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ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW
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作者 谭忠 李心亮 杨惠 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期851-864,共14页
In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in... In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain. 展开更多
关键词 compressible nematic liquid crystal flow weak solutions energy conservation
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Energy Saving Analysis of Coal Gas Resource Utilization in Iron and Steel Enterprises
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作者 Lu Yan Kai Wang 《Frontiers of Metallurgical Industry》 2024年第2期32-36,共5页
The article discusses the preparation of a gas balance sheet,as well as the recovery,storage,transporta-tion,and use of gas.An analysis was conducted on the occurrence and consumption quotas of various gas media,and s... The article discusses the preparation of a gas balance sheet,as well as the recovery,storage,transporta-tion,and use of gas.An analysis was conducted on the occurrence and consumption quotas of various gas media,and specific energy-saving measures were elaborated for each process.This provides a theoretical reference for saving gas and reducing energy consumption in steel enterprises. 展开更多
关键词 steel enterprises GAS energy conservation
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Exploration and Application Practice of Energy Conservation Theory and Method in Steel Manufacturing Process System
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作者 Jiaxiang Hao Yuanyuan Wu 《Frontiers of Metallurgical Industry》 2024年第2期37-42,共6页
This article briefly discusses the theoretical basis and overall goals of energy conservation in the steel manufacturing process system.It is proposed that in the process of implementing system energy conservation,it ... This article briefly discusses the theoretical basis and overall goals of energy conservation in the steel manufacturing process system.It is proposed that in the process of implementing system energy conservation,it is necessary to fully recognize and utilize the characteristics and functional advantages of the steel manufacturing process,pay more attention to energy quality,firmly grasp the overall goal of system optimization,focus on the integrated optimization of gas,steam,and waste heat systems,and propose the idea of constructing a"steel chemi-cal gas electricity heating cooling multi generation system".Based on practice,the main principles,models,and effects of implementing systematic energy conservation in steel enterprises have been proposed. 展开更多
关键词 steel manufacturing process system energy-saving system optimization energy conservation and emis-sion reduction waste heat and energy generation POLYGENERATION
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Adaptive energy-preserving algorithms for guiding center system
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作者 朱贝贝 刘健 +2 位作者 张嘉炜 祝爱卿 唐贻发 《Plasma Science and Technology》 SCIE EI CAS CSCD 2023年第4期11-22,共12页
We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized plasmas.The adaptive scheme is applied to the Gauss... We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized plasmas.The adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving algorithms.These new adaptive algorithms are second order,and their algebraic order is carefully studied.Numerical results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost. 展开更多
关键词 guiding center system energy-preserving methods ADAPTIVE energy conservation
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THE ENERGY CONSERVATION OF VLASOV-POISSON SYSTEMS
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作者 吴景鹏 张显文 《Acta Mathematica Scientia》 SCIE CSCD 2023年第2期668-674,共7页
We prove that energy conservation holds for weak solutions to classical VlasovPoisson systems with proper regularity.In particular,there exists a solution that conserves energy with|v|^(m)f0∈L^(1)_(x,v)for m>9/4.
关键词 Vlasov-Poisson system weak solutions energy conservation
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THE ENERGY CONSERVATION OF THE LANDAU-LIFSHITZ-BLOCH EQUATION
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作者 许秋菊 王华桥 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1841-1851,共11页
In this paper,we consider the three-dimensional Landau-Lifshitz-Bloch equation in the whole space,which can describe the micromagnetic dynamic behavior of material at all temperatures,especially near the Curie tempera... In this paper,we consider the three-dimensional Landau-Lifshitz-Bloch equation in the whole space,which can describe the micromagnetic dynamic behavior of material at all temperatures,especially near the Curie temperature.We establish a sufficient condition of energy conservation for when weak solutions of the Landau-Lifshitz-Bloch equation with the temperature higher than the Curie temperature and its gradient belong to the Besov space L_(loc)^(3);B_(p,c0)^(α)(R^(3)))for some α∈(1/2,1)and p=9/(3α+1).Moreover,we also use the dimensional homogeneity to explain that the restrictions on the indicators are reasonable. 展开更多
关键词 Landau-Lifshitz-Bloch equation weak solutions energy conservation
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An IoT-Based Energy Conservation Smart Classroom System
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作者 Talal H.Noor El-Sayed Atlam +2 位作者 Abdulqader M.Almars Ayman Noor Amer S.Malki 《Intelligent Automation & Soft Computing》 SCIE 2023年第3期3785-3799,共15页
