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Generalized gradient projection neural networks for nonsmooth optimization problems

science china({2. sciences) 2010年第5期53卷 990-1005页

作者： li guocheng 1 , song {2. 2.? & wu cheng 2.1 department of mathematics, beijing information science and technology university, beijing 100192. china 2.department of Automation, Tsinghua university, beijing 100084, {12. 1. department of mathematics Beijing Information Science and Technology University Beijing 100192 China2. Department of Automation Tsinghua University Beijing 100084 China

Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of R n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimization problems, the quasi convergence results similar to those achieved by previous work are proved. For convex optimization problems, the global convergence results are proved, i.e. any trajectory of the neural network converges to an asymptotically stable equilibrium point, which is an optimal solution of the primal problem whenever it exists. This result remains valid even if the initial condition is chosen outside the feasible set. In addition, an asymptotic control result involving a Tykhonov like regularization shows that any trajectory of the revised neural network can be forced to converge toward a particular optimal solution of the primal problem. Finally, two simulation optimization algorithms for solving the optimization and control problems are designed respectively, and three typical simulation experiments are illustrated to present the accuracy and efficiency of theoretical convergence results of this paper.

关键词： nonsmooth optimization problem generalized gradient projection networks differential inclu sions convergence

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Heuristic for no-wait flow shops with makespan minimization based on total idle-time increments

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science in china(Series F) 2008年第7期51卷 896-909页

作者： li XiaoPing1,2.& wu cheng3 1 School of Computer {2. & Engineering, Southeast university, Nanjing 2.0096, china 2.Key Laboratory of Computer Network and information Integration (Southeast university), Ministry of Education, Nanjing 2.0096, china 3 department of Automation, Tsinghua university, beijing 100084, china 1. School of Computer science & Engineering Southeast University Nanjing 210096 China 2. Key Laboratory of Computer Network and information Integration (Southeast university) Ministry of Education Nanjing 210096 China 3. department of Automation Tsinghua University Beijing 100084 China

No-wait flow shops with makespan minimization are classified as NP-hard. In this paper, the optimization objective is equivalently transformed to total idle-time minimization. The independence relationship between tasks is analyzed, and objective increment properties are established for the fundamental operators of the heuristics. The quality of the new schedules generated during a heuristic is judged only by objective increments and not by the traditional method, which computes and compares the objective of a whole schedule. Based on objective increments, the time complexity of the heuristic can be decreased by one order. A seed phase is presented to generate an initial solution according to the transformed objective. Construction and improvement phases are introduced by experimental analysis. The FCH （fast composite heuristic） is proposed and compared with the most effective algorithms currently available for the considered problem. Experimental results show that the effectiveness of the FCH is similar to that of the best methods but requires far less computation time. The FCH can also be efficient in real time scheduling and rescheduling for no-wait flow shops.

关键词： no-wait flow shops heuristic makespan Tabu search

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Time series models in prediction of severe fever with thrombocytopenia syndrome cases in Shandong province,china

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Infectious Disease Modelling 2024年第1期9卷 224-233页

作者： Zixu Wang Wenyi Zhang Ting wu Nianhong Lu Junyu He Junhu Wang Jixian Rao Yuan Gu Xianxian cheng Yuexi li Yong Qi Pest Control department Huadong Research Institute for Medicine and BiotechniquesNanjingJiangsu province210002China Bengbu Medical College BengbuAnhui province233030China Chinese PLA Center for Disease Control and Prevention Beijing100071China Jinling Hospital Medical School of Nanjing UniversityNanjingJiangsu province210002China Ocean College Zhejiang UniversityZhoushan316021China Ocean Academy Zhejiang UniversityZhoushan316021China

Severe fever with thrombocytopenia syndrome (SFTS) is an emerging infectious disease caused by the SFTS virus (SFTSV). Predicting the incidence of this disease in advance is crucial for policymakers to develop prevention and control strategies. In this study, we utilized historical incidence data of SFTS ({2.3–2.2.) in Shandong Province, china to establish three univariate prediction models based on two time-series forecasting algorithms Autoregressive Integrated Moving Average (ARIMA) and Prophet, as well as a special type of recurrent neural network Long Short-Term Memory (LSTM) algorithm. We then evaluated and compared the performance of these models. All three models demonstrated good predictive capabilities for SFTS cases, with the predicted results closely aligning with the actual cases. Among the models, the LSTM model exhibited the best fitting and prediction performance. It achieved the lowest values for mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE). The number of SFTS cases in the subsequent 5 years in this area were also generated using this model. The LSTM model, being simple and practical, provides valuable information and data for assessing the potential risk of SFTS in advance. This information is crucial for the development of early warning systems and the formulation of effective prevention and control measures for SFTS.

