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Equilibrium Strategies in M/M/1 Retrial Queues with Variable Service Rate
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作者 LIU Yuanyuan YAN Zhaozeng YANG Qin 《应用概率统计》 北大核心 2025年第3期448-466,共19页
We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponen... We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples. 展开更多
关键词 variable service rate retrial queues real-time adaptability equilibrium strategies ALGORITHM
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Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of i.i.d.Random Variables under Sublinear Expectations
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作者 XU Mingzhou CHENG Kun 《应用概率统计》 北大核心 2025年第3期339-352,共14页
The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the... The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space. 展开更多
关键词 complete convergence weighted sums i.i.d.random variables sublinear expectation
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Complete f-Moment Convergence for Sung’s Type Weighted Sums of Negatively Superadditive Dependent Random Variables
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作者 HU Xueping WANG Liuliu +1 位作者 HU Ke XU Zhonghao 《应用概率统计》 北大核心 2025年第4期585-601,共17页
In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergen... In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors. 展开更多
关键词 Marcinkiewicz-Zygmund inequality Rosenthal-type inequality Sung’s type randomly weighted sums negatively superadditive dependent random variables complete f-moment convergence
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Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables 被引量:1
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作者 MENG Bing WU Qunying 《应用概率统计》 CSCD 北大核心 2024年第5期710-724,共15页
In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distri... In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them. 展开更多
关键词 ANA random variables complete convergence complete moment convergence weighted sums
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Finite element approach for free vibration and transient response of bi-directional functionally graded sandwich porous skew-plates with variable thickness subjected to blast load
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作者 Hong Nguyen Thi 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第12期83-104,共22页
At the first time,the finite element method was used to model and analyze the free vibration and transient response of non-uniform thickness bi-directional functionally graded sandwich porous(BFGSP)skew plates.The who... At the first time,the finite element method was used to model and analyze the free vibration and transient response of non-uniform thickness bi-directional functionally graded sandwich porous(BFGSP)skew plates.The whole BFGSP skew-plates is placed on a variable visco-elastic foundation(VEF)in the hygro-thermal environment and subjected to the blast load.The BFGSP skew-plate thickness is permitted to vary non-linearly over both the length and width of the skew-plate,thereby faithfully representing the real behavior of the structure itself.The analysis is based on a four-node planar quadrilateral element with eight degrees of freedom per node,which is approximated using Lagrange Q_(4)shape function and C^(1)level non-conforming Hermite shape function based on refined higher-order shear deformation plate theory.The forced vibration parameters of the non-uniform thickness BFGSP skew-plate are fully determined using Hamilton's principle and the Newmark-βdirect integration technique.Accuracy of the calculation program is validated by comparing its numerical results with those from reputable sources.Furthermore,a thorough assessment is conducted to determine the impact of various parameters on the free and forced vibration responses of the non-uniform thickness BFGSP skew-plate.The findings of the paper may be used in the development of civil and military structures in situations that are prone to exceptional forces,such as explosions and impacts load. 展开更多
关键词 Finite element modeling Hygro-thermal environment variable thickness Free and forced vibration Visco-elastic foundation Skew-plate
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Is Terzaghi's effective stress a stress variable under seepage conditions? 被引量:1
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作者 雷国辉 赵仲辉 吴宏伟 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第6期2316-2321,共6页
From the continuum mechanics perspective, an attempt was made to clarify the role of Terzaghi's effective stress in the theoretical analysis of saturated soil subjected to seepage. The necessity of performing a co... From the continuum mechanics perspective, an attempt was made to clarify the role of Terzaghi's effective stress in the theoretical analysis of saturated soil subjected to seepage. The necessity of performing a coupled hydromechanical analysis to solve the seepage-deformation interaction problem was illustrated by examining the equations of static equilibrium among the effective stress, seepage force, pore-water pressure and total stress. The conceptual definition of stress variable that satisfies the principles of continuum mechanics is applied in the coupled hydromechanical analysis. It is shown that Terzaghi's effective stress is in fact not a stress variable under seepage conditions, and the seepage force acting on the soil skeleton cannot be viewed as a body force. This offers a clue to the underlying cause of a paradox between the real Pascal's hydrostatic state and the hydrostatic state predicted by a class of continuum hydromechanical theories. 展开更多
