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Fatigue reliability quantitative analysis of cement concrete for highway pavement under high stress ratio 被引量:5
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作者 薛彦卿 黄晓明 +2 位作者 钱吮智 马涛 邹湘衡 《Journal of Southeast University(English Edition)》 EI CAS 2012年第1期94-99,共6页
In order to obtain the change law of the fatigue reliability of cement concrete for highway pavement under high stress ratios, first, the probability densities of monotonic random variables including concrete fatigue ... In order to obtain the change law of the fatigue reliability of cement concrete for highway pavement under high stress ratios, first, the probability densities of monotonic random variables including concrete fatigue life are deduced. And then, the fatigue damage probability densities of the Miner and Chaboche-Zhao models are deduced. By virtue of laboratory fatigue test results, the fatigue damage probability density functions of the two models can be obtained, considering different stress ratios. Finally, substituting load cycles into them, the change law of cement concrete fatigue reliability about load cycles can be acquired. The results show that under the same stress ratio, with the increase in the load cycle, the fatigue reliability declines from almost 100% to 0% gradually. No matter under what stress ratio, during the initial stage of the load action, there is always a relatively stable phase for fatigue reliability. With the increase in the stress ratio, the stable phase gradually shortens and the load cycle corresponding to the reliability of 0% also decreases. In the descent phase of reliability, the higher the stress ratio is, the lower the concrete reliability is for the same load cycle. Besides, compared with the Chaboche-Zhao fatigue damage model, the Miner fatigue damage model is safer. 展开更多
关键词 cement concrete fatigue life fatigue damage probability density function high stress ratio fatigue reliability
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Spin Polarization Effect for Molecule Fe_(2)
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作者 炎正馨 谢安东 +2 位作者 阎世英 胡栋 杨向东 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 北大核心 2006年第2期149-151,共3页
Density functional method (B3p86) was used to optimize the structure of the molecule Fe2. The result showed that the ground electronic state for the molecule Fe2 is nonet state instead of septet state, which indicat... Density functional method (B3p86) was used to optimize the structure of the molecule Fe2. The result showed that the ground electronic state for the molecule Fe2 is nonet state instead of septet state, which indicates that there is a spin polarization effect in the molecule Fe2, i.e., in which there are 8 parallel spin electrons.In this case, the number of the unpaired d-orbit electrons is the largest, and these electrons occupy different spatial orbitals so that the energy of the molecule Fe2 is minimized. Meanwhile, the spin pollution was not found because the wave functions of the ground state do not mix with those of the higher energy states. In addition, the Murrell-Sorbie potential functions with the parameters for the ground electronic state and other exited electronic states of the molecule Fe2 were derived. The dissociation energy, equilibrium bond length and the vibration frequency for the ground electronic state of the molecule Fe2 are 3.5522 eV, 0.2137 nm and 292.914 cm^-1, respectively. Its force constants f2, f3 and f4 are 1.4115×1^02 a J/nm^2, -37.1751×103^aJ/nm^3 and 98.7596× 10^4 a J/nm^4, respectively. The other spectroscopic parameters ωexe, Be and αe for the ground electronic state of Fe2 are 0.3522, 0.0345 and 0.4963× 10^-4 cm^-1, respectively. 展开更多
关键词 FE2 Spin polarization Density functional theory Potential function
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Research on velocity and acceleration geophones and their acquired information 被引量:5
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作者 刘振东 吕庆田 +1 位作者 董世学 陈明春 《Applied Geophysics》 SCIE CSCD 2012年第2期149-158,234,共11页
Based on the research of two geophone types (10 Hz moving-coil velocity and piezoelectric acceleration) and their velocity and acceleration parameters, frequency response functions have been determined, as well as t... Based on the research of two geophone types (10 Hz moving-coil velocity and piezoelectric acceleration) and their velocity and acceleration parameters, frequency response functions have been determined, as well as the differences between them. Also, shock- vibration tests have been accomplished, not only to explain the two shock response signal differences, but also to analyze the response signal characteristics and its ability to carry information. In addition, seismic data acquisition experiments have been carried out under comparable conditions in the field. A contrast analysis of shot gathers and stack profiles acquired with the two geophone types is given in this paper. The results show that the acceleration signal from the acceleration geophone has a better advantage in terms of high signal-to-noise ratio, high accuracy, high resolution, and quantity of information to better meet current and future requirements for seismic exploration. 展开更多