关键词： Severe fever with thrombocytopenia syndrome Long short-term memory Prediction model Autoregressive integrated moving average Prophet

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The 2.2. report of synergetic roadmap on carbon neutrality and clean air for china:Accelerating transition in key sectors

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Environmental science and Ecotechnology 2024年第3期19卷 4-18页

作者： Yu Lei Zhicong Yin Xi Lu Qiang Zhang Jicheng Gong Bofeng Cai Cilan Cai Qimin Chai Huopo Chen Renjie Chen Shi Chen Wenhui Chen Jing cheng Xiyuan Chi Hancheng Dai Xiangzhao Feng Guannan Geng Jianlin Hu Shan Hu Cunrui Huang Tiantian li Wei li Xiaomei li Jun liu Xin liu Zhu liu Jinghui Ma Yue Qin Dan Tong Xuhui Wang Xuying Wang Rui wu Qingyang Xiao Yang Xie Xiaolong Xu Tao Xue Haipeng Yu Da Zhang Ning Zhang Shaohui Zhang Shaojun Zhang Xian Zhang Xin Zhang Zengkai Zhang Bo Zheng Yixuan Zheng Jian Zhou Tong Zhu Jinnan Wang Kebin He Center of Air Quality Simulation and System Analysis Chinese Academy of Environmental PlanningBeijing100041China Center for Carbon Neutrality Chinese Academy of Environmental PlanningBeijing100041China Key Laboratory of Meteorological Disaster Ministry of Education/Joint International Research Laboratory of Climate and Environment Change(ILCEC)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters(CIC-FEMD)Nanjing University of Information Science&TechnologyNanjing210044China State Key Joint Laboratory of Environment Simulation and Pollution Control School of EnvironmentTsinghua UniversityBeijing100084China Institute for Carbon Neutrality Tsinghua UniversityBeijing100084China Ministry of Education Key Laboratory for Earth System Modelling Department of Earth System ScienceTsinghua UniversityBeijing100084China State Key Joint Laboratory for Environment Simulation and Pollution Control College of Environmental Sciences and Engineering and Center for Environment and HealthPeking UniversityBeijing100871China National Center for Climate Change Strategy and International CooperationBeijing100035China Nansen-Zhu International Research Centre Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing100029China School of Public Health Key Lab of Public Health Safety of the Ministry of Education and Key Lab of Health Technology Assessment of the Ministry of HealthFudan UniversityShanghai200032China School of Economics and Management Beijing University of Chemical TechnologyBeijing100029China department of Earth System science University of CaliforniaIrvineCA92697USA National Meteorological Center China Meteorological AdministrationBeijing100081China College of Environmental sciences and Engineering Peking UniversityBeijing100871China Policy Research Center for Environment and Economy Ministry of Ecology and Environment of the People's Republic of ChinaBeijing100029China Jiangsu Key Laboratory of Atmospheric Environment Monitoring

china is now confronting the intertwined challenges of air pollution and climate *** the high synergies between air pollution abatement and climate change mitigation,the Chinese government is actively promoting synergetic control of these two *** Synergetic Roadmap project was launched in 2.2. to track and analyze the progress of synergetic control in china by developing and monitoring key *** Synergetic Roadmap 2.2. report is the first annual update,featuring 2. indicators across five aspects:synergetic governance system and practices,progress in structural transition,air pollution and associated weather-climate interactions,sources,sinks,and mitigation pathway of atmospheric composition,and health impacts and benefits of coordinated *** to the comprehensive review presented in the 2.2. report,the Synergetic Roadmap 2.2. report places particular emphasis on progress in 2.2. with highlights on actions in key sectors and the relevant *** milestones include the proportion of non-fossil power generation capacity surpassing coal-fired capacity for the first time,a decline in the production of crude steel and cement after years of growth,and the surging penetration of electric ***,in 2.2.,china issued the first national policy that synergizes abatements of pollution and carbon emissions,marking a new era for china's pollution-carbon *** changes highlight china's efforts to reshape its energy,economic,and transportation structures to meet the demand for synergetic control and sustainable ***,the country has witnessed a slowdown in carbon emission growth,improved air quality,and increased health benefits in recent years.