关键词 seepage-deformation interaction coupled hydromechanical analysis representative elementary volume stress variable stress state variable
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Hybrid artificial bee colony algorithm with variable neighborhood search and memory mechanism 被引量:59
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作者 FAN Chengli FU Qiang +1 位作者 LONG Guangzheng XING Qinghua 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第2期405-414,共10页
Artificial bee colony(ABC) is one of the most popular swarm intelligence optimization algorithms which have been widely used in numerical optimization and engineering applications. However, there are still deficiencie... Artificial bee colony(ABC) is one of the most popular swarm intelligence optimization algorithms which have been widely used in numerical optimization and engineering applications. However, there are still deficiencies in ABC regarding its local search ability and global search efficiency. Aiming at these deficiencies,an ABC variant named hybrid ABC(HABC) algorithm is proposed.Firstly, the variable neighborhood search factor is added to the solution search equation, which can enhance the local search ability and increase the population diversity. Secondly, inspired by the neuroscience investigation of real honeybees, the memory mechanism is put forward, which assumes the artificial bees can remember their past successful experiences and further guide the subsequent foraging behavior. The proposed memory mechanism is used to improve the global search efficiency. Finally, the results of comparison on a set of ten benchmark functions demonstrate the superiority of HABC. 展开更多
关键词 artificial bee colony(ABC) hybrid artificial bee colony(HABC) variable neighborhood search factor memory mechanism
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New normalized LMS adaptive filter with a variable regularization factor 被引量:9
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作者 LI Zhoufan LI Dan +1 位作者 XU Xinlong ZHANG Jianqiu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2019年第2期259-269,共11页
A new normalized least mean square(NLMS) adaptive filter is first derived from a cost function, which incorporates the conventional one of the NLMS with a minimum-disturbance(MD)constraint. A variable regularization f... A new normalized least mean square(NLMS) adaptive filter is first derived from a cost function, which incorporates the conventional one of the NLMS with a minimum-disturbance(MD)constraint. A variable regularization factor(RF) is then employed to control the contribution made by the MD constraint in the cost function. Analysis results show that the RF can be taken as a combination of the step size and regularization parameter in the conventional NLMS. This implies that these parameters can be jointly controlled by simply tuning the RF as the proposed algorithm does. It also demonstrates that the RF can accelerate the convergence rate of the proposed algorithm and its optimal value can be obtained by minimizing the squared noise-free posteriori error. A method for automatically determining the value of the RF is also presented, which is free of any prior knowledge of the noise. While simulation results verify the analytical ones, it is also illustrated that the performance of the proposed algorithm is superior to the state-of-art ones in both the steady-state misalignment and the convergence rate. A novel algorithm is proposed to solve some problems. Simulation results show the effectiveness of the proposed algorithm. 展开更多
关键词 adaptive filtering normalized least mean SQUARE (NLMS) minimum-disturbance (MD) constraint variable REGULARIZATION variable STEP-SIZE NLMS
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Variable structure guidance law for attacking surface maneuver targets 被引量:16
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作者 Han Yanhua Xu Bo 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第2期337-341,共5页
The characteristics of surface maneuver targets are analyzed and a 3-D relative motion model for missiles and targets is established. A variable structure guidance law is designed considering the characteristics of ta... The characteristics of surface maneuver targets are analyzed and a 3-D relative motion model for missiles and targets is established. A variable structure guidance law is designed considering the characteristics of targets. In the guidance law, the distance between missiles and targets as well as the missile-target relative velocity are all substituted by estimation values. The estimation errors, the target's velocity, and the maneuver acceleration are all treated as bounded disturbance. The guidance law proposed can be implemented conveniently in engineering with little target information. The performance of the guidance system is analyzed theoretically and the numerical simulation result shows the effectiveness of the guidance law. 展开更多
关键词 air-to-surface missile guidance law variable structure control surface maneuver target.
