A new traffic model on compulsive lane-changing caused by off-ramp
Xiao-He Liu(刘小禾), Hung-Tang Ko(柯鸿堂), Ming-Min Guo(郭明旻), Zheng Wu(吴正) Citation:Chin. Phys. B . 2016, 25(4): 048901. doi: 10.1088/1674-1056/25/4/048901
Journal homepage: http://cpb.iphy.ac.cn; http://iopscience.iop.org/cpb
What follows is a list of articles you may be interested in
Pedestrian evacuation at the subway station under the fire
Xiao-Xia Yang(杨晓霞), Hai-Rong Dong(董海荣), Xiu-Ming Yao(姚秀明), Xu-Bin Sun(孙绪彬) Chin. Phys. B . 2016, 25(4): 048902. doi: 10.1088/1674-1056/25/4/048902
Dynamic feature analysis in bidirectional pedestrian flows
Xiao-Xia Yang(杨晓霞), Winnie Daamen, Serge Paul Hoogendoorn, Hai-Rong Dong(董海荣), Xiu-Ming Yao(姚秀明) Chin. Phys. B . 2016, 25(2): 028901. doi: 10.1088/1674-1056/25/2/028901
A new traffic model with a lane-changing viscosity term
Ko Hung-Tang, Liu Xiao-He, Guo Ming-Min, Wu Zheng Chin. Phys. B . 2015, 24(9): 098901. doi: 10.1088/1674-1056/24/9/098901
Establishment, maintenance, and re-establishment of the safe and efficient steady-following state
Pan Deng, Zheng Ying-Ping Chin. Phys. B . 2015, 24(8): 088901. doi: 10.1088/1674-1056/24/8/088901
A genetic resampling particle filter for freeway traffic-state estimation
Bi Jun, Guan Wei, Qi Long-Tao Chin. Phys. B . 2012, 21(6): 068901. doi: 10.1088/1674-1056/21/6/068901 ------
Chinese Physics B (中中中国国国物物物理理理 B) Published monthly in hard copy by the Chinese Physical Society and online by IOP Publishing, Temple Circus, Temple Way, Bristol BS1 6HG, UK Institutional subscription information: 2016 volume For all countries, except the United States, Canada and Central and South America, the subscription rate per annual volume is UK£974 (electronic only) or UK£1063 (print + electronic). Delivery is by air-speeded mail from the United Kingdom. Orders to: Journals Subscription Fulfilment, IOP Publishing, Temple Circus, Temple Way, Bristol BS1 6HG, UK For the United States, Canada and Central and South America, the subscription rate per annual volume is US$1925 (electronic only) or US$2100 (print + electronic). Delivery is by transatlantic airfreight and onward mailing. Orders to: IOP Publishing, P. O. Box 320, Congers, NY 10920-0320, USA ⃝c 2016 Chinese Physical Society and IOP Publishing Ltd All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright owner. Supported by the China Association for Science and Technology and Chinese Academy of Sciences Editorial Office: Institute of Physics, Chinese Academy of Sciences, P. O. Box 603, Beijing 100190, China Tel: (86 - 10) 82649026 or 82649519, Fax: (86 - 10) 82649027, E-mail: [email protected] 主管单位: 中国科学院 国际统一刊号: ISSN 1674–1056 主办单位: 中国物理学会和中国科学院物理研究所 国内统一刊号: CN 11–5639/O4 主 编: 欧阳钟灿 编辑部地址: 北京中关村中国科学院物理研究所内 出 版: 中国物理学会 通 讯 地 址: 100190 北京 603 信箱 印刷装订: 北京科信印刷有限公司 电 话: (010) 82649026, 82649519 编 辑: Chinese Physics B 编辑部 传 真: (010) 82649027 国内发行: Chinese Physics B 出版发行部 “Chinese Physics B”网址: 国外发行: IOP Publishing Ltd http://cpb.iphy.ac.cn (编辑部) 发行范围: 公开发行 http://iopscience.iop.org/cpb (IOPP)
Published by the Chinese Physical Society 顾顾顾问问问 Advisory Board 陈佳洱教授 , 院士 Prof. Academician Chen Jia-Er 北京大学物理学院, 北京 100871 School of Physics, Peking University, Beijing 100871, China 冯 端 教授, 院士 Prof. Academician Feng Duan 南京大学物理系, 南京 210093 Department of Physics, Nanjing University, Nanjing 210093, China 李政道教授 , 院士 Prof. Academician T. D. Lee Department of Physics, Columbia University, New York, NY 10027, USA 李荫远研究员 , 院士 Prof. Academician Li Yin-Yuan 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 丁肇中教授 , 院士 Prof. Academician Samuel C. C. Ting LEP3, CERN, CH-1211, Geneva 23, Switzerland 杨振宁教授 , 院士 Prof. Academician C. N. Yang Institute for Theoretical Physics, State University of New York, USA 杨福家教授 , 院士 Prof. Academician Yang Fu-Jia 复旦大学物理二系, 上海 200433 Department of Nuclear Physics, Fudan University, Shanghai 200433, China 周光召研究员 , 院士 Prof. Academician Zhou Guang-Zhao (Chou Kuang-Chao) 中国科学技术协会, 北京 100863 China Association for Science and Technology, Beijing 100863, China 王乃彦研究员 , 院士 Prof. Academician Wang Nai-Yan 中国原子能科学研究院, 北京 102413 China Institute of Atomic Energy, Beijing 102413, China 梁敬魁研究员 , 院士 Prof. Academician Liang Jing-Kui 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2012–2015 主主主 编编编 Editor-in-Chief 欧阳钟灿研究员 , 院士 Prof. Academician Ouyang Zhong-Can 中国科学院理论物理研究所, Institute of Theoretical Physics, Chinese Academy of Sciences, 北京 100190 Beijing 100190, China 副副副主主主编编编 Associate Editors 赵忠贤研究员 , 院士 Prof. Academician Zhao Zhong-Xian 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 杨国桢研究员 , 院士 Prof. Academician Yang Guo-Zhen 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 张 杰 研究员, 院士 Prof. Academician Zhang Jie 上海交通大学物理与天文系, Department of Physics and Astronomy, Shanghai Jiao Tong University, 上海 200240 Shanghai 200240, China 邢定钰 教授, 院士 Prof. Academician Xing Ding-Yu 南京大学物理学院, 南京 210093 School of Physics, Nanjing University, Nanjing 210093, China 沈保根 研究员, 院士 Prof. Academician Shen Bao-Gen 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 龚旗煌 教授, 院士 Prof. Academician Gong Qi-Huang 北京大学物理学院, 北京 100871 School of Physics, Peking University, Beijing 100871, China 薛其坤 教授, 院士 Prof. Academician Xue Qi-Kun 清华大学物理系, 北京 100084 Department of Physics, Tsinghua University, Beijing 100084, China 沈 平 教授 Prof. Sheng Ping 香港科技大学物理学系, 香港九龍 Department of Physics, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China 编编编辑辑辑委委委员员员 Editorial Board 2011–2016 Prof. F. R. de Boer van der Waals-Zeeman Institute der Universiteit van Amsterdam Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands Prof. H. F. Braun Physikalisches Institut, Universit¨atBayreuth, D-95440 Bayreuth, Germany 陈东敏 教授 Prof. Chen Dong-Min Rowland Institute for Science, Harvard University, USA 冯世平 教授 Prof. Feng Shi-Ping 北京师范大学物理系, 北京 100875 Department of Physics, Beijing Normal University, Beijing 100875, China 高鸿钧 研究员, 院士 Prof. Academician Gao Hong-Jun 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 顾长志 研究员 Prof. Gu Chang-Zhi 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 胡 岗 教授 Prof. Hu Gang 北京师范大学物理系, 北京 100875 Department of Physics, Beijing Normal University, Beijing 100875, China 侯建国 教授, 院士 Prof. Academician Hou Jian-Guo 中国科学技术大学中国科学院结构分析 Structure Research Laboratory, University of Science and Technology of 重点实验室, 合肥 230026 China, Hefei 230026, China 李方华 研究员, 院士 Prof. Academician Li Fang-Hua 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 闵乃本 教授, 院士 Prof. Academician Min Nai-Ben 南京大学物理系, 南京 210093 Department of Physics, Nanjing University, Nanjing 210093, China 聂玉昕 研究员 Prof. Nie Yu-Xin 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 潘建伟 教授, 院士 Prof. Academician Pan Jian-Wei 中国科学技术大学近代物理系, Department of Modern Physics, University of Science and Technology of 合肥 230026 China, Hefei 230026, China 沈志勋 教授 Prof. Shen Zhi-Xun Stanford University, Stanford, CA 94305–4045, USA 苏肇冰 研究员, 院士 Prof. Academician Su Zhao-Bing 中国科学院理论物理研究所, Institute of Theoretical Physics, Chinese Academy of Sciences, 北京 100190 Beijing 100190, China 孙昌璞 研究员, 院士 Prof. Academician Sun Chang-Pu 中国工程物理研究院北京计算科学 Beijing Computational Science Research Center, China Academy of 研究中心, 北京 100094 Engineering Physics, Beijing 100094, China 王恩哥 研究员, 院士 Prof. Academician Wang En-Ge 北京大学物理学院, 北京 100871 School of Physics, Peking University, Beijing 100871, China 夏建白 研究员, 院士 Prof. Academician Xia Jian-Bai 中国科学院半导体研究所, Institute of Semiconductors, Chinese Academy of Sciences, 北京 100083 Beijing 100083, China 向 涛 研究员, 院士 Prof. Academician Xiang Tao 中国科学院理论物理研究所, Institute of Theoretical Physics, Chinese Academy of Sciences, 北京 100190 Beijing 100190, China 谢心澄 教授，院士 Prof. Academician Xie Xin-Cheng 北京大学物理学院, 北京 100871 School of Physics, Peking University, Beijing 100871, China 詹文龙 研究员, 院士 Prof. Academician Zhan Wen-Long 中国科学院, 北京 100864 Chinese Academy of Sciences, Beijing 100864, China 朱邦芬 教授, 院士 Prof. Academician Zhu Bang-Fen 清华大学物理系, 北京 100084 Department of Physics, Tsinghua University, Beijing 100084, China 2013–2018 Prof. Antonio H. Castro Neto Physics Department, Faculty of Science, National University of Singapore, Singapore 117546, Singapore Prof. Chia-Ling Chien Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA Prof. David Andelman School of Physics and Astronomy，Tel Aviv University，Tel Aviv 69978, Israel Prof. Masao Doi Toyota Physical and Chemical Research Institute，Yokomichi, Nagakute, Aichi 480-1192, Japan Prof. Michiyoshi Tanaka Research Institute for Scientific Measurements, Tohoku University, Katahira 2–1–1, Aoba-ku 980, Sendai, Japan Prof. Werner A. Hofer Stephenson Institute for Renewable Energy, The University of Liverpool, Liverpool L69 3BX, UK 丁 军 教授 Prof. Ding Jun Department of Materials Science & Engineering, National University of Singapore, Singapore 117576, Singapore 贺贤土 研究员, 院士 Prof. Academician He Xian-Tu 北京应用物理与计算数学研究所, Institute of Applied Physics and Computational Mathematics, Beijing 100088, 