With the increase of energy consumption worldwide in several domains such as industry,education,and transportation,several technologies played an influential role in energy conservation such as the Internet of Things(I... With the increase of energy consumption worldwide in several domains such as industry,education,and transportation,several technologies played an influential role in energy conservation such as the Internet of Things(IoT).In this article,we describe the design and implementation of an IoT-based energy conser-vation smart classroom system that contributes to energy conservation in the edu-cation domain.The proposed system not only allows the user to access and control IoT devices(e.g.,lights,projectors,and air conditions)in real-time,it also has the capability to aggregate the estimated energy consumption of an IoT device,the smart classroom,and the building based on the energy consumption and cost model that we propose.Moreover,the proposed model aggregates the estimated energy cost according to the Saudi Electricity Company(SEC)rates.Furthermore,the model aggregates in real-time the estimated energy conservation percentage and estimated money-saving percentage compared to data collected when the system wasn't used.The feasibility and benefits of our system have been validated on a real-world scenario which is a classroom in the college of computer science and engineering,Taibah University,Yanbu branch.The results of the experimental studies are promising in energy conservation and cost-saving when using our proposed system. 展开更多
关键词 energy consumption energy conservation energy cost Internet of Things(IoT) smart classroom
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Optimizing Storage for Energy Conservation in Tracking Wireless Sensor Network Objects
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作者 Vineet Sharma Mohammad Zubair Khan +2 位作者 Shivani Batra Abdullah Alsaeedi Prakash Srivastava 《Computer Systems Science & Engineering》 SCIE EI 2023年第5期1211-1231,共21页
The amount of needed control messages in wireless sensor networks(WSN)is affected by the storage strategy of detected events.Because broadcasting superfluous control messages consumes excess energy,the network lifespa... The amount of needed control messages in wireless sensor networks(WSN)is affected by the storage strategy of detected events.Because broadcasting superfluous control messages consumes excess energy,the network lifespan can be extended if the quantity of control messages is decreased.In this study,an optimized storage technique having low control overhead for tracking the objects in WSN is introduced.The basic concept is to retain observed events in internal memory and preserve the relationship between sensed information and sensor nodes using a novel inexpensive data structure entitled Ordered Binary Linked List(OBLL).Whenever an object passes over the sensor area,the recognizing sensor can immediately produce an OBLL along the object’s route.To retrieve the entire information,the OBLL can be traversed with logarithmic complexity which is much less than the traversing complexity of existing linked list structures.Performance evaluation and simulations were carried out to ensure that the suggested technique minimizes the number of messages and thus saving energy and extending the network life. 展开更多
关键词 energy conservation linked list object tracking wireless sensor networks
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Application Research and Case Analysis of Green Technology in Building Engineering under the Direction of Energy Conservation Demands
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作者 SONG Rui TIAN Juanjuan +1 位作者 YANG Xin LI Xingyi 《Journal of Landscape Research》 2023年第2期1-5,共5页
With the rapid development of the economy,the scale of construction projects in China is gradually expanding.In terms of construction technology,continuous innovation is being made to meet the needs of sustainable dev... With the rapid development of the economy,the scale of construction projects in China is gradually expanding.In terms of construction technology,continuous innovation is being made to meet the needs of sustainable development strategies,and green energy conservation technologies have emerged.It has a brand new design concept,and advocates for maximum energy conservation and environmental protection,fundamentally promoting the rational use of resources and space,and preventing the expansion of air and land pollution.First of all,a brief explanation is given on the current development status of green energy conservation technology in this paper.Secondly,through the introduction and analysis of energy conservation technologies and related building cases,the in-depth research on energy conservation measures of buildings is conducted.Finally,the prospects of green energy conservation technologies are proposed based on the current development status in China.This paper has certain reference value for its related engineering and theoretical research. 展开更多
关键词 Green technology energy conservation Architectural engineering PEDF
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Assessment of the Implementation of Energy Conservation Opportunities Arising from Energy Audits;A Study of Four-Star and Five-Star Hotels in Nairobi Kenya
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作者 Nicholas Ogola Peter Musau Cyrus Wekesa 《Journal of Power and Energy Engineering》 2023年第9期15-44,共30页