关键词 seismic exploration GEOPHONE acceleration signal INTEGRITY ACCURACY
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Effects of electrolysis process parameters on alumina dissolution and their optimization 被引量:9
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作者 Wen-yuan HOU He-song LI +2 位作者 Mao LI Ben-jun CHENG Yuan FENG 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2020年第12期3390-3403,共14页
The Box–Behnken design and desirability approach were used to investigate and optimize the process parameters for aluminum reduction cells related to alumina dissolution. The bath temperature, alumina content, curren... The Box–Behnken design and desirability approach were used to investigate and optimize the process parameters for aluminum reduction cells related to alumina dissolution. The bath temperature, alumina content, current and alumina temperature were chosen as the design parameters. The content of cumulative dissolved alumina(CCDA) and the relative deviation from the target content(RDTC) were adopted as the responses. The interactive influence results show that increasing the bath temperature and alumina temperature, as well as decreasing the alumina content, can increase CCDA. Increasing the bath temperature and lowering the current are beneficial for obtaining a more uniform alumina distribution. The optimal operating parameters were determined to be as follows: bath temperature of 958.8 ℃, alumina content of 2.679 wt.%, current of 300 kA and alumina temperature of 200 ℃. 展开更多
关键词 aluminum reduction cell alumina dissolution response surface methodology desirability approach heat and mass transfer
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Improved response surface method and its application in stability reliability degree analysis of tunnel surrounding rock 被引量:10
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作者 苏永华 张鹏 赵明华 《Journal of Central South University of Technology》 EI 2007年第6期870-876,共7页
An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mend... An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mended, and peak value and deflection degree of basic random variables distribution curve were took into account in the mended sampling method. A calculation way of probability moment, based on mended Rosenbluth method, suitable for non-explicit performance function was put forward. The first, second, third and fourth order moments of functional function value were calculated by mended Rosenbluth method through the first, second, third and fourth order moments of basic random variable. A probability density the function(PDF) of functional function was deduced through its first, second, third and fourth moments, the PDF in the new method took the place of the method of quadratic polynomial to approximate real functional function and reliability probability was calculated through integral by the PDF for random variable of functional function value in the new method. The result shows that the improved response surface method can adapt to various statistic distribution types of basic random variables, its calculation process is legible and need not itemtive circulation. In addition, a stability probability of surrounding rock for a tunnel was calculated by the improved method, whose workload is only 30% of classical method and its accuracy is comparative. 展开更多
关键词 response surface method Rosenbluth method statistic moment entropy density function quadratic polynomial
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Modified nonlinear chirp scaling algorithm for curvilinear trajectory synthetic aperture radar 被引量:1
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作者 王建涛 秦玉亮 +2 位作者 范波 王宏强 黎湘 《Journal of Central South University》 SCIE EI CAS 2014年第7期2751-2758,共8页
The original nonlinear chirp scaling(NCS) algorithm was extended for high precision processing of the highly squinted curvilinear trajectory synthetic aperture radar(CTSAR).Based on the analysis of slant range model a... The original nonlinear chirp scaling(NCS) algorithm was extended for high precision processing of the highly squinted curvilinear trajectory synthetic aperture radar(CTSAR).Based on the analysis of slant range model and the frequency spectrum characteristics of the echo signal,a novel nonlinear chirp scaling function and more complex phase compensation factors with both velocity and acceleration parameters were proposed in the new algorithm for accommodation to curvilinear trajectory.The processing flow and computational complexity of modified NCS algorithm were fundamentally the same as the original NCS algorithm.However,the higher order phase compensation,range cell migration correction(RCMC) and range-variant secondary range compression(SRC) caused by the non-linear aperture and the severe range-azimuth coupling were accomplished accurately and efficiently without interpolation.Simulation results show that data acquired with a curvilinear aperture and a squint angle up to about 50° for X-band can be processed with no evident degradation of impulse response function. 展开更多