北京 100088 China 金晓峰 教授 Prof. Jin Xiao-Feng 复旦大学物理系, 上海 200433 Department of Physics, Fudan University, Shanghai 200433, China 李儒新 研究员 Prof. Li Ru-Xin 中国科学院上海光学精密机械研究所, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of 上海 201800 Sciences, Shanghai 201800, China 吕 力 研究员 Prof. L¨uLi 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 李晓光 教授 Prof. Li Xiao-Guang 中国科学技术大学物理系, 合肥 230026 Department of Physics, University of Science and Technology of China, Hefei 230026, China 沈元壤 教授 Prof. Shen Yuan-Rang Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 王亚愚 教授 Prof. Wang Ya-Yu 清华大学物理系, 北京 100084 Department of Physics, Tsinghua University, Beijing 100084, China 王玉鹏 研究员 Prof. Wang Yu-Peng 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 王肇中 教授 Prof. Wang Zhao-Zhong Laboratory for Photonics and Nanostructures(LPN) CNRS–UPR20, Route de Nozay, 91460 Marcoussis, France 闻海虎 教授 Prof. Wen Hai-Hu 南京大学物理学院系, 南京 210093 School of Physics, Nanjing University, Nanjing 210093, China 徐至展 研究员, 院士 Prof. Academician Xu Zhi-Zhan 中国科学院上海光学精密机械研究所, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of 上海 201800 Sciences, Shanghai 201800, China 许岑珂 助理教授 Assist. Prof. Xu Cen-Ke Department of Physics，University of California, Santa Barbara, CA 93106, USA 叶 军 教授 Prof. Ye Jun Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA 张振宇 教授 Prof. Z. Y. Zhang Oak Ridge National Laboratory, Oak Ridge, TN 37831–6032, USA 2015–2020 Prof. J. Y. Rhee Department of Physics, Sungkyunkwan University, Suwon, Korea Prof. Robert J. Joynt Physics Department, University of Wisconsin-Madison, Madison, USA 程建春 教授 Prof. Cheng Jian-Chun 南京大学物理学院, 南京 210093 School of Physics, Nanjing University, Nanjing 210093, China 戴 希 研究员 Prof. Dai Xi 中国科学院物理研究所，北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 郭光灿 教授, 院士 Prof. Academician Guo Guang-Can 中国科学技术大学物理学院, School of Physical Sciences, University of Science and Technology of China, 合肥 230026 Hefei 230026, China 刘朝星 助理教授 Assist. Prof. Liu Chao-Xing Department of Physics, Pennsylvania State University, PA 16802-6300, USA 刘 荧 教授 Prof. Liu Ying 上海交通大学物理与天文系, Department of Physics and Astronomy, Shanghai Jiao Tong University, 上海 200240 Shanghai 200240, China 龙桂鲁 教授 Prof. Long Gui-Lu 清华大学物理系, 北京 100084 Department of Physics, Tsinghua University, Beijing 100084, China 牛 谦 教授 Prof. Niu Qian Department of Physics, University of Texas, Austin, TX 78712, USA 欧阳颀 教授, 院士 Prof. Academician Ouyang Qi 北京大学物理学院, 北京 100871 School of Physics, Peking University, Beijing 100871, China 孙秀冬 教授 Prof. Sun Xiu-Dong 哈尔滨工业大学物理系, 哈尔滨 150001 Department of Physics, Harbin Institute of Technology, Harbin 150001, China 童利民 教授 Prof. Tong Li-Min 浙江大学光电信息工程学系, Department of Optical Engineering, Zhejiang University, 杭州 310027 Hangzhou 310027, China 童彭尔 教授 Prof. Tong Penger 香港科技大学物理系, 香港九龍 Department of Physics, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China 王开友 研究员 Prof. Wang Kai-You 中国科学院半导体研究所, 北京 100083 Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China 魏苏淮 教授 Prof. Wei Su-Huai 中国工程物理研究院北京计算科学研究 Beijing Computational Science Research Center, China Academy of 中心, 北京 100094 Engineering Physics, Beijing 100094, China 解思深 研究员, 院士 Prof. Academician Xie Si-Shen 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 叶朝辉 研究员, 院士 Prof. Academician Ye Chao-Hui 中国科学院武汉物理与数学研究所, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 武汉 430071 Wuhan 430071, China 郁明阳 教授 Prof. Yu Ming-Yang Theoretical Physics I, Ruhr University, D-44780 Bochum, Germany 张富春 教授 Prof. Zhang Fu-Chun 香港大学物理系, 香港 Department of Physics, The University of Hong Kong, Hong Kong, China 张 勇 教授 Prof. Zhang Yong Electrical and Computer Engineering Department, The University of North Carolina at Charlotte, Charlotte, USA 郑 波 教授 Prof. Zheng Bo 浙江大学物理系, 杭州 310027 Physics Department, Zhejiang University, Hangzhou 310027, China 周兴江 研究员 Prof. Zhou Xing-Jiang 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 编编编 辑辑辑 Editorial Staff 王久丽 Wang Jiu-Li 章志英 Zhang Zhi-Ying 蔡建伟 Cai Jian-Wei 翟 振 Zhai Zhen 郭红丽 Guo Hong-Li Chin. Phys. B Vol. 25, No. 4 (2016) 048901
A new traffic model on compulsive lane-changing caused by off-ramp∗
Xiao-He Liu(刘小禾)2, Hung-Tang Ko(柯鸿堂)3, Ming-Min Guo(郭明旻)1,†, and Zheng Wu(吴正)1
1Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China 2School of Engineering, Brown University, Providence, RI 02903, USA 3Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
(Received 7 October 2015; revised manuscript received 13 December 2015; published online 25 February 2016)