关键词： Synergetic roadmap Carbon neutrality Clean air

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Two-dimensional materials for future information technology: status and prospects

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science china({2. sciences) 2024年第6期67卷 1-147页

作者： Hao QIU Zhihao YU Tiange ZHAO Qi ZHANG Mingsheng XU Peifeng li Taotao li Wenzhong BAO Yang CHAI Shula CHEN Yiqi CHEN Hui-Ming {2. Daoxin DAI Zengfeng DI Zhuo DONG Xidong DUAN Yuhan FENG Yu FU Jingshu GUO Pengwen GUO Yue HAO Jun HE Xiao HE Jingyi HU Weida HU Zehua HU Xinyue HUANG Ziyang HUANG Ali IMRAN Ziqiang KONG Jia li Qian li Weisheng li Lei liAO Bilu liU Can liU Chunsen liU Guanyu liU Kaihui liU liwei liU Sheng liU Yuan liU Donglin LU likuan MA Feng MIAO Zhenhua NI Jing NING Anlian PAN Tian-ling REN Haowen SHU litao SUN Yue SUN Quanyang TAO Zi-Ao TIAN Dong WANG Hao WANG Haomin WANG Jialong WANG Junyong WANG Wenhui WANG Xingjun WANG Yeliang WANG Yuwei WANG Zhenyu WANG Yao WE... School of Electronic science and Engineering Nanjing University School of Integrated Circuits Interdisciplinary Research Center for Future Intelligent Chips (Chip-X)Nanjing University School of Integrated Circuit science and Engineering Nanjing University of Posts and Telecommunications State Key Laboratory of Infrared Physics Shanghai Institute of Technical Physics Chinese Academy of Sciences School of Physics and Key Lab of Quantum Materials and Devices of the Ministry of Education School of Electronic Science & EngineeringSoutheast University College of Integrated Circuits State Key Laboratory of Silicon and Advanced Semiconductor MaterialsZhejiang University Suzhou Laboratory State Key Laboratory of Integrated Chips and Systems School of MicroelectronicsFudan University Shaoxin Laboratory department of Applied Physics The Hong Kong Polytechnic University Key Laboratory for Micro-Nano Physics and technology of Hunan Province College of Materials Science and EngineeringHunan University College of Integrated Circuits Zhejiang University Shenzhen Geim Graphene Center Shenzhen Key Laboratory of Layered Materials for Value-Added ApplicationsTsinghua-Berkeley Shenzhen Institute & Institute of Materials ResearchTsinghua Shenzhen International Graduate SchoolTsinghua University State Key Laboratory of Extreme Photonics and Instrumentation College of Optical Science and EngineeringInternational Research Center for Advanced PhotonicsZijingang CampusZhejiang University National Key Laboratory of Materials for Integrated Circuits Shanghai Institute of Microsystem and Information TechnologyChinese Academy of Sciences CAS Key Laboratory of Nanophotonic Materials and Devices & Key Laboratory of Nanodevices and Applications i-LabSuzhou Institute of Nano-Tech and Nano-Bionics (SINANO)Chinese Academy of Sciences College of Chemistry and Chemical Engineering Hunan University Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education) Department of PhysicsRenmin University of China School

Over the past 70 years, the semiconductor industry has undergone transformative changes,largely driven by the miniaturization of devices and the integration of innovative structures and materials. Two-dimensional(2.) materials like transition metal dichalcogenides(TMDs) and graphene are pivotal in overcoming the limitations of silicon-based technologies, offering innovative approaches in transistor design and functionality, enabling atomic-thin channel transistors and monolithic 3D integration. We review the important progress in the application of 2. materials in future information technology, focusing in particular on microelectronics and optoelectronics. We comprehensively summarize the key advancements across material production, characterization metrology, electronic devices, optoelectronic devices, and heterogeneous integration on silicon. A strategic roadmap and key challenges for the transition of 2. materials from basic research to industrial development are outlined. To facilitate such a transition, key technologies and tools dedicated to 2. materials must be developed to meet industrial standards, and the employment of AI in material growth, characterizations, and circuit design will be essential. It is time for academia to actively engage with industry to drive the next 10 years of 2. material research.

