Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance

To enhance the comprehensive performance of artillery internal ballistics—encompassing power,accuracy,and service life—this study proposed a multi-stage multidisciplinary design optimization(MS-MDO)method.First,the comprehensive artillery internal ballistic dynamics(AIBD)model,based on propellant combustion,rotation band engraving,projectile axial motion,and rifling wear models,was established and validated.This model was systematically decomposed into subsystems from a system engineering perspective.The study then detailed the MS-MDO methodology,which included Stage I(MDO stage)employing an improved collaborative optimization method for consistent design variables,and Stage II(Performance Optimization)focusing on the independent optimization of local design variables and performance metrics.The methodology was applied to the AIBD problem.Results demonstrated that the MS-MDO method in Stage I effectively reduced iteration and evaluation counts,thereby accelerating system-level convergence.Meanwhile,Stage II optimization markedly enhanced overall performance.These comprehensive evaluation results affirmed the effectiveness of the MS-MDO method.

Uncertainties of ENSO-related Regional Hadley Circulation Anomalies within Eight Reanalysis Datasets

El Nino-Southern Oscillation(ENSO),the leading mode of global interannual variability,usually intensifies the Hadley Circulation(HC),and meanwhile constrains its meridional extension,leading to an equatorward movement of the jet system.Previous studies have investigated the response of HC to ENSO events using different reanalysis datasets and evaluated their capability in capturing the main features of ENSO-associated HC anomalies.However,these studies mainly focused on the global HC,represented by a zonal-mean mass stream function(MSF).Comparatively fewer studies have evaluated HC responses from a regional perspective,partly due to the prerequisite of the Stokes MSF,which prevents us from integrating a regional HC.In this study,we adopt a recently developed technique to construct the three-dimensional structure of HC and evaluate the capability of eight state-of-the-art reanalyses in reproducing the regional HC response to ENSO events.Results show that all eight reanalyses reproduce the spatial structure of HC responses well,with an intensified HC around the central-eastern Pacific but weakened circulations around the Indo-Pacific warm pool and tropical Atlantic.The spatial correlation coefficient of the three-dimensional HC anomalies among the different datasets is always larger than 0.93.However,these datasets may not capture the amplitudes of the HC responses well.This uncertainty is especially large for ENSO-associated equatorially asymmetric HC anomalies,with the maximum amplitude in Climate Forecast System Reanalysis(CFSR)being about 2.7 times the minimum value in the Twentieth Century Reanalysis(20CR).One should be careful when using reanalysis data to evaluate the intensity of ENSO-associated HC anomalies.

Research on Regulation Method of Energy Storage System Based on Multi-Stage Robust Optimization

To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.

Fracture sealing performance of granular lost circulation materials at elevated temperature:A theoretical and coupled CFD-DEM simulation study

Lost circulation is a common downhole problem of drilling in geothermal and high-temperature,high-pressure(HTHP)formations.Lost circulation material(LCM)is a regular preventive and remedial measure for lost circulation.However,conventional LCMs seem ineffective in high-temperature formations.This may be due to the changes in the mechanical properties of LCMs and their sealing performance under high-temperature conditions.To understand how high temperature affects the fracture sealing performance of LCMs,we developed a coupled computational fluid dynamics-discrete element method(CFD-DEM)model to simulate the behavior of granular LCMs in fractures.We summarized the literature on the effects of high temperature on the mechanical properties of LCMs and the rheological properties of drilling fluid.We conducted sensitivity analyses to investigate how changing LCM slurry properties affected the fracture sealing efficiency at increasing temperatures.The results show that high temperature reduces the size,strength,and friction coefficient of LCMs as well as the drilling fluid viscosity.Smaller,softer,and less frictional LCM particles have lower bridging probability and slower bridging initiation.Smaller particles tend to form dual-particle bridges rather than single-particle bridges.These result in a deeper,tighter,but unstable sealing zone.Reduced drilling fluid viscosity leads to faster and shallower sealing zones.