This study assesses the implementation of energy conservation opportunities in four-star and five-star hotels in Nairobi. The Covid-19 pandemic had a significant impact on the Hospitality Industry. Currently, there is... This study assesses the implementation of energy conservation opportunities in four-star and five-star hotels in Nairobi. The Covid-19 pandemic had a significant impact on the Hospitality Industry. Currently, there is a growing inclination to furnish guests with superior and sustainable services in an energy-efficient and eco-friendly way. Comprehensive research was conducted from energy audits gathered from the establishments and contracted auditing companies, on top of this, hotel staff were given digital questionnaires. To add to the data, the researcher surveyed the hotels with engineering managers. The Energy Audits found that all 10 hotels had adopted Energy Conservation Opportunities (ECOs). After further analysis, the mean adoption rate of Energy Conservation Opportunities (ECOs) during the past three years was 55.83%, which was below the aim of 100%. According to studies, hotel staff manages energy to cut costs. The researcher found that hotels use up a lot of energy. However, they have conservation potential, depending on government policies, costs, ease of implementation, and management commitment to sustainable practices. Essentially, Energy Conservation Opportunities (ECOs) reduce energy expenditures and boost reliable revenues, especially during high energy prices and uncertainty. 展开更多
关键词 energy Conservation Opportunities (ECOs) energy Regulation 2012 energy Audit 4-Star Hotel 5-Star Hotel energy Management Environmental Sustainability energy Efficiency
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Energy Consumption Analysis and Optimization of Electric Submersible Pump System
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作者 Lingyu Li 《Engineering(科研)》 CAS 2023年第5期269-274,共6页
Electric submersible pumps account for a considerable proportion in the development of the Bohai Oilfield. Improving the system efficiency of the electric submersible pump wells, ensuring that the units operate in the... Electric submersible pumps account for a considerable proportion in the development of the Bohai Oilfield. Improving the system efficiency of the electric submersible pump wells, ensuring that the units operate in the high-efficiency zone, is essential. Analysis shows that the efficiency of the electric submersible pump system depends on the wear and tear of each component of the submersible pump equipment, the setting of operational parameters, and more importantly, the production status and daily management level of the oil well. Therefore, improving the structural performance of the submersible pump product, optimizing the parameters setting of the oil well, strengthening daily management, establishing a scientific management system, and improving the production management process and system can effectively improve the production efficiency and economic benefits of the oil well, and further achieve the goal of energy saving and emission reduction. In addition, it is necessary to actively promote the concept and technology of energy saving and emission reduction, encourage oilfield enterprises to explore effective measures to reduce the energy consumption of the electric submersible pump system by strengthening the scientific management system, and achieve a green, low-carbon, and high-quality development of oilfield production to achieve the unity of economic benefits, social benefits, and environmental benefits. This article applies the above measures in the P oilfield to achieve energy optimization of submersible electric pump systems, reducing the daily power consumption of single well submersible electric pump systems by 371 kWh per day, increasing the submersible electric pump's lifespan by 200 days, generating considerable project benefits. 展开更多
关键词 Offshore Oil Fields Electric Submersible Pumps System energy Consump-tion System Efficiency energy Conservation and Consumption Reduction
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A Local Macroscopic Conservative(LoMaC)Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics
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作者 Wei Guo Jannatul Ferdous Ema Jing-Mei Qiu 《Communications on Applied Mathematics and Computation》 EI 2024年第1期550-575,共26页
In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.... In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method. 展开更多
关键词 Hierarchical Tucker(HT)decomposition Conservative SVD energy conservation Discontinuous Galerkin(DG)method
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Application of Key Technologies in Green School Buildings: Taking Sino-German Future City Primary School as an Example
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作者 Yang Liu Dong Huang +2 位作者 Chunhua Yang Jian Zhou Yunda Tang 《Journal of World Architecture》 2024年第3期36-42,共7页
Green building is a manifestation of the response to the national“dual carbon”strategy.With the large-scale promotion of green buildings,the country has successively issued multiple evaluation standards for green bu... Green building is a manifestation of the response to the national“dual carbon”strategy.With the large-scale promotion of green buildings,the country has successively issued multiple evaluation standards for green buildings.Schools are places for preaching,teaching,and solving doubts,and the campus environment plays an important role in improving students’learning efficiency and promoting their physical and mental health.This article is based on the“Green Building Evaluation Standards”GB/T 50378-2019,analyzing and exploring the integration and application of key technologies in green schools,providing reference for green building designers. 展开更多
关键词 Green buildings energy conservation and environmental protection Key technologies High-quality buildings
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Analysis of Oxygen Consumption in Lead and Zinc Metallurgy
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作者 Lun Sheng Pengpeng Zhang 《Frontiers of Metallurgical Industry》 2024年第2期5-9,共5页