关键词 synthetic aperture radar nonlinear chirp scaling curvilinear trajectory ACCELERATION
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Scheme optimization of AT shifting element based on genetic algorithm
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作者 岳会军 刘艳芳 +2 位作者 马明月 徐向阳 王书翰 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第2期539-545,共7页
In order to realize the computer aided design of AT shifting element schemes, a mathematical model of shifting element schemes which can be easily identified by computers was built. Taking the transmission ratio seque... In order to realize the computer aided design of AT shifting element schemes, a mathematical model of shifting element schemes which can be easily identified by computers was built. Taking the transmission ratio sequence as an optimization objective and simple shifting logic between adjacent gears through operating only one shifting element as a constraint condition, a fitness function of shifting element schemes was proposed. ZF-8AT shifting element schemes were optimized based on GA work-box of MATLAB, and the feasibility of the optimization algorithm was verified. 展开更多
关键词 hydrodynamic automatic transmission shifting element scheme optimization
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Dynamic anti-plane interaction between an impermeable crack and a circular cavity in an infinite piezoelectric medium
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作者 宋天舒 李冬 任正义 《Journal of Marine Science and Application》 2008年第4期297-301,共5页
Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green's function and the crack-divisi... Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green's function and the crack-division technique.Theoretical solutions were derived for the whole elastic displacement and electric potential field in the interaction between the circular cavity and the impermeable crack.Expressions were obtained on the dynamic stress concentration factor(DSCF) at the cavity's edge,the dynamic stress intensity factor(DSIF) and the dynamic electric displacement intensity factor(DEDIF) at the crack tip.Numerical solutions were performed and plotted with different incident wave numbers,parameters of piezoelectric materials and geometries of the structure.Finally,some of the calculation results were compared with the case of dynamic anti-plane interaction of a permeable crack and a circular cavity in an infinite piezoelectric medium.This paper can provide a valuable reference for the design of piezoelectric actuators and sensors widely used in marine structures. 展开更多
关键词 piezoelectric medium impermeable crack dynamic stress intensity factor dynamic stress concentration factor dynamic electric disnlacement intensity factor Green's function
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The inter-annual variability of the Yellow Sea Warm Current surface axis and its influencing factors 被引量:8
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作者 宋德海 鲍献文 +3 位作者 王小华 徐玲玲 林霄沛 吴德星 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 2009年第3期607-613,共7页
Based on the Pathfinder sea surface temperature(PFSST),the surface axis and its pattern of the Yellow Sea Warm Current(YSWC) are discussed.A structure of double-warm-tongue is found in February and it varies in differ... Based on the Pathfinder sea surface temperature(PFSST),the surface axis and its pattern of the Yellow Sea Warm Current(YSWC) are discussed.A structure of double-warm-tongue is found in February and it varies in different years.Two indexes are calculated to represent the westward shift(WSI) and northward extension(NEI) of the warm water in the Yellow Sea(YS).Wavelet analysis illustrates that the WSI and NEI have prominent periods of 3-6 years and 3-4 years,respectively.The Empirical Orthogonal Function(EOF) decomposition is applied to the winter wind stress curl and the Kuroshio Current(KC) transport,which are believed to play important roles in forcing the variability of the YSWC surface axis.Statistics shows that the WSI is significantly related with the second EOF mode of the wind stress curl in February,which may force the YSWC surface axis moving westward and maintaining the double warm tongues because of its opposite curl in the YSWC domain.The first EOF mode of wind stress curl in January is propitious for inducing the warm tongue in the YS to advance more northward.Hence,the wind stress curls both in January and in February could force variations of the YSWC surface axis;however,the effect of the January wind stress curl is relatively weaker than that of the February.The relationship between the NEI and the KC transport is remarkable,and it seems that the stronger KC supplies more power to push the YSWC northward against the southward wind. 展开更多