A novel predictor of unsustained return of spontaneous circulation in cardiac arrest patients through a combination of capnography and pulse oximetry: a multicenter observational study

BACKGROUND:Unsustained return of spontaneous circulation(ROSC)is a critical barrier to survival in cardiac arrest patients.This study examined whether end-tidal carbon dioxide(ETCO_(2))and pulse oximetry photoplethysmogram(POP)parameters can be used to identify unsustained ROSC.METHODS:We conducted a multicenter observational prospective cohort study of consecutive patients with cardiac arrest from 2013 to 2014.Patients’general information,ETCO_(2),and POP parameters were collected and statistically analyzed.RESULTS:The included 105 ROSC episodes(from 80 cardiac arrest patients)comprised 51 sustained ROSC episodes and 54 unsustained ROSC episodes.The 24-hour survival rate was significantly higher in the sustained ROSC group than in the unsustained ROSC group(29.2%vs.9.4%,P<0.05).The logistic regression analysis showed that the difference between after and before ROSC in ETCO_(2)(ΔETCO_(2))and the difference between after and before ROCS in area under the curve of POP(ΔAUCp)were independently associated with sustained ROSC(odds ratio[OR]=0.931,95%confi dence interval[95%CI]0.881-0.984,P=0.011 and OR=0.998,95%CI 0.997-0.999,P<0.001).The area under the receiver operating characteristic curve ofΔETCO_(2),ΔAUCp,and the combination of both to predict unsustained ROSC were 0.752(95%CI 0.660-0.844),0.883(95%CI 0.818-0.948),and 0.902(95%CI 0.842-0.962),respectively.CONCLUSION:Patients with unsustained ROSC have a poor prognosis.The combination ofΔETCO_(2) andΔAUCp showed signifi cant predictive value for unsustained ROSC.

Application Effect of External Diaphragm Pacemaker Combined with Active Respiratory Circulation Technology in Pulmonary Rehabilitation of Perioperative Lung Cancer Patients

Aim: To explore the application effect of external diaphragm pacemaker combined with active respiratory circulation technology in pulmonary rehabilitation of perioperative lung cancer patients. Methods: A total of 98 lung cancer patients admitted to our hospital from April 2020 to November 2021 were selected as the observation objects, and then divided into a control group and an observation group using the random number table method, with 49 cases in each group. The control group received routine admission guidance and active respiratory circulation training, while the observation group was supplemented with external diaphragm pacemaker on the basis of the control group. The intervention effect was evaluated by blood gas indicators, pulmonary function indicators, diaphragm function indicators, sputum comfort degree, and activity tolerance indicators before and after intervention. Results: Before intervention, there were no significant differences in blood gas analysis indicators, pulmonary function indicators, diaphragm function indicators, sputum comfort degree, and activity tolerance indicators between the two groups (P > 0.05). After intervention, the improvement degree of the above indicators in the observation group was higher than that in the control group (P < 0.05). Conclusions: The application of external diaphragm pacemaker combined with active respiratory circulation technology in pulmonary rehabilitation of perioperative lung cancer patients is significant, which can effectively improve the pulmonary function, blood gas function, and diaphragm function of lung cancer patients after surgery, and improve the activities of daily living and quality of life of patients.

Numerical simulations of Atlantic meridional overturning circulation(AMOC)from OMIP experiments and its sensitivity to surface forcing

Atlantic meridional overturning circulation(AMOC)plays an important role in transporting heat meridionally in the Earth’s climate system and is also a key metrical tool to verify oceanic general circulation models.Two OMIP(Ocean Model Intercomparison Project phase 1 and 2)simulations with LICOM3(version 3 of the LASG/IAP Climate System Ocean Model)developed at the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG),Institute of Atmospheric Physics(IAP),are compared in this study.Both simulations well reproduce the fundamental characteristics of the AMOC,but the OMIP1 simulation shows a significantly stronger AMOC than the OMIP2 simulation.Because the LICOM3 configurations are identical between these two experiments,any differences between them must be attributed to the surface forcing data.Further analysis suggests that sea surface salinity(SSS)differences should be mainly responsible for the enhanced AMOC in the OMIP1 simulation,but sea surface temperature(SST)also play an unignorable role in modulating AMOC.In the North Atlantic,where deep convection occurs,the SSS in OMIP1 is more saline than that in OMIP1.We find that in the major region of deep convection,the change of SSS has more significant effect on density than the change of SST.As a result,the SSS was more saline than that in OMIP2,leading to stronger deep convection and subsequently intensify the AMOC.We conduct a series of numerical experiments with LICOM3,and the results confirmed that the changes in SSS have more significant effect on the strength of AMOC than the changes in SST.