This article analyzes the role of oxygen in lead zinc metallurgy,including shortening the metallurgical process,promoting energy conservation and environmental protection,improving metallurgical strength,enhancing raw... This article analyzes the role of oxygen in lead zinc metallurgy,including shortening the metallurgical process,promoting energy conservation and environmental protection,improving metallurgical strength,enhancing raw material adaptability,and enhancing comprehensive recovery efficiency.This article introduces different lead zinc metallurgical processes and their oxygen consumption characteristics,including oxygen enriched side blowing lead smelting,oxygen bottom blowing lead smelting,oxygen enriched top blowing lead smelting,flash smelting lead,oxygen pressure leaching zinc smelting,and atmospheric pressure oxygen leaching zinc smelting.It is pointed out that oxygen enhanced metallurgy is the direction for the transformation and upgrading of lead zinc metallurgy. 展开更多
关键词 lead zinc metallurgy oxygen rich smelting oxygen pressure leaching energy conservation and emission reduction
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Distributed Power Control for Energy Conservation in Hybrid Cellular Network with Device-to-Device Communication 被引量:13
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作者 TANG Rui ZHAO Jihong QU Hua 《China Communications》 SCIE CSCD 2014年第3期27-39,共13页
Device-to-Device(D2D) communication has been proposed as a promising implementation of green communication to benefit the existed cellular network.In order to limit cross-tier interference while explore the gain of sh... Device-to-Device(D2D) communication has been proposed as a promising implementation of green communication to benefit the existed cellular network.In order to limit cross-tier interference while explore the gain of short-range communication,we devise a series of distributed power control(DPC) schemes for energy conservation(EC)and enhancement of radio resource utilization in the hybrid system.Firstly,a constrained opportunistic power control model is built up to take advantage of the interference avoidance methodology in the presence of service requirement and power constraint.Then,biasing scheme and admission control are added to evade ineffective power consumption and maintain the feasibility of the system.Upon feasibility,a non-cooperative game is further formulated to exploit the profit in EC with minor influence on spectral efficiency(SE).The convergence of the DPC schemes is validated and their performance is confirmed via simulation results. 展开更多
关键词 Device-to-Device communication distributed power control energy conservation interference avoidance biasing scheme admission control non-cooperative game
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On the energy conservation and critical velocities for the propagation of a "steady-shock" wave in a bar made of cellular material 被引量:8
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作者 Li-Li Wang Li-Ming Yang Yuan-Yuan Ding 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2013年第3期420-428,共9页
The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking (D-R-PP-L... The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking (D-R-PP-L) model and the dynamic rigid, linear hardening plastic, locking (D-R-LHP-L) model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the "energy conservation condition" and the "kinematic existence condition" as proposed by Tan et al. (2005) is re-examined, showing that the "energy conservation condition" and the consequent "critical velocity", i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants. 展开更多
关键词 Cellular solids 1D shock theory D-R-PP-L model D-R-SHP-L model energy conservation across shock Critical velocities
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Run-to-run Optimization for Fed-batch Fermentation Process with Swarm Energy Conservation Particle Swarm Optimization Algorithm 被引量:7
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作者 王建林 薛尧予 +1 位作者 于涛 赵利强 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2010年第5期787-794,共8页
An iterative optimization strategy for fed-batch fermentation process is presented by combining a run-to-run optimization with swarm energy conservation particle swarm optimization (SEC-PSO). SEC-PSO, which is designe... An iterative optimization strategy for fed-batch fermentation process is presented by combining a run-to-run optimization with swarm energy conservation particle swarm optimization (SEC-PSO). SEC-PSO, which is designed with the concept of energy conservation, can solve the problem of premature convergence frequently appeared in standard PSO algorithm by partitioning its population into several sub-swarms according to the energy of the swarm and is used in the optimization strategy for parameter identification and operation condition optimization. The run-to-run optimization exploits the repetitive nature of fed-batch processes in order to deal with the optimal problems of fed-batch fermentation process with inaccurate process model and unsteady process state. The kinetic model parameters, used in the operation condition optimization of the next run, are adjusted by calculating time-series data obtained from real fed-batch process in the run-to-run optimization. The simulation results show that the strategy can adjust its kinetic model dynamically and overcome the instability of fed-batch process effectively. Run-to-run strategy with SEC-PSO provides an effective method for optimization of fed-batch fermentation process. 展开更多
关键词 run-to-run optimization fed-batch process particle swarm optimization swarm energy conservation particle swarm optimization