In the field of traffic flow studies, compulsive lane-changing refers to lane-changing (LC) behaviors due to traffic rules or bad road conditions, while free LC happens when drivers change lanes to drive on a faster or less crowded lane. LC studies based on differential equation models accurately reveal LC influence on traffic environment. This paper presents a second-order partial differential equation (PDE) model that simulates both compulsive LC behavior and free LC behavior, with lane-changing source terms in the continuity equation and a lane-changing viscosity term in the momentum equation. A specific form of this model focusing on a typical compulsive LC behavior, the ‘off-ramp problem’, is derived. Numerical simulations are given in several cases, which are consistent with real traffic phenomenon.
Keywords: traffic flow model, compulsive lane-changing, off-ramp, fluid dynamics, numerical simulation PACS: 89.40.–a, 02.60.–x, 47.11.–j, 45.70.Vn DOI: 10.1088/1674-1056/25/4/048901
1. Introduction equation. Let ρ be the traffic density, u be the speed, then ∂ρ ∂ρ ∂u As an important driving behavior, lane-changing behavior + u + ρ = Φ(x,t), (LC) has gained increasing attention in the past few years, and ∂t ∂x ∂x ∂u ∂u a2 ∂ρ 1 has become a remarkable problem in traffic flow studies. Re- + u + = (Ue − u), (1) ∂t ∂x ρ ∂x Tr cent papers revealed that LC is crucial for traffic relaxation[1,2] and safety.[3–7] Therefore, researches on LC problems may where Φ(x,t) is the traffic source term, a is the sonic speed, carry great significance. Tr is the time delay parameter, and Ue is the equilibrium speed Toledo,[8] Moridpour et al.,[9] and Zheng[10] have re- function. Later, various models were built based on Payne’s [14–17] viewed LC, which categorized LC behavior as free LC (i.e., model. Papageogiou’s model adds a term to the momen- discretionary LC) and compulsive LC (i.e., mandatory LC), tum equation to simulate the influence of the ramp on the main road traffic:[14] according to how the decision of LC is made. Free LC is 2 executed to improve driving conditions, such as changing to ∂u ∂u a ∂ρ 1 uΦ + u + = (Ue − u) − δ , (2) a faster lane to achieve higher speed, and changing to a less ∂t ∂x ρ ∂x Tr ρ crowded lane to be more comfortable. Compulsive LC is ex- where Φ is the on-ramp traffic flow per unit width of the ramp, ecuted when the driver has to leave the current lane due to and δ ∈ [0,1], is a dimensionless coefficient related to the certain traffic rules or bad road conditions, for example, the speed difference between the ramp and the main road. off-ramp problem: a driver who intends to leave the main road In the past few years, several continuum traffic models on from the off-ramp ahead always moves into the right-hand lane free LC have been published. Laval and Daganzo adopted the [7] or the auxiliary lane in advance to prepare for leaving (in right- speed difference between adjacent lanes to construct, while [18] driving traffics). This problem is modeled and studied in this Zhu and Wu used the density difference instead. Ko et [19] paper. al. integrated the two forms of the source term to fully char- In traffic flow studies, the continuum model is an effec- acterize the free LC phenomenon. For a section with n lanes, tive tool and yields good results of studies about how driving numbered by l = 1,2,...,n from left to right, the continuum behaviors affect the surroundings. Lighthill and Whitham,[11] equation and momentum equation of Ko et al.’s model are [12] and Richards respectively originated the model by apply- ∂ρl ∂ρl ∂ul + ul + ρl = ∑ Φfree,l0l, (3) ing the continuity equation in fluid mechanics to traffic flow, ∂t ∂x ∂x l0=l±1 known as the LWR theory. Payne built a second-order contin- 2 ∂ul ∂ul a ∂ρl 1 [13] + ul + = (Ue − u)l + fviscous,l, (4) uum model, which has a similar form to the Navier-Stokes ∂t ∂x ρl ∂x Tr ∗Project supported by the National Natural Science Foundation of China (Grant Nos. 11002035 and 11372147). †Corresponding author. E-mail: [email protected] © 2016 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn 048901-1 Chin. Phys. B Vol. 25, No. 4 (2016) 048901