Correction:Establishment of a prediction model for prehospital return of spontaneous circulation in out-of-hospital patients with cardiac arrest

This is an erratum to an already published paper named“Establishment of a prediction model for prehospital return of spontaneous circulation in out-ofhospital patients with cardiac arrest”.We found errors in the affiliated institution of the authors.We apologize for our unintentional mistake.Please note,these changes do not affect our results.

Circulation Pattern Controls of Summer Temperature Anomalies in Southern Africa

This study investigates the relationship between circulation patterns and austral summer temperature anomalies in southern Africa. The results show that the formation of continental lows tends to increase the thickness of the lower atmosphere. Further, the distinct variabilities of high and low pressure under the circulation types, influence air mass advection from the adjacent oceans, as well as atmospheric stability over land. Stronger anticyclonic circulation at the western branch of the Mascarene high-pressure system enhances the low-level cold air advection by southeast winds,decreases the thickness, and lowers the temperature over a majority of the land in southern Africa. Conversely, a weaker Mascarene High, coupled with enhanced cyclonic activity in the southwest Indian Ocean increases low-level warm air advection and increases temperature anomalies over vast regions in southern Africa. The ridging of a closed South Atlantic anticyclone at the southern coast of southern Africa results in colder temperatures near the tip of southern Africa due to enhanced low-level cold air advection by southeast winds. However, when the ridge is weak and westerly winds dominate the southern coast of southern Africa, these areas experience temperature increases. The northward track of the Southern Hemisphere mid-latitude cyclone, which can be linked to the negative Southern Annular Mode, reduces the temperature in the southwestern part of southern Africa. Also, during the analysis period, El Ni?o was associated with temperature increases over the central parts of southern Africa;while the positive Indian Ocean dipole was linked to a temperature increase over the northeastern, northwestern, and southwestern parts of southern Africa.

Spatio-temporal Variation Characteristics of Extreme Climate Events and Their Teleconnections to Large-scale Ocean-atmospheric Circulation Patterns in Huaihe River Basin,China During 1959–2019

Huaihe River Basin(HRB) is located in China’s north-south climatic transition zone,which is very sensitive to global climate change.Based on the daily maximum temperature,minimum temperature,and precipitation data of 40 meteorological stations and nine monthly large-scale ocean-atmospheric circulation indices data during 1959–2019,we present an assessment of the spatial and temporal variations of extreme temperature and precipitation events in the HRB using nine extreme climate indices,and analyze the teleconnection relationship between extreme climate indices and large-scale ocean-atmospheric circulation indices.The results show that warm extreme indices show a significant(P < 0.05) increasing trend,while cold extreme indices(except for cold spell duration) and diurnal temperature range(DTR) show a significant decreasing trend.Furthermore,all extreme temperature indices show significant mutations during 1959-2019.Spatially,a stronger warming trend occurs in eastern HRB than western HRB,while maximum 5-d precipitation(Rx5day) and rainstorm days(R25) show an increasing trend in the southern,central,and northwestern regions of HRB.Arctic oscillation(AO),Atlantic multidecadal oscillation(AMO),and East Atlantic/Western Russia(EA/WR) have a stronger correlation with extreme climate indices compared to other circulation indices.AO and AMO(EA/WR) exhibit a significant(P < 0.05) negative(positive)correlation with frost days and diurnal temperature range.Extreme warm events are strongly correlated with the variability of AMO and EA/WR in most parts of HRB,while extreme cold events are closely related to the variability of AO and AMO in eastern HRB.In contrast,AMO,AO,and EA/WR show limited impacts on extreme precipitation events in most parts of HRB.