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Dynamic analysis and simulation of four-axis forced synchronizing banana vibrating screen of variable linear trajectory 被引量:8
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作者 刘初升 张士民 +4 位作者 周海沛 李珺 夏云飞 彭利平 王宏 《Journal of Central South University》 SCIE EI CAS 2012年第6期1530-1536,共7页
A new concept of banana vibrating screen which has the same effect as traditional banana vibrating screen in a new way was put forward.The dynamic model of vibrating screen was established and its working principle wa... A new concept of banana vibrating screen which has the same effect as traditional banana vibrating screen in a new way was put forward.The dynamic model of vibrating screen was established and its working principle was analyzed when the action line of the exciting force did not act through the centroid of screen box.Moreover,the dynamic differential equations of centroid and screen surface were obtained.The motions of centroid and screen surface were simulated with actual parameters of the design example in Matlab/Simulink.The results show that not only the amplitude has a significant decrease from 9.38 to 4.10 mm,but also the throwing index and vibrating direction angle have a significant decrease from 10.49 to 4.59,and from 58.10° to 33.29°,respectively,along the screen surface,which indicates that motion characteristics of vibrating screen are consistent with those of traditional banana vibrating screen only by means of a single angle of screen surface.What's more,such banana vibrating screen of variable linear trajectory with greater processing capacity could be obtained by adjusting the relative position of force center and the centroid of screen box properly. 展开更多
关键词 four-axis banana vibrating screen forced synchronizing variable linear trajectory dynamics simulation
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Risk assessment of floor water inrush in coal mines based on MFIM-TOPSIS variable weight model 被引量:9
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作者 ZHANG Guan-da XUE Yi-guo +3 位作者 BAI Cheng-hao SU Mao-xin ZHANG Kai TAO Yu-fan 《Journal of Central South University》 SCIE EI CAS CSCD 2021年第8期2360-2374,共15页
Floor water inrush is one of the main types of coal mine water hazards.With the development of deep mining,the prediction and evaluation of floor water inrush is particularly significant.This paper proposes a variable... Floor water inrush is one of the main types of coal mine water hazards.With the development of deep mining,the prediction and evaluation of floor water inrush is particularly significant.This paper proposes a variable weight model,which combines a multi-factor interaction matrix(MFIM)and the technique for order performance by similarity to ideal solution(TOPSIS)to implement the risk assessment of floor water inrush in coal mines.Based on the MFIM,the interaction between seven evaluation indices,including the confined water pressure,water supply condition and aquifer water yield property,floor aquifuge thickness,fault water transmitting ability,fracture development degree,mining depth and thickness and their influence on floor water inrush were considered.After calculating the constant weights,the active degree evaluation was used to assign a variable weight to the indices.The values of the middle layer and final risk level were obtained by TOPSIS.The presented model was successfully applied in the 9901 working face in the Taoyang Mine and four additional coal mines and the results were highly consistent with the engineering situations.Compared with the existing nonlinear evaluation methods,the proposed model had advantages in terms of the weighting,principle explanation,and algorithm structure. 展开更多
关键词 floor water inrush risk assessment multi-factor interaction matrix(MFIM) technique for order performance by similarity to ideal solution(TOPSIS) variable weight
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Analysis of the mass of behind-armor debris generated by RHA subjected to normal penetration of variable cross-section EFP 被引量:4
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作者 Boyang Xing Dongjiang Zhang +7 位作者 Zhenyan Guo Yunhui Hou Rui Guo Rongzhong Liu Liang Chen Hao Zhou Yongliang Yang Jianhua Luo 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2019年第3期390-397,共8页
Analyzing the mass of behind-armor debris (BAD) generated by Rolled Homogeneous Armor (RHA) subjected to normal penetration of variable cross-section Explosively Formed Projectile (EFP) is the purpose of this paper. S... Analyzing the mass of behind-armor debris (BAD) generated by Rolled Homogeneous Armor (RHA) subjected to normal penetration of variable cross-section Explosively Formed Projectile (EFP) is the purpose of this paper. So theoretical analysis, numerical simulation and experimental data are combined to analyze the influence of variable cross-section characteristic on the time history of crater radius. Moreover the relationships between time history of crater radius (as well as mass of BAD) and the thickness of RHA (from 30mm to 70 mm) and the impact velocity of EFP (1650 m/s to 1860 m/s) are also investigated. The results indicate that: 1) being compared to the variable cross-section characteristic is ignored, the theoretical time history of crater radius is in better agreement with the simulation results when the variable cross-section characteristic is considered;2) being compared to the other three conditions of plug, the theoretical mass of BAD is in the best agreement with the simulation results when the shape of plug is frustum of a cone and the angle between generatrix and bottom is 45- and the axial length of mushroom is considered. 展开更多
关键词 Explosively formed PROJECTILE Behind-armor DEBRIS variable CROSS-SECTION characteristic Shape of plug Axial length of MUSHROOM Theoretical model
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Variation characteristics of aquifer parameters induced by groundwater source heat pump operation under variable flow 被引量:5
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作者 王松庆 张旭 《Journal of Central South University》 SCIE EI CAS 2011年第4期1272-1277,共6页