(Note that terms where l0 exceeds the range of l should not be free and compulsive LC is as follows: included in the summation ∑ Φfree,l0l, and likewise here- l0=l±1 ∂ρl ∂ρl ∂ul + ul + ρl inafter), where Φfree,l0l is the free LC source term, defined as ∂t ∂x ∂x the number of vehicles that change from the l0-th lane to the = ∑ Φfree,l0l − Φcmpl,l, 0 l =l±1 l-th lane due to free LC per hour per kilometer, and is deter- 2 ∂ul ∂ul a ∂ρl + ul + mined as ∂t ∂x ρ ∂x l 1 u = (U − u) + f + l Φ , Φfree,l0l = C1 [ρl0 ul0 max(ul − ul0 ,0) + ρlul min(ul − ul0 ,0)] e l viscous,l cmpl,l Tr ρl +C2 [ρl0 max(ρl0 − ρl,0) + ρl min(ρl0 − ρl,0)]. (5) Φfree,l0l = C1 [ρl0 ul0 max(ul − ul0 ,0) + ρlul min(ul − ul0 ,0)] (7) +C [ρ 0 max(ρ 0 − ρ ,0) + ρ min(ρ 0 − ρ ,0)], 2 l l l l l l In the momentum equation (4), fviscous,l is the viscosity term, 1 derived through the analogy between free LC behavior and the fviscous,l = ∑ Φfree,l0l ρ 0 l l =l±1 viscosity of fluids. Its expression is (uf − ul), ρl ≤ 0.2ρjam, (uf − ul), ρl ≤ 0.2ρjam, 1 · 1 f = 0 (6) viscous,l ∑ Φfree,l l 1 − uf − ul , ρl > 0.2ρjam. ρl 0 − uf − ul , ρl > 0.2ρjam. 4 l =l±1 4 where ρ and u are the traffic density and the speed on lane l However, the LC models taking into account both com- l l respectively; a is the sonic speed and Tr is the time delay pa- pulsive LC and free LC behaviors rarely appear in the existing rameter from Payne’s model; U (ρ) is the equilibrium speed literature. This paper presents such a second-order differential e function; Φ 0 and Φ are the free LC rate and compul- equation model, derived based on Ko et al.’s free LC model. free,l l cmp,l sive LC rate, which are both in units of veh/(h·km); f is The remainder of this paper is organized as follows. In Sec- viscous,l the LC viscosity from Ko et al.’s model[19] in units of (km/h2; tion 2, a new continuum traffic model addressing compulsive C is a constant parameter that addresses the effect of speed LC and free LC together is derived. In Section 3, a numer- 1 ical discretization method of the model is given. Numerical difference between adjacent lanes on the free LC rate, while C results on low-/high-density traffic and non-equilibrium traffic 2 is a constant parameter that addresses the influence of den- are presented in Section 4. Section 5 summarizes the results sity difference on the free LC rate, C1 and C2 are in units of 2 in the whole paper, and presents a prospect of further work. h/km and (km/h)/veh respectively; uf is the free flow speed; ρjam is the jam density. 2. Model In the off-ramp problem, attraction of the off-ramp ahead is the only considered compulsive LC factor. Thus the compul- 2.1. Derivation sive LC source term (namely, the compulsive LC rate) Φcmpl,l Compulsive LC behaviors affect the density of the sur- in Eq. (7) is given as rounding traffic environment, which can be depicted by adding a source term Φcmpl,l, the compulsive LC rate, to the right- Φcmpl,l = Φramp,l − Φramp,l−1, (8) hand side of the free LC continuity equation (3). Φcmpl,l is where Φ represents the number of vehicles that change defined as the number of vehicles that leave the l-th lane due ramp,l from lane l to the adjacent right-hand lane per unit time and to compulsive LC per hour per kilometer. A typical example length due to the off-ramp ahead. of Φcmpl,l is given by Eq. (8) below. From the inspection of real traffic phenomenon, we find The vehicles that conduct compulsive LC may have dif- that the compulsive LC intensity has a general pattern: from ferent speeds from the target lane’s average speed, which will the inlet to the upper stream of an off-ramp, the compulsive change the speed profile nearby, and the free LC momentum LC rate keeps increasing up to a peak at some point before the equation (4) should be changed accordingly. Using Papageo- off-ramp, after which it decreases to zero at the point of the giou’s idea in his single-lane traffic model with ramp[14,15] for off-ramp. This rate then remains zero, because no compulsive reference, we consider the influence of compulsive LC on mo- LC behavior happens downstream of the off-ramp. According mentum to be proportional to local speed and inversely pro- to this inspection, the expression of Φramp,l can be given as portional to local density, so we add a term (ul/ρl)/Φcmpl,l to the right-hand side of the momentum equation. sech(γ(x − x0)), x ≤ x0, Φramp,l = αlA To summarize, for an n-lane road section, the partial dif- sech(β(x − x0)), x > x0, ferential equation (PDE) traffic model with considering both (γ β,α1 < α2 < ··· < αn), (9) 048901-2 Chin. Phys. B Vol. 25, No. 4 (2016) 048901 where αl is a dimensionless parameter, representing the rela- 