Evaluation of the Mechanisms Acting on the Atlantic Meridional Overturning Circulation in CESM2 for the 1pctCO_(2) Experiment

The Atlantic Meridional Overturning Circulation(AMOC)is a crucial component of the Earth’s climate system due to its fundamental role in heat distribution,carbon and oxygen transport,and the weather.Other climate components,such as the atmosphere and sea ice,influence the AMOC.Evaluating the physical mechanisms of those interactions is paramount to increasing knowledge about AMOC’s functioning.In this study,the authors used outputs from the Community Earth System Model version 2 and observational data to investigate changes in theAMOC and the associated physical processes.Two DECK experiments were evaluated:piControl and 1pctCO_(2),with an annual increase of 1%of atmospheric CO_(2).The analysis revealed a significant decrease in the AMOC,associated with changes in mixed layer depth and buoyancy in high latitudes of the North Atlantic,resulting in the shutdown of deep convection and potentially affecting the formation of North Atlantic Deep Water and Antarctic Bottom Water.A vital aspect observed in this study is the association between increased runoff and reduced water evaporation,giving rise to a positive feedback process.Consequently,the rates of freshwater spreading have intensified during this period,which could lead to an accelerated disruption of the AMOC beyond the projections of existing models.

Westward extension of summer atmospheric circulation over the North Pacific after the 1990s

本文研究了20世纪90年代前后夏季北太平洋大气环流(NPcirculation)向西扩展,并探讨了其可能的原因.结果表明,在1961-1983年期间NP中心主要位于东北太平洋,而在1994-2016年期间NP中心发生西移,至北太平洋中部进一步分析指出,90年代以后NP活动中心的西移和春季中纬度北太平洋海温(SST_NP)与NP关系的加强有关.春季SST_NP异常通过引起后期夏季北太平洋中部地表热通量(即感热通量和潜热通量)和垂直运动异常,有利于NP活动中心向西移动,此外,20世纪90年代以后,北太平洋中部海平面气压的年际变率增加,这可能是NP向西扩展的另一原因。

Unprecedented Heatwave in Western North America during Late June of 2021: Roles of Atmospheric Circulation and Global Warming

An extraordinary and unprecedented heatwave swept across western North America(i.e.,the Pacific Northwest)in late June of 2021,resulting in hundreds of deaths,a massive die-off of sea creatures off the coast,and horrific wildfires.Here,we use observational data to find the atmospheric circulation variabilities of the North Pacific and Arctic-Pacific-Canada patterns that co-occurred with the development and mature phases of the heatwave,as well as the North America pattern,which coincided with the decaying and eastward movement of the heatwave.Climate models from the Coupled Model Intercomparison Project(Phase 6)are not designed to simulate a particular heatwave event like this one.Still,models show that greenhouse gases are the main reason for the long-term increase of average daily maximum temperature in western North America in the past and future.

Trace Elements of Multi-stage Minerals and Titanite U-Pb Dating for the Gneisses from Liansan Island,Sulu UHPM Belt

Gneisses with anatectic characteristics from the Liansan island in the Sulu UHPM(ultra-high pressure metamorphic)belt were studied for petrography,titanite U-Pb dating and mineral geochemistry.Three origins of garnets are distinguished:metamorphic garnet,peritectic garnet and anatectic garnet,which are formed in the stages of peak metamorphism,retrograde anatexis and melt crystallization,respectively.The euhedral titanite has a high content of REE and high Th/U ratios,which is interpreted as indicating that it was newly-formed from an anatectic melt.The LA-ICP-MS titanite U-Pb dating yields 214-217 Ma ages for the titanite(melt)crystallization.The distribution of trace elements varies in response to the different host minerals at different stages.At the peak metamorphic stage,Y and HREE are mainly hosted by garnet,Ba and Rb by phengite,Sr,Nb,Ta,Pb,Th,U and LREE by allanite and Y,U and HREE by zircon.During partial melting,Y,Pb,Th,U and REE are released into the melt,which causes a dramatic decline of these element contents in the retrograde minerals.Finally,titanite absorbs most of the Nb,U,LREE and HREE from the melt.Therefore,the different stages of metamorphism have different mineral assemblages,which host different trace elements.