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A Moored Underwater Energy Conservation System for Profiling Measurement 被引量:5
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作者 龚德俊 陈永华 +2 位作者 李思忍 徐永平 姜静波 《China Ocean Engineering》 SCIE EI 2007年第3期541-548,共8页
There is a need to obtain the hydrologic data including ocean current, wave, temperature and so on in the South China Sea. A new profiling instrument which does not suffer from the damage due to nature forces or incid... There is a need to obtain the hydrologic data including ocean current, wave, temperature and so on in the South China Sea. A new profiling instrument which does not suffer from the damage due to nature forces or incidents caused by passing ships, is under development to acquire data from this area. This device is based on a taut single point mid-water mooring system. It incorporates a small, instrumented vertically profiling float attached via an electromechanical cable to a winch integral with the main subsurface flotation. On a pre-set schedule, the instrument float with sensors is winched up to the surface if there is no ship passing by, which is defined by an on-board miniature sonar. And it can be. inunediately winched down to a certain depth if the sonar sensor finds something is coming. Since, because of logistics, the area can only be visited once for a long time and a minimum of 10 times per day profiles are desired, energy demands are severe. To respond to these concerns, the system has been designed to conserve a substantial portion of the potential energy lost during the ascent phase of each profile and subsequently use this energy to pull the instrument down. Compared with the previous single-point layered measuring mode, it is advanced and economical. At last the paper introduces the test in the South China Sea. 展开更多
关键词 energy conservation profiling measurement hydrologic data moored underwater system security and continuity
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Energy distribution and effective components analysis of 2^(n) sequence pseudo-random signal 被引量:5
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作者 Yang YANG Ji-shan HE Di-quan LI 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2021年第7期2102-2115,共14页
In order to extract usable harmonics from real 2^(n) sequence pseudo-random data,a technical method is proposed.An equation for predicting the average amplitude of the main frequencies is proposed to guide the choice ... In order to extract usable harmonics from real 2^(n) sequence pseudo-random data,a technical method is proposed.An equation for predicting the average amplitude of the main frequencies is proposed to guide the choice of signal type for different exploration tasks.By the threshold of the amplitude of the transmitted signal,a set of candidate frequencies are first selected.Then,by operating a spectrum envelope method at these candidate frequencies on received data,effective components in data are extracted.A frequency density calculation method is proposed based on a logical number summation method,to reasonably characterize the frequency density in different frequency bands.By applying this method to real data in Sichuan,China,with signal Type 13,75 effective components are extracted,including both main frequencies and harmonics.The result suggests that the number of effective frequencies in the 2^(n) sequence pseudo-random signal can be increased by extracting usable harmonics,without any additional fieldwork. 展开更多
关键词 electromagnetic prospecting 2^(n) pseudo-random signal energy conservation harmonic extraction frequency density
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Generalised energy conservation law for chaotic phenomena 被引量:4
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作者 Jing-Tang Xing 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2019年第6期1257-1268,共12页
Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is... Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is normally understood as“a state of disorder”,for which there is as yet no universally accepted mathematical definition.A commonly used concept states that,for a dynamical system to be classified as chaotic,it must have the following properties:be sensitive to initial conditions,show topological transitivity,have densely periodical orbits etc.Revealing the rules that govern chaotic motion is thus an important unsolved task for exploring nature.W e present herein a generalised energy conservation law governing chaotic phenomena.Based on two scalar variables,viz.generalised potential and kinetic energies defined in the phase space describing nonlinear dynamical systems,we find that chaotic motion is periodic motion with infinite time period whose time-averaged generalised potential and kinetic energies are conserved over its time period.This implies that,as the averaging time is increased,the time-averaged generalised potential and kinetic energies tend to constants while the time-averaged energy flows,i.e.,their rates of change with time,tend to zero.Numerical simulations on reported chaotic motions,such as the forced van der Pol system,forced Duffing system,forced smooth and discontinuous oscillator,Lorenz’s system,and Rossler's system,show the above conclusions to be correct according to the results presented herein.This discovery may indicate that chaotic phenomena in nature could be controlled because,even though their instantaneous states are disordered,their long-time averages can be predicted. 展开更多
关键词 CHAOS Generalised energy Generalised energy conservation Nonlinear dynamical systems energy flow theory
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