2.2. Non-dimensionalization tive intensity of occurrence for compulsive LC on lane l, and Let uf be the characteristic speed, ρjam the characteris- the inequalities in brackets indicate that the compulsive LC ∗ tic density, and L the characteristic length. Let u = u/uf, behavior caused by the off-ramp happens more frequently at ∗ ∗ ∗ ∗ ∗ ρ = ρ/ρjam, x = x/L, t = t/(L/uf), a = a/uf, Tr = the lane on the right-hand side than on the left-hand side. This ∗ ∗ ∗ Tr/(L/u ), U = Ue/u , Φ = Φ /(ρ u /L), Φ = inequality is analytical for the phenomenon observed in real f e f free free jam f cmpl Φ /(ρ u /L), and f ∗ = f /(u2/L), which are the dimen- traffic,[20] where the LC within two adjacent lanes increases cmpl jam f f sionless speed, density, length, time, sonic speed, time delay, from the median lane to the shoulder lane at the weaving sec- equilibrium speed function, free LC source term, compulsive tion. The A is the overall intensity of occurrence, in the same LC source term, and free LC viscosity term. Substituting these units as Φ, i.e., veh/(h · km). The range of A value is deter- mined through the experiment in Subsection 2.3. Parameters into Eq. (7), the dimensionless model equations can be ob- β and γ, in units of km−1, are determined so that the curve tained as follows (the symbol ∗ is dropped): shape of function Φramp,l correctly reflects the pattern of off- ∂ρl ∂ρl ∂ul ramp compulsive LC. Parameter x in units of km is the point + ul + ρl = ∑ Φfree,l0l − Φcmpl,l, 0 ∂t ∂x ∂x 0 l =l±1 where the LC rate reaches its peak. A test drawing (Fig.1 with 2 ∂ul ∂ul a ∂ρl γ = 1.5, β = 150, and x∗ = 0.6) demonstrates that the function + ul + 0 ∂t ∂x ρl ∂x curve of Φramp,l is in accordance with what we desire. 1 ul = (U − u) + f + Φ , Tr e l viscous,l ρ cmpl,l 1.0 l (12) ∗ Φfree,l0l = C1 [ρl0 ul0 max(ul − ul0 ,0) + ρlul min(ul − ul0 ,0)] ∗ 0.8 +C [ρl0 max(ρl0 − ρl,0) + ρl min(ρl0 − ρl,0)], 2 A n (1 − ul), ρl ≤ 0.2, α 0.6 1
/ fviscous,l = ∑ Φfree,l0l · 1 ρl l0=l±1 − − ul , ρl > 0.2, ramp 0.4 4 Φ
0.2 where the dimensionless parameters are
0 ∗ ∗ ρjamL 0 0.2 0.4 0.6 0.8 1.0 C1 = ufLC1, C2 = C2. (13) x uf
Fig. 1. Test drawing of Φramp against x. 2.3. Empirical study For the most right-hand side lane (i.e., the one that is ad- The parameter A in Eq. (9), according to its definition, jacent to the auxiliary lane), the value of αn can be determined can be estimated by counting the number of vehicles that came through the following derivation. The definition of Φramp,n im- through an off-ramp in a certain period of time on a real road plies that the integral of Φramp,n with respect to x will be the section. We choose the Guoding Rd. off-ramp on the Shang- total flow rate at which vehicles change to the auxiliary lane, hai Middle Ring Expressway, China, as our observation ob- and since all vehicles intending to leave the main lane must ject. This off-ramp is 3.5 km away from the nearest off-ramp change to the auxiliary lane at some point before the ramp, upstream at Guangyue Rd. The traffic between the two off- the integral is thus the overall flow rate of leaving through the ramps is mostly isolated and thus will not be influenced by the off-ramp. On the other hand, we define the overall intensity of traffic environment outside. It is a four-lane section. occurrence A as the average flow rate at the off-ramp divided We repeate the experiment three times, each lasting half by the length of the road section. Therefore, the integral of an hour. The number of vehicles passing from the off-ramp Φramp,n/A with respect to x should be 1. We can thus deduce is counted and recorded every 5 min. Results are shown in that αn can be obtained by the following expression: Table1. In this table, the maximum value is in boldface and Z x 0 its corresponding compulsive LC intensity is denoted as A . αn = 1/ sech(γ(x − x0))dx max 0 Let the characteristic length L = 3 km, then Amax values of Z 1 + sech(β(x − x0))dx , (10) the three entries are respectively as follows: 116 veh/(h · km), x 0 120 veh/(h · km), and 92 veh/(h · km), and for all the entries, where the integral terms can be calculated analytically by us- A ∈[40,120] veh/(h · km). Therefore, the upper limit of com- ing the following formula: pulsive LC intensity on any four-lane highway is given as Z x 2 α sech(αξ)dξ = arctan tanh x . (11) A ≤ 120 veh/(h · km). 0 α 2 048901-3 Chin. Phys. B Vol. 25, No. 4 (2016) 048901
Table 1. Empirical data for the estimation of A.