Circulation Patterns Linked to the Positive Sub-Tropical Indian Ocean Dipole

The positive phase of the subtropical Indian Ocean dipole(SIOD)is one of the climatic modes in the subtropical southern Indian Ocean that influences the austral summer inter-annual rainfall variability in parts of southern Africa.This paper examines austral summer rain-bearing circulation types(CTs)in Africa south of the equator that are related to the positive SIOD and the dynamics through which specific rainfall regions in southern Africa can be influenced by this relationship.Four austral summer rain-bearing CTs were obtained.Among the four CTs,the CT that featured(i)enhanced cyclonic activity in the southwest Indian Ocean;(ii)positive widespread rainfall anomaly in the southwest Indian Ocean;and(iii)low-level convergence of moisture fluxes from the tropical South Atlantic Ocean,tropical Indian Ocean,and the southwest Indian Ocean,over the south-central landmass of Africa,was found to be related to the positive SIOD climatic mode.The relationship also implies that positive SIOD can be expected to increase the amplitude and frequency of occurrence of the aforementioned CT.The linkage between the CT related to the positive SIOD and austral summer homogeneous regions of rainfall anomalies in Africa south of the equator showed that it is the principal CT that is related to the inter-annual rainfall variability of the south-central regions of Africa,where the SIOD is already known to significantly influence its rainfall variability.Hence,through the large-scale patterns of atmospheric circulation associated with the CT,the SIOD can influence the spatial distribution and intensity of rainfall over the preferred landmass through enhanced moisture convergence.

Overview of multi-stage charging strategies for Li-ion batteries

To reduce the carbon footprint in the transportation sector and improve overall vehicle efficiency,a large number of electric vehicles are being manufactured.This is due to the fact that environmental concerns and the depletion of fossil fuels have become significant global problems.Lithium-ion batteries(LIBs)have been distinguished themselves from alternative energy storage technologies for electric vehicles(EVs) due to superior qualities like high energy and power density,extended cycle life,and low maintenance cost to a competitive price.However,there are still certain challenges to be solved,like EV fast charging,longer lifetime,and reduced weight.For fast charging,the multi-stage constant current(MSCC) charging technique is an emerging solution to improve charging efficiency,reduce temperature rise during charging,increase charging/discharging capacities,shorten charging time,and extend the cycle life.However,there are large variations in the implementation of the number of stages,stage transition criterion,and C-rate selection for each stage.This paper provides a review of these problems by compiling information from the literature.An overview of the impact of different design parameters(number of stages,stage transition,and C-rate) that the MSCC charging techniques have had on the LIB performance and cycle life is described in detail and analyzed.The impact of design parameters on lifetime,charging efficiency,charging and discharging capacity,charging speed,and rising temperature during charging is presented,and this review provides guidelines for designing advanced fast charging strategies and determining future research gaps.

Establishment of a prediction model for prehospital return of spontaneous circulation in out-of-hospital patients with cardiac arrest

BACKGROUND Out-of-hospital cardiac arrest(OHCA)is a leading cause of death worldwide.AIM To explore factors influencing prehospital return of spontaneous circulation(P-ROSC)in patients with OHCA and develop a nomogram prediction model.METHODS Clinical data of patients with OHCA in Shenzhen,China,from January 2012 to December 2019 were retrospectively analyzed.Least absolute shrinkage and selection operator(LASSO)regression and multivariate logistic regression were applied to select the optimal factors predicting P-ROSC in patients with OHCA.A nomogram prediction model was established based on these influencing factors.Discrimination and calibration were assessed using receiver operating charac-teristic(ROC)and calibration curves.Decision curve analysis(DCA)was used to evaluate the model’s clinical utility.RESULTS Among the included 2685 patients with OHCA,the P-ROSC incidence was 5.8%.LASSO and multivariate logistic regression analyses showed that age,bystander cardiopulmonary resuscitation(CPR),initial rhythm,CPR duration,ventilation mode,and pathogenesis were independent factors influencing P-ROSC in these patients.The area under the ROC was 0.963.The calibration plot demonstrated that the predicted P-ROSC model was concordant with the actual P-ROSC.The good clinical usability of the prediction model was confirmed using DCA.CONCLUSION The nomogram prediction model could effectively predict the probability of P-ROSC in patients with OHCA.