关键词： two-dimensional (2.) materials information technology production technology standardization of characterization microelectronic devices optoelectronic devices multi-functional integration

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Localization effect in single crystal of RuAs2

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Chinese Physics B 2024年第4期33卷 620-625页

作者：易哲铠刘琪光双魁徐升岳小宇梁慧李娜周颖吴丹丹孙燕李秋菊程鹏夏天龙孙学峰王义炎 Anhui Key Laboratory of Magnetic Functional Materials and Devices Institute of Physical Science and Information TechnologyAnhui University department of Physics and Key Laboratory of Strongly-Coupled Quantum Matter Physics (CAS) University of Science and Technology of China department of Physics and beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices Renmin University of China School of Optical and Electronic information Suzhou City University School of Physics and Optoelectronic Engineering Anhui University Collaborative Innovation Center of Advanced Microstructures Nanjing University

We report the magnetotransport and thermal properties of RuAs2.ingle crystal. RuAs2.xhibits semiconductor behavior and localization effect. The crossover from normal state to diffusive transport in the weak localization（WL） state and then to variable range hopping（VRH） transport in the strong localization state has been observed. The transitions can be reflected in the measurement of resistivity and Seebeck coefficient. Negative magnetoresistance（NMR） emerges with the appearance of localization effect and is gradually suppressed in high magnetic field. The temperature dependent phase coherence length extracted from the fittings of NMR also indicates the transition from WL to VRH. The measurement of Hall effect reveals an anomaly of temperature dependent carrier concentration caused by localization effect. Our findings show that RuAs2.s a suitable platform to study the localized state.

关键词： weak localization variable range hopping RuAs_2.single crystal

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二维铁电半导体层级处理模块设计及低功耗高性能人工视觉系统应用

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science Bulletin 2024年第4期69卷 473-482页

作者：吴广成向立王文强姚程栋颜泽毅张成吴家鑫刘勇郑弼元刘华伟胡城伟孙兴霞朱晨光王一喆熊雄吴燕庆高亮李东潘安练李晟曼 Key Laboratory for Micro-Nano Physics and technology of Hunan Province State Key Laboratory of Chemo/Biosensing and ChemometricsCollege of Materials Science and EngineeringHunan UniversityChangsha 410082China Hunan Institute of Optoelectronic Integration Hunan UniversityChangsha 410082China Hunan Institute of Advanced Sensing and information technology Xiangtan UniversityXiangtan 411105China School of Integrated Circuits Peking UniversityBeijing 100871China wuhan National Laboratory for Optoelectronics(WNLO) Huazhong University of Science and Technology(HUST)Wuhan 430074China

The growth of data and Internet of Things challenges traditional hardware,which encounters efficiency and power issues owing to separate functional units for sensors,memory,and *** this study,we designed an a-phase indium selenide(a-In_(2.Se_(3))transistor,which is a two-dimensional ferroelectric semiconductor as the channel material,to create artificial optic-neural and electro-neural synapses,enabling cutting-edge processing-in-sensor(PIS)and computing-in-memory(CIM)*** an optic-neural synapse for low-level sensory processing,the a-In_(2.Se_(3)transistor exhibits a high photoresponsivity(2.55 A/W)and detectivity(2.91×10^(14)Jones),facilitating efficient feature *** high-level processing tasks as an electro-neural synapse,it offers a fast program/erase speed of 40 ns/50μs and ultralow energy consumption of 0.37 aJ/*** AI vision system using a-In_(2.Se_(3)transistors has been *** achieved an impressive recognition accuracy of 92.63%within 12.epochs owing to the synergistic combination of the PIS and CIM *** study demonstrates the potential of the a-In_(2.Se_(3)transistor in future vision hardware,enhancing processing,power efficiency,and AI applications.

