900)(Financial Risk)
文摘This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.
基金supported by National Natural Science Foundation of China (Grant No. 50476068)Jiangsu Provincial Postgraduate Cultivation Innovation Project of China (Grant No. CX07B_093z)
文摘The vortex pump is suitable for salt solution transportation. But the salt-out flow mechanism in the pump has not been understood fully. Salt-out layer formation and growth rate are closely related to crystal particle motion and concentration distribution. Study on the particle hydrodynamic characteristics in the pump volute becomes a key problem, because the crystal particles are mainly distributing in this zone after they enter the pump. Phase Doppler particle analyzer（PDPA） is used to measure the two-phase flow field in a model pump volute to get more understanding about the salt-out phenomenon. The crystal particle velocities are obtained in all three peripheral, radial and axial directions. Particle size and particle number density（PND） measurements are also performed in the experiment. Results are presented and discussed along the radial direction under different pump operating conditions, as well as various axial measurement positions. It is found that particle velocity gradient of peripheral component varies with the pump discharge. There is a turning point of relation between peripheral velocity component and discharge. Radial flow velocity curves look like a saddle shape and velocity magnitudes are changing greatly with the discharge. The non-equilibrium velocity feature between liquid and solid phase on this direction is also remarkable. Particles flow into the impeller at radial position R〈I, and the axial velocity component increases in this region. The particle size curve shows an open-up parabola distribution. The largest particles are distributing near the casing peripheral wall. As flow rate increases, accordingly PND increases. It also grows up in the axial-outward direction towards the suction cover. Crystal particle aggregation phenomenon can be revealed from the analysis of particle size and PND distribution, and the aggregation region is determined as well. Research results are helpful for optimal design of this kind of pump preventing salt-out.
基金supported by Public Sector (Meteorology) Research of China (Grant Nos.GYHY 201306012 and GYHY201506007)the National Natural Science Foundation of China (Grant Nos.40875025,41175050,41475039 and 41475041)the Shanghai Natural Science Foundation of China (Grant No.08ZR1422900)
文摘The precipitation during landfall of typhoon Haitang （2005） showed asymmetric structures （left side/right side of the track）. Analysis of Weather Research and Forecasting model simulation data showed that rainfall on the right side was more than 15 times stronger than on the left side. The causes were analyzed by focusing on comparing the water vapor flux, stability and upward motion between the two sides. The major results were as follows： （1） Relative humidity on both sides was over 80%, whereas the convergence of water vapor flux in the lower troposphere was about 10 times larger on the right side than on the left side. （2） Both sides featured conditional symmetric instability [MPV （moist potential vorticity） 〈0], but the right side was more unstable than the left side. （3） Strong （weak） upward motion occurred throughout the troposphere on the right （left） side. The Q vector diagnosis suggested that large-scale and mesoscale forcing accounted for the difference in vertical velocity. Orographic lift and surface friction forced the development of the asymmetric precipitation pattern. On the right side, strong upward motion from the forcing of different scale weather systems and topography caused a substantial release of unstable energy and the transportation of water vapor from the lower to the upper troposphere, which produced torrential rainfall. However, the above conditions on the left side were all much weaker, which led to weaker rainfall. This may have been the cause of the asymmetric distribution of rainfall during the landfall of typhoon Haitang.
基金supported by the Natural Science Foundation of Sichuan province of"Settlement and Transport Mechanism of Biomimetic Dandelion Proppant in Fracture"(grant No.23NSFSC5596).
文摘Particle-fluid transport and placement mechanism in tortuous fracture played a crucial role in uncon-ventional reservoirs.Currently,most studies focused on mono-size proppant with fluid transport pro-cesses in tortuous fractures.However,the mixture-size proppant with fluid movement mechanism in tortuous fracture was still uncommon.Therefore,this study designed and applied a series of experiments with a physical analog model of a tortuous fracture with 120°and 90°-angled bends and combined high-speed camera-based equipment.This experimental system was used to track different-mixture-sized proppant particle motion trajectories for a series of proppant injection schemes;The following conclu-sions were drawn from this study:1.The pile-up processes mechanism in all investigated schemes were similar and could be reduced to four main stages.2.The packing structure at both sides of the fracture wall had different variation rates,which were controlled by the mix ratio(change from 1∶1-1∶5)of proppant size.3.Some new packing patterns,such as Zebra Stripe,had occurred,controlled by the different proppant injection sequences.4.Small-sized mono-proppant(30/50 mesh)had the highest transport efficiency in the tortuous fracture,followed by the mixed-sized multi-proppant(10/20 mesh:30/50 mesh),large-sized proppant(10/20 mesh)was the worst.5.An optimized alternating in-jection mode was recommended as injecting small-sized proppant first(30/50 mesh)and followed by mixed-sized multi-proppant(10/20 mesh:30/50 mesh),which could contribute to obtaining the optimal both proppant packing height and travel distance in tortuous fracture.6.Two correlations were devel-oped for predicting the proppant packing height and transportation distance.