The variation characteristics of aquifer parameters,induced by groundwater source heat pump(GWSHP) operation under variable flow,were theoretically analyzed through a case study,in which the characteristics of buildin... The variation characteristics of aquifer parameters,induced by groundwater source heat pump(GWSHP) operation under variable flow,were theoretically analyzed through a case study,in which the characteristics of building air conditioning load were considered.The results,compared with the constant flow operation,indicate that the influence on the variations of porosity,hydraulic conductivity and confined water head is decreased by 48%,51% and 71%,respectively,under variable flow operation.The security of variable flow operation is superior to that of constant flow.It is also concluded that the climate region and function of the buildings are primary factors which affect the suitability of variable flow operation in GWSHP. 展开更多
关键词 groundwater source heat pump variation characteristic aquifer parameter variable flow
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Compensation for secondary uncertainty in electro-hydraulic servo system by gain adaptive sliding mode variable structure control 被引量:11
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作者 张友旺 桂卫华 《Journal of Central South University of Technology》 EI 2008年第2期256-263,共8页
Based on consideration of the differential relations between the immeasurable variables and measurable variables in electro-hydraulic servo system,adaptive dynamic recurrent fuzzy neural networks(ADRFNNs) were employe... Based on consideration of the differential relations between the immeasurable variables and measurable variables in electro-hydraulic servo system,adaptive dynamic recurrent fuzzy neural networks(ADRFNNs) were employed to identify the primary uncertainty and the mathematic model of the system was turned into an equivalent linear model with terms of secondary uncertainty.At the same time,gain adaptive sliding mode variable structure control(GASMVSC) was employed to synthesize the control effort.The results show that the unrealization problem caused by some system's immeasurable state variables in traditional fuzzy neural networks(TFNN) taking all state variables as its inputs is overcome.On the other hand,the identification by the ADRFNNs online with high accuracy and the adaptive function of the correction term's gain in the GASMVSC make the system possess strong robustness and improved steady accuracy,and the chattering phenomenon of the control effort is also suppressed effectively. 展开更多
关键词 electro-hydraulic servo system adaptive dynamic recurrent fuzzy neural network(ADRFNN) gain adaptive slidingmode variable structure control(GASMVSC) secondary uncertainty
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Optimal variable structure control with sliding modes for unstable processes 被引量:4
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作者 KUMAR Satyendra AJMERI Moina 《Journal of Central South University》 SCIE EI CAS CSCD 2021年第10期3147-3158,共12页
In this work,a variable structure control(VSC)technique is proposed to achieve satisfactory robustness for unstable processes.Optimal values of unknown parameters of VSC are obtained using Whale optimization algorithm... In this work,a variable structure control(VSC)technique is proposed to achieve satisfactory robustness for unstable processes.Optimal values of unknown parameters of VSC are obtained using Whale optimization algorithm which was recently reported in literature.Stability analysis has been done to verify the suitability of the proposed structure for industrial processes.The proposed control strategy is applied to three different types of unstable processes including non-minimum phase and nonlinear systems.A comparative study ensures that the proposed scheme gives superior performance over the recently reported VSC system.Furthermore,the proposed method gives satisfactory results for a cart inverted pendulum system in the presence of external disturbance and noise. 展开更多
关键词 variable structure control sliding mode control Whale optimization algorithm ROBUSTNESS non-linear system
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Variable scheduling interval task scheduling for phased array radar 被引量:5
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作者 ZHANG Haowei XIE Junwei +2 位作者 ZHANG Zhaojian SHAO Lei CHEN Tangjun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第5期937-946,共10页
A scheduling algorithm is presented aiming at the task scheduling problem in the phased array radar. Rather than assuming the scheduling interval(SI) time, which is the update interval of the radar invoking the schedu... A scheduling algorithm is presented aiming at the task scheduling problem in the phased array radar. Rather than assuming the scheduling interval(SI) time, which is the update interval of the radar invoking the scheduling algorithm, to be a fixed value,it is modeled as a fuzzy set to improve the scheduling flexibility.The scheduling algorithm exploits the fuzzy set model in order to intelligently adjust the SI time. The idle time in other SIs is provided for SIs which will be overload. Thereby more request tasks can be accommodated. The simulation results show that the proposed algorithm improves the successful scheduling ratio by 16%,the threat ratio of execution by 16% and the time utilization ratio by 15% compared with the highest task mode priority first(HPF)algorithm. 展开更多
关键词 phased array radar task scheduling variable scheduling interval(SI) fuzzy set
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Effect of variable thickness cross rolling on edge crack and microstructure gradient of AZ31 magnesium alloy 被引量:4
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作者 JI Ya-feng DUAN Jin-rui +3 位作者 YUAN Hao LI Hua-ying SUN Jie MALi-feng 《Journal of Central South University》 SCIE EI CAS CSCD 2022年第4期1124-1132,共9页