Multi-Stage Improvement of Marine Predators Algorithm and Its Application

The metaheuristic algorithms are widely used in solving the parameters of the optimization problem.The marine predators algorithm(MPA)is a novel population-based intelligent algorithm.Although MPA has shown a talented foraging strategy,it still needs a balance of exploration and exploitation.Therefore,a multi-stage improvement of marine predators algorithm(MSMPA)is proposed in this paper.The algorithm retains the advantage of multistage search and introduces a linear flight strategy in the middle stage to enhance the interaction between predators.Predators further away from the historical optimum are required to move,increasing the exploration capability of the algorithm.In the middle and late stages,the searchmechanism of particle swarmoptimization(PSO)is inserted,which enhances the exploitation capability of the algorithm.This means that the stochasticity is decreased,that is the optimal region where predators jumping out is effectively stifled.At the same time,self-adjusting weight is used to regulate the convergence speed of the algorithm,which can balance the exploration and exploitation capability of the algorithm.The algorithm is applied to different types of CEC2017 benchmark test functions and threemultidimensional nonlinear structure design optimization problems,compared with other recent algorithms.The results show that the convergence speed and accuracy of MSMPA are significantly better than that of the comparison algorithms.

An internal circulation iron-carbon micro-electrolysis reactor for aniline wastewater treatment:Parameter optimization,degradation pathways and mechanism

Aniline is a vital industrial raw material.However,highly-toxic aniline wastewater usually deteriorated effluent quality,posed a threat to human health and ecosystem safety.Therefore,this study reported a novel internal circulation iron-carbon micro-electrolysis(ICE)reactor to treat aniline wastewater.The effects of reaction time,pH,aeration rate and iron-carbon(Fe/C)ratio on the removal rate of aniline and the chemical oxygen demand were investigated using single-factor experiments.This process exhibited high aniline degradation performance of approximately 99.86% under optimal operating conditions(reaction time=20 min,pH=3,aeration rate=0.5 m3·h^(-1),and Fe/C=1:2).Based on the experimental results,the response surface method was applied to optimize the aniline removal rate.The Box–Behnken method was used to obtain the interaction effects of three main factors.The result showed that the reaction time had a dominant effect on the removal rate of aniline.The highest aniline removal rate was obtained at pH of 2,aeration rate of 0.5 m^(3)·h^(-1)and reaction time of 30 min.Under optional experimental conditions,the aniline content of effluent was reduced to 3 mg·L^(-1)and the removal rate was as high as 98.24%,within the 95% confidence interval(97.84%-99.32%)of the predicted values.The solution was treated and the reaction intermediates were identified by high-performance liquid chromatography,ultraviolet-visible spectroscopy,Fourier-transform infrared spectroscopy,gas chromatography-mass spectrometry,and ion chromatography.The main intermediates were phenol,benzoquinone,and carboxylic acid.These were used to propose the potential mechanism of aniline degradation in the ICE reactor.The results obtained in this study provide optimized conditions for the treatment of industrial wastewater containing aniline and can strengthen the understanding of the degradation mechanism of iron-carbon micro-electrolysis.

The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

The internal flow of a droplet in the nonlinear extensional flow field will exhibit more than two internal circulations with the variation of nonlinear intensity(E).In this paper,the effect of positions and sizes of internal circulations on internal mass transfer rate of a single spherical droplet in a nonlinear extensional flow field is studied and compared with that in a linear extensional flow field.The simulation results show that when E≥0,there are two symmetrical internal circulations in the droplet,which is the same with that in a linear extensional flow.The limit value of mass transfer rate Sh is 15,which is equal to that in a linear extensional flow,no matter how large E is.When E≤-3/7,the number of internal flow circulation of a droplet increase to four and the transfer rate Sh increases.When E=-1,the maximum internal transfer rate Sh equals 30 which is twice of that in a linear extensional flow.The generation of new flow circulations in droplets and the circulation positions will enhance mass transfer when E≤-3/7,which provides a new idea for enhancing the internal mass transfer rate of droplets.