关键词： Two-dimensional ferroelectric semiconductor Processing-in-sensor Computing-in-memory Synaptic device Artificial-intelligence vision system

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Response of North Pacific and North Atlantic decadal variability to weak global warming

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Advances in Climate Change Research 2018年第2期9卷 95-101页

作者： wu Sheng liU Zheng-Yu cheng Jun li Chun Laboratory for Climate and Ocean-Atmosphere Studies (LaCOAS) and department of Atmospheric and Oceanic {2.s School of Physics Peking University Beijing 100871 China Atmospheric science Program Department of Geography Ohio State University Columbus 43210 USA Key Laboratory of Meteorological Disaster Ministry of Education (KLME)/Joint International Research Laboratory of Climate and Environment Chenge (ILCEC) Climate Dynamics Research Center Nunjing University of Information Science and Technology Nunjing 210044 China Physical Oceanography Lab Ocean University of China Qingdao 266100 China

The Pacific Decadal Oscillation （PDO） and the Atlantic Multidecadal Variability （AMV） are the two dominant low-frequency modes in the climate system. This research focused on the response of these two modes under weak global warming. Observational data were derived from the Hadley Center Sea Ice and Sea Surface Temperature dataset （HadISST） and coupled model outputs from the Coupled Model Intercomparison Project Phase 5 （CMIP5）. Changes in PDO and AMV were examined using four models （bcc-csml-1, CCSM4, IPSL-CM5A-LR, and MPI- ESM-LR） with long weak global warming scenarios （RCP2.6）. These models captured the two low-frequency modes in both pre-industrial run and RCP2.6 run. Under weak global warming, the time scales of PDO and AMV significantly decreased while the amplitude only slightly decreased. Interestingly, the standard deviation of the North Pacific sea surface temperature anomaly （SSTA） decreased only in decadal time scale, and that of the North Atlantic SSTA decreased both in interannual and decadal time scales. The coupled system consists of a slow ocean component, which has a decadal time scale, and a fast atmospheric component, which is calculated by subtracting the decadal from the total. Results suggest that under global warming, PDO change is dominated by ocean dynamics, and AMV change is dominated by ocean dynamics and stochastic atmosphere forcing.

关键词： Pacific decadal oscillation Atlantic multidecadal variability RCP2.6

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Emerging contaminants:A One Health perspective

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The Innovation 2024年第4期5卷 140-170,139页