关键词 Yellow Sea Yellow Sea Warm Current (YSWC) surface axis inter-annual variability sea surface temperature (SST)
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Short-Time Decoherence of Solid-State Qubit at Optimal Operation Points
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作者 ZHAO Xu LIANG Xian-Ting 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第5X期827-832,共6页
We investigate the short-time decoherence of a solid-state qubit under Ohmic noise at optimal operation points. The decoherence is analyzed by maximum norm of the deviation density operator. It is shown that at the te... We investigate the short-time decoherence of a solid-state qubit under Ohmic noise at optimal operation points. The decoherence is analyzed by maximum norm of the deviation density operator. It is shown that at the temperature T = 3 mK, the loss of the fidelity due to decoherence is much smaller than the DiVincenzo low decoherence criterion, which means that the mode/may be an optimal candidate of qubit for quantum computation. 展开更多
关键词 short-time decoherence Josephson junction qubit ohmic noise
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Unemployment Period Approach with Infinite Servers Queue Systems
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作者 Manuel Alberto M. Ferreira 《Journal of Modern Accounting and Auditing》 2017年第3期134-136,共3页
With results on the infinite servers queue systems with Poisson arrivals - M|G|∞ queues - busy period, it is displayed an application of those queue systems in the unemployment periods time length parameters and di... With results on the infinite servers queue systems with Poisson arrivals - M|G|∞ queues - busy period, it is displayed an application of those queue systems in the unemployment periods time length parameters and distribution function study. These queue systems are adequate to the study of many population processes, and this quality is brought in here. The results presented are mainly on unemployment periods length and their number in a certain time interval. Also, some questions regarding the practical applications of the outlined formulas are briefly discussed. 展开更多
关键词 infinite servers queues busy period UNEMPLOYMENT
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Macroscopic Frost Heave Model Based on Segregation Potential Theory
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作者 吉植强 徐学燕 于琳琳 《Transactions of Tianjin University》 EI CAS 2010年第4期304-308,共5页
A macroscopic frost heave model with more clear parameters was established. Based on a porosity rate frost heave model and segregation potential theory, a porosity rate function was deduced and introduced into the str... A macroscopic frost heave model with more clear parameters was established. Based on a porosity rate frost heave model and segregation potential theory, a porosity rate function was deduced and introduced into the stress-strain relationship. Numerical simulation was conducted and verified by frost heave tests. Results show that the porosity rate within the frozen fringe is proportional to the square of temperature gradient and current porosity, and is also proportional to the exponential function of applied pressure. The relative errors between the calculated and measured results of frost depth and frost heave are within 3% and 15% respectively, demonstrating that the temperature gradient, applied pressure and current porosity are the main influencing factors, while temperature is just the constraint of frozen fringe. The improved model have meaningful and accessible parameters, which can be used in engineering with good accuracy. 展开更多
关键词 frost heave model porosity rate segregation potential frost heave test temperature gradient
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Influence of surface treatments on fatigue life of a two-stroke free piston linear engine component using random loading
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作者 RAHMAN M.M. ARIFFIN A.K. +1 位作者 JAMALUDIN N. HARON C.H.C. 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第11期1819-1830,共12页