Set 1 2015.4.6, Set 2 2015.4.10, Set 3 2015.4.21, Monday rainy to cloudy Friday sunny Tuesday sunny Starting at No. of vehicles Starting at No. of vehicles Starting at No. of vehicles 14:13 10 14:13 24 17:42 16 14:18 17 14:18 24 17:47 20 14:23 16 14:23 26 17:52 19 14:28 25 14:28 25 17:57 16 14:33 29 14:33 24 18:02 23 14:38 21 14:38 30 18:07 19
2 However, traffic conditions may differ from those of this n+1 n ∆t n n n a n n ui = ui − ui (ui − ui−1) + n (ρi+1 − ρi ) experiment, depending on the local flow rate, the scale of the ∆x ρi n studied off-ramp, the average demand for leaving from the off- 1 u +∆t (Ue − u) + fviscous,l + Φcmpl,l . (15) ramp, and how many lanes that section consists of. Therefore, Tr ρ i when using our model for simulation, the value of A should be (Note: here n represents the number of spatial grids, which is determined accordingly with reference to our empirical data. different from the meaning of the number of lanes, as defined For example, in the simulation of the traffic on a two-lane road, above.) the value of A should be half that on a four-lane road, that is, When using the discretization scheme for simulation, let A ∈[20,60] veh/(h · km). dx = 0.05, dt = 0.005, J = 20, and N = 2000, where J and N are the total number of spatial grids and temporal steps re- ∗ 3. Numerical simulation method spectively. Constants are set to be Tr = 0.02, a = 0.4, x0 = 0.6, γ∗ = 15, and β ∗ = 150. According to Subsection 2.1, we set Now we present a numerical simulation method for the α2 = 8.6824 and α1 = 0.8682 (assuming that only 10% of the model to study the off-ramp problem. The model equations vehicles in the first lane wish to exit from this off-ramp). Char- are Eqs. (12), (8), and (9). Hereinafter, a two-lane road sec- acteristic values are set to be L = 3 km, ρjam = 143 veh/km, tion is taken in each numerical case, that is, the number of and uf = 105 km/h. lanes n = 2. As for the boundary conditions, let all profiles keep un- The finite difference scheme is designed by referring to changed at the inlet, and use the Neumann condition at the Refs. [21] and [22]. Use the forward difference formula for outlet, then we will have time derivatives, the backward difference formula for spatial n+1 n+1 n+1 n+1 n+1 n+1 derivatives with the coefficient of speed, and the forward dif- ρ0 = ρ0, u0 = u0, ρJ = ρJ−1 , uJ = uJ−1. (16) ference formula for spatial derivatives with the coefficient of density, then the scheme will be obtained as follows (subscript 4. Case study l is omitted): Three numerical cases of the off-ramp problem are stud- ∆t ied to demonstrate the reasonability and the applicability in ρn+1 = ρn − [un(ρn − ρn ) + ρn(un − un)] i i ∆x i i i−1 i i+1 i equilibrium and non-equilibrium traffic of our model. Fig- n ure2 illustrates the sketch of a two-lane road section with an +∆t ∑ Φl0l − Φcompl,l , (14) l06=l i off-ramp adopted in these cases.
lane 1
lane 2
offramp
x/ x/ x0=0.6
Fig. 2. (color online) Sketch of the off-ramp problem.