The hot rolling experiment of AZ31 magnesium alloy was carried out by laying anoverlay mold at the initial temperature of 400℃.According to the Mizushima automatic plan view pattern control system(MAS)rolling theory ... The hot rolling experiment of AZ31 magnesium alloy was carried out by laying anoverlay mold at the initial temperature of 400℃.According to the Mizushima automatic plan view pattern control system(MAS)rolling theory and the cross rolling process,different reductions in the middle and edges of the magnesium alloy were realized,and the influence of the regional controlled reduction rolling on the edge cracks and microstructure gradient of the magnesium alloy were analyzed.It is shown that this rolling approach has reduced the maximum edge crack depth of the rolled piece by 56.85%,and there is a weakening tendency in the base surface texture of the strip edge,the base surface texture density drops from 23.97 to 17.48 after ordinary flat rolling.It exhibits basal texture gradients from the edge to the middle of the sheet along the RD direction,which reflected the uneven deformation of the sheets.It is suitable for the processing of metal molds that require large edge reductions such as mobile phone shells,and provided a theoretical basis for the variable thickness rolling of the magnesium alloy strip. 展开更多
关键词 AZ31 magnesium alloys variable thickness cross rolling edge cracks MICROSTRUCTURES tissue gradients
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Variable mass and thermal properties in three-dimensional viscous flow: Application of Darcy law 被引量:4
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作者 Iffat JABEEN Muhammad FAROOQ Nazir A. MIR 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第5期1271-1282,共12页
This article concentrates on the properties of three-dimensional magneto-hydrodynamic flow of a viscous fluid saturated with Darcy porous medium deformed by a nonlinear variable thickened surface.Analysis of flow is d... This article concentrates on the properties of three-dimensional magneto-hydrodynamic flow of a viscous fluid saturated with Darcy porous medium deformed by a nonlinear variable thickened surface.Analysis of flow is disclosed in the neighborhood of stagnation point.Features of heat transport are characterized with Newtonian heating and variable thermal conductivity.Mass transport is carried out with first order chemical reaction and variable mass diffusivity.Resulting governing equations are transformed by implementation of appropriate transformations.Analytical convergent series solutions are computed via homotopic technique.Physical aspects of numerous parameters are discussed through graphical data.Drag force coefficient,Sherwood and Nusselt numbers are illustrated through graphs corresponding to various pertinent parameters.Graphical discussion reveals that conjugate and constructive chemical reaction parameters enhance the temperature and concentration distributions,respectively. 展开更多
关键词 Newtonian heating chemical reaction variable mass diffusivity Darcy law
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Optimum control strategy for all-variable speed chiller plant 被引量:3
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作者 蒋小强 龙惟定 李敏 《Journal of Central South University》 SCIE EI CAS 2011年第2期573-579,共7页
The optimum control strategy and the saving potential of all variable chiller plant under the conditions of changing building cooling load and cooling water supply temperature were investigated. Based on a simulation ... The optimum control strategy and the saving potential of all variable chiller plant under the conditions of changing building cooling load and cooling water supply temperature were investigated. Based on a simulation model of water source chiller plant established in dynamic transient simulation program (TRNSYS),the four-variable quadratic orthogonal regression experiments were carried out by taking cooling load,cooling water supply temperature,cooling water flow rate and chilled water flow rate as variables,and the fitting formulas expressing the relationships between the total energy consumption of chiller plant with the four selected parameters was obtained. With the SAS statistical software and MATHEMATICA mathematical software,the optimal chilled water flow rate and cooling water flow rate which result in the minimum total energy consumption were determined under continuously varying cooling load and cooling water supply temperature. With regard to a chiller plant serving an office building in Shanghai,the total energy consumptions under different control strategies were computed in terms of the forecasting function of cooling load and water source temperature. The results show that applying the optimal control strategy to the chiller plant can bring a saving of 23.27% in power compared with the corresponding conventional variable speed plant,indicating that the optimal control strategy can improve the energy efficiency of chiller plant. 展开更多
关键词 chiller plant control strategy variable speed cooling water flow rate chilled water flow rate
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Effect of some operational variables on bubble size in a pilot-scale mechanical flotation machine 被引量:4
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作者 张炜 J.E.Nesset J.A.Finch 《Journal of Central South University》 SCIE EI CAS 2014年第3期1077-1084,共8页
This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble (D32). The study was performed using pilot-scale equipment (0.8 m^3) that ... This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble (D32). The study was performed using pilot-scale equipment (0.8 m^3) that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n (number of C-atoms in alkyl group) and m (number of propylene oxide group). Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s (representing the industrial operating range), although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution (BSD) being created do not change with increasing impeller speed in the quiescent zone of the flotation. 展开更多
关键词 FLOTATION bubble size operational variables critical coalescence concentration hydrophile-lipophile balance impellerspeed
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