This paper describes the finite element (FE) analysis technique to predict fatigue life using the narrow band frequency response approach. The life prediction results are useful for improving the component design meth... This paper describes the finite element (FE) analysis technique to predict fatigue life using the narrow band frequency response approach. The life prediction results are useful for improving the component design methodology at the very early development stage. The approach is found to be suitable for a periodic loading but requires very large time records to accurately describe random loading processes. This paper is aimed at investigating the effects of surface treatments on the fatigue life of the free piston linear engine’s components. Finite element modelling and frequency response analysis were conducted using computer aided design and finite element analysis commercial codes, respectively. In addition, the fatigue life prediction was carried out using finite element based fatigue analysis commercial code. Narrow band approach was specially applied to predict the fatigue life of the free piston linear engine cylinder block. Significant variation was observed between the surface treatments and untreated cylinder block of free piston engine. The obtained results indicated that nitrided treatment yielded the longest life. This approach can determine premature products failure phenomena, and therefore can reduce time to market, improve product reliability and customer confidence. 展开更多
关键词 Vibration fatigue Finite element (FE) Power spectral density function Frequency response Surface treatment
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Method of correlation function for analyzing cross-sensitivity of strain and temperature in fiber grating sensors
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作者 HAN Gui-hua ZHANG Wei-gang 《Optoelectronics Letters》 EI 2007年第3期195-198,共4页
A novel method of correlation function for analyzing cross-sensitivity between strain and temperature is reported for the first time in this paper. Using the new method,the correlative characteristics between strain a... A novel method of correlation function for analyzing cross-sensitivity between strain and temperature is reported for the first time in this paper. Using the new method,the correlative characteristics between strain and temperature of fiber Bragg grating sensors are studied both theoretically and experimentally The experimental results accord with the theoretical calculations. 展开更多
关键词 纤维光栅传感器 应变 温度 交叉敏感问题 相关函数
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Parameters Estimation and Evaluation for the Probability Density Function of Structural Fatigue Stress of a Container Vessel
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作者 ZHOU Feng 《Journal of Shipping and Ocean Engineering》 2017年第1期1-8,共8页
Fatigue stress measurement has been playing a significant role in the ship structural health monitoring and ship structural safety assessment. The PDF (probability density function) of the measured stress is one of ... Fatigue stress measurement has been playing a significant role in the ship structural health monitoring and ship structural safety assessment. The PDF (probability density function) of the measured stress is one of the essentials for the further studyin this domain. This paper, based on the strain-stress data collected from a container ship, focuses on the spectrum feature of the ship structural fatigue stress. A general analysis procedure for ship hull health estimation was firstly demonstrated. With the guidance of this procedure, the estimation and test of the parameters for the PDF of the stress were conducted, which showed that the stress spectrums fit well with the Weibull distribution. To review the fatigue state, the PDF and distribution function of fatigue damage increment were further developed and examined. The structural healthy assessment of this vessel shown the daily relative fatigue damage increment obeys log-normal or Weibull distribution and the increment of the fatigue damage on steel box girders of the ship hull was very low. Finally, the analyzing results yielded that the girder structure of the ship hull had a very low failure probability, matching well with the actual relative low working load of the ship. 展开更多
关键词 PDF STRESS fatigue damage container ship.
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Effects of Nonlinear Couplings on Entanglement in a Two-Qutrit Heisenberg XXX Chain under an Inhomogeneous Magnetic Field
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作者 QIN Meng GE Xing ZHAI Xiao-Yue LIU Cui-Cui WANG Bi-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第3期431-433,共3页
This paper investigates the entanglement of a two-qutrit Heisenberg XXX chain with nonlinear couplings under an inhomogeneous magnetic field. By the concept of negativity, we find that the critical temperature increas... This paper investigates the entanglement of a two-qutrit Heisenberg XXX chain with nonlinear couplings under an inhomogeneous magnetic field. By the concept of negativity, we find that the critical temperature increases with the increase of inhomogeneous magnetic field b. Our study indicates that for any |K| 〉 |J|, or |K| 〈 |J| entanglement always exists for certain regions. We also find that at the critical point, the entanglement becomes a nonanalytic function of B and a quantum phase transition occurs. 展开更多