作者： Fang Wang Leilei Xiang Kelvin Sze-Yin Leung Martin Elsner Ying Zhang Yuming Guo Bo Pan Hongwen Sun Taicheng An Guangguo Ying Bryan WBrooks Deyi Hou Damian EHelbling Jianqiang Sun Hao Qiu Timothy MVogel Wei Zhang Yanzheng Gao Myrna JSimpson Yi Luo Scott XChang Guanyong Su Bryan MWong Tzung-May Fu Dong Zhu Karl JJobst chengjun Ge Frederic Coulon Jean Damascene Harindintwali Xiankui Zeng Haijun Wang Yuhao Fu Zhong Wei Rainer Lohmann Changer Chen Yang song Concepcion Sanchez-Cid Yu Wang Ali El-Naggar Yiming Yao Yanran Huang Japhet Cheuk-Fung Law chenggang Gu Huizhong Shen Yanpeng Gao Chao Qin Hao li Tong Zhang Natàlia Corcoll Min liu Daniel SAlessi Hui li Kristian KBrandt Yolanda Pico cheng Gu Jianhua Guo Jianqiang Su Philippe Corvini Mao Ye Teresa Rocha-Santos Huan He Yi Yang Meiping Tong Weina Zhang Fidèle Suanon Ferdi Brahushi Zhenyu Wang Syed AHashsham Marko Virta Qingbin Yuan Gaofei Jiang Louis A.Tremblay Qingwei Bu Jichun wu Willie Peijnenburg Edward Topp Xinde Cao Xin Jiang Minghui Zheng Taolin Zhang Yongming Luo lizhong Zhu Xiangdong li DamiàBarceló Jianmin Chen Baoshan Xing wulf Amelung Zongwei Cai Ravi Naidu Qirong Shen Janusz Pawliszyn Yong-guan Zhu Andreas Schaeffer Matthias C.Rillig Fengchang wu Gang Yu James M.Tiedje State Key Laboratory of Soil and Sustainable Agriculture Institute of Soil ScienceChinese Academy of SciencesNanjing 210008China university of Chinese Academy of sciences Beijing 100049China department of Chemistry Hong Kong Baptist UniversityHong KongChina HKBU Institute of Research and Continuing Education Shenzhen Virtual University ParkShenzhenChina Technical university of Munich TUM School of Natural SciencesInstitute of Hydrochemistry85748 GarchingGermany School of Resources&Environment Northeast Agricultural UniversityHarbin 150030China Climate Air Quality Research UnitSchool of Public Health and Preventive MedicineMonash UniversityMelbourneVICAustralia Faculty of Environmental science&Engineering Kunming University of Science&TechnologyKunming 650500China Ministry of Education Key Laboratory of Pollution Processes and Environmental Criteria College of Environmental Science and EngineeringNankai UniversityTianjin 300350China Guangdong Key Laboratory of Environmental Catalysis and Health Risk Control School of Environmental Science and EngineeringInstitute of Environmental Health and Pollution ControlGuangdong University of TechnologyGuangzhou 510006China Ministry of Education Key Laboratory of Environmental Theoretical Chemistry South China Normal UniversityGuangzhouGuangdong 510006China department of Environmental science Baylor UniversityWacoTXUSA Center for Reservoir and Aquatic Systems Research(CRASR) Baylor UniversityWacoTXUSA School of Environment Tsinghua UniversityBeijing 100084China School of Civil and Environmental Engineering Cornell UniversityIthacaNY 14853USA Key Laboratory of Microbial technology for Industrial Pollution Control of Zhejiang Province Zhejiang University of TechnologyHangzhou 310014China School of Environmental science and Engineering Shanghai Jiao Tong UniversityShanghai 200240China Laboratoire d’Ecologie Microbienne Universite Claude Bernard Lyon 1UMR CNRS 5557UMR INRAE 1418VetAgro Sup69622 VilleurbanneFrance department of Pla

Environmental pollution is escalating due to rapid global development that often prioritizes human needs over planetary *** global efforts to mitigate legacy pollutants,the continuous introduction of new substances remains a major threat to both people and the *** response,global initiatives are focusing on risk assessment and regulation of emerging contaminants,as demonstrated by the ongoing efforts to establish the UN’s Intergovernmental science-Policy Panel on Chemicals,Waste,and Pollution *** review identifies the sources and impacts of emerging contaminants on planetary health,emphasizing the importance of adopting a One Health *** for monitoring and addressing these pollutants are discussed,underscoring the need for robust and socially equitable environmental policies at both regional and international *** actions are needed to transition toward sustainable pollution management practices to safeguard our planet for future generations.

关键词： pollution planet contaminants

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Directed transport of coupled Brownian motors in a two-dimensional traveling-wave potential

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Chinese Physics B 2020年第9期29卷 244-248页

作者： Wei-Xia wu Zhi-Gang Zheng Yan-li song Ying-Rong Han Zhi-{2. Sun Chen-Pu li science Education department Beijing Institute of Graphic CommunicationBeijing 102600China Institute of Systems science and College of information science and Engineering Huaqiao UniversityXiamen 361021China School of science Tianjin UniversityTianjin 300072China School of science Hebei University of TechnologyTianjin 300401China School of Printing and Packaging Engineering Beijing Institute of Graphic CommunicationBeijing 102600China College of science Hebei Institute of Architecture and Civil EngineeringZhangjiakou 075000China

Considering an elastically coupled Brownian motors system in a two-dimensional traveling-wave potential, we investigate the effects of the angular frequency of the traveling wave, wavelength, coupling strength, free length of the spring, and the noise intensity on the current of the system. It is found that the traveling wave is the essential condition of the directed transport. The current is dominated by the traveling wave and varies nonmonotonically with both the angular frequency and the wavelength. At an optimal angular frequency or wavelength, the current can be optimized. The coupling strength and the free length of the spring can locally modulate the current, especially at small angular frequencies. Moreover, the current decreases rapidly with the increase of the noise intensity, indicating the interference effect of noise on the directed transport.

关键词： directed transport Brownian motors coupled system two-dimensional traveling-wave potential

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