关键词 ENTANGLEMENT NEGATIVITY nonlinear couplings inhomogeneous magnetic field
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First-Principles Study on Switching Performance and Spin Filtering Efficiency of Dimethyldihydropyrene/Cyclophanediene Single-Molecule Devices with Zigzag Graphene Nanoribbon Electrodes
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作者 Chang-Feng Zheng Yan-Qi Mu +1 位作者 Zong-Liang Li Guang-Ping Zhang 《Chinese Journal of Chemical Physics》 SCIE EI CAS 2024年第5期644-652,I0066-I0072,I0100,共17页
Moleculardeviceswith highswitchingperformance and/or the perfect spin filtering effect have always been the pursuit with the development of molecular electronics.Hereb,yusingthe 2001.0V nonequilibrium.Green's func... Moleculardeviceswith highswitchingperformance and/or the perfect spin filtering effect have always been the pursuit with the development of molecular electronics.Hereb,yusingthe 2001.0V nonequilibrium.Green's function method in combination with the density functionaltheory,the switching performance and spin filtering properties of dimethyldihydropyrene(DHP)/cyclophanediene(CPD)photoswitchable molecule connected by carbon atomic chains(CACs)to two zigzag graphene nanoribbon electrodes have been theoretically investigated.The results show that DHP is more conductive than CPD and therefore an evident switching effect is demonstrated,and the switching ratio(RON/OFF)can reach 4.5×103.It is further revealed that the RoON/OF of DHP/CPD closely depends on the length of CACs.More specifically,the RoN/OFF values of DHP/CPD with odd-numbered CACs are larger than those with even-numbered CACs.More interestingly,a high or even perfect spin filtering effect can be obtained in these investigated DHP/CPD single-molecule devices.Our study is helpful for future design of single-molecule switches and spin filters and provides a way to optimize their performance by means of varying the length of bridging CACs. 展开更多
关键词 Single-molecule switch Spin filtering effect Odd-even effect Nonequilibrium Green's function method Density functional theory
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电梯群控遗传算法调度及应用
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作者 朱德文 《中国电梯》 2015年第20期55-61,共7页
解决使用遗传算法调度电梯群控系统中的任意1台轿厢最优响应层站呼叫问题。给出了使用遗传算法的电梯群控系统结构和目标函数,电梯群控遗传算法流程,及遗传算法流程操作,使用笔者构造的适应度函数作为评价标准,通过电梯群控轿厢调... 解决使用遗传算法调度电梯群控系统中的任意1台轿厢最优响应层站呼叫问题。给出了使用遗传算法的电梯群控系统结构和目标函数,电梯群控遗传算法流程,及遗传算法流程操作,使用笔者构造的适应度函数作为评价标准,通过电梯群控轿厢调度实例进行编码、种群设定、选择、交叉和变异操作,完成对层站呼叫的最优调度。为电梯群控使用其他智能算法的最优调度打下了基础。 展开更多
关键词 电梯群控系统 遗传算法 应度函数 最优调度
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Phase-response synchronization in neuronal population 被引量:5
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作者 JIAO XianFa ZHU DanFeng 《Science China(Technological Sciences)》 SCIE EI CAS 2014年第5期923-928,共6页
In this study,we have formulated the phase description of the neuronal oscillator with non-instantaneous synaptic inputs and external periodic stimulus by using the phase sensitivity function.By numerical simulation,w... In this study,we have formulated the phase description of the neuronal oscillator with non-instantaneous synaptic inputs and external periodic stimulus by using the phase sensitivity function.By numerical simulation,we have found that the phase of a neuronal oscillator undergoes periodic evolution or locked state,which is determined by the synaptic time constant.The synaptic time constant is also an important condition under which the global network is synchronized.When the synaptic time constant is relatively small,perfectly synchronized behavior quickly occurs in the neuronal population.As the synaptic time constant becomes slightly larger,periodic synchronization emerges in the neuronal population.However,synchronized activity in the neuronal population is lost for larger synaptic time constant.The external periodic stimulus can change the synchronization patterns in the neuronal population.With a weak low-frequency stimulus,the neuronal populations quick synchronized bursting;whereas a high-frequency stimulus can produce synchronized overlapping bursting.We have also found that neuronal oscillators with type-II phase response curves are more susceptible to synchronization than those with type-I phase response curves. 展开更多
关键词 neuronal population phase response curve synaptic input external periodic stimulus
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ON THE EXISTENCE OF GLOBAL ATTRACTOR FOR A CLASS OF INFINITE DIMENSIONAL DISSIPATIVE NONLINEAR DYNAMICAL SYSTEMS 被引量:10
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作者 ZHONGCHENGKUI SUNCHUNYOU NIUMINGFEI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2005年第3期393-400,共8页
By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attrac... By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained. 展开更多
关键词 Global attractor Measures of noncompactness Reaction-diffusion equations
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