048901-4 Chin. Phys. B Vol. 25, No. 4 (2016) 048901
4.1. Case 1: Low-density state Then figures5 and6 show the equilibrium traffic states at Case 1 is designed to validate the model and the dis- t = 5. Three parts with distinct patterns can be found in the cretization scheme, and also to study LC influence on the traf- figures. fic environment. Suppose that traffic density is low on both (i) From x = 0 to x = 0.3, the influence of free LC is lanes, and the speed and density on both lanes are evenly dis- dominant, which makes speeds and densities of the two lanes tributed. The initial conditions are converge towards each other, while compulsive LC has little influence on this part. ρ10 = 0.10, ρ20 = 0.12, u10 = 0.90, u20 = 0.88. (17) 0.120 Equilibrium speed Ue is given by the dimensionless lane 2 [23] Greenshields speed-density relationship: 0.115 no LC Ue(ρ) = 1 − ρ. (18) pure free LC 0.110 pure cmpl LC Calculate the following four conditions: ρ free+cmpl ∗ ∗ no LC: C1 = 0, C2 = 0, A = 0 veh/(h · km); 0.105 ∗ ∗ pure free LC: C1 = 0.25, C2 = 1.5, A = 0 veh/(h · km); ∗ ∗ pure compulsive LC: C1 = 0, C2 = 0, A = 35 veh/(h · 0.100 km); lane 1 free + compulsive LC: C∗ = 0.25, C∗ = 1.5, A = 0.095 1 2 0 0.2 0.4 0.6 0.8 1.0 35 veh/(h · km). x,∂t/ Numerical results of the four conditions are drawn in Fig.3 to Fig.6. Fig. 5. (color online) ρ–x in low density state.
0.120 0.905 no LC lane 1 lane 2 pure free LC 0.900 0.115 pure cmpl LC free+cmpl 0.895 no LC 0.110 pure free LC pure cmpl LC ρ
u 0.890 free+cmpl 0.105
lane 1 0.885 0.100 lane 2 0.880 0.095 0 1 2 3 4 5 0.875 t,∂x/ 0 0.2 0.4 0.6 0.8 1.0 x,∂t/ Fig. 3. (color online) ρ–t in low density state. Fig. 6. (color online) u–x in low density state. Figures3 and4 show how the traffic state evolves against time at the end of the road section (x = 1). The equilibrium (ii) From x = 0.3 to x = 0.6, compulsive LC starts to affect state is achieved after t = 1.7 (about 2.9 s). traffic. As the influence turns stronger downstream, the speed of lane 2 drops dramatically and its speed increases, while the 0.905 lane 1 no LC speed and density of lane 1 have similar but slighter changes. pure free LC The influence of free LC still exists, but becomes less impor- tant than that of compulsive LC. 0.895 (iii) From x = 0.6 to x = 1, which is the downstream of the off-ramp, the influence of free LC becomes dominant again, u as no compulsive LC happens there. However, the equilib- 0.885 rium state changes due to the influence of the compulsive LC pure cmpl LC lane 2 free+cmpl upstream. It is shown in this case that our model simulates traffic
0.875 with free and compulsive LC well at low density, and the pure 0 1 2 3 4 5 free LC case yields the same results as the low density case t,∂x/ in Ref. [19] (at medium and high density, our results of the Fig. 4. (color online) u–t in the low density state. pure free LC case agree with those in Ref. [19] as well). Two 048901-5 Chin. Phys. B Vol. 25, No. 4 (2016) 048901 kinds of LCs show different influence patterns in the traffic speeds and densities of the two lanes are very close. Thus the state. The discretization scheme is stable, and the parameters initial conditions for the high-density state are given as are well set so as to obtain reasonable results. ρ10 = 0.70, ρ20 = 0.70, u10 = 0.31, and u20 = 0.31. (21) 4.2. Case 2: Medium- and high-density states As traffic becomes congested, the compulsive LC happens less The model (12) should adopt different values of equilib- frequently. Let A = 20 veh/(h · km). rium speed Ue when simulating medium- and high-density Figures9 and 10 show the equilibrium traffic states at traffic states. In these cases, the dimensionless equilibrium t = 100. The changing patterns of the curves are similar to speed Ue is given by Payne’s function: those of medium-density traffic, except that the intersection point changes to x = 0 due to the initial conditions. Ue = min{1,1.94 − 6ρ + 8ρ2 − 3.93ρ3}. (19)
0.70 lane 1 The initial conditions for medium-density state are lane 2
0.66 ρ10 = 0.38, ρ20 = 0.40, u10 = 0.60, and u20 = 0.55. (20)
ρ
We simulate a free-and-compulsive LC situation with the 0.62 ∗ ∗ model. Let A = 30 veh/(h · km), C1 = 0.25, and C2 = 1.5. Figures7 and8 show the equilibrium traffic states at 0.58 0 0.2 0.4 0.6 0.8 1.0 t = 70. The speed curves of the two lanes intersect at x = 0.25, x,∂t/ after which the speed of lane 2 drops lower than that of lane 1. In the downstream off-ramp, speed curves of the two lanes Fig. 9. ρ–x in high density state. converge. A similar pattern exists in the density curve in 0.38 Fig.8, as the density of lane 2 increases over that of lane 1 after 0.37 x = 0.25, and after crossing the off-ramp, the density curves of 0.36 the two lanes converge. 0.35 0.40 u 0.34 lane 1 0.33 lane 1 0.38 lane 2 lane 2 0.32
0.36 0.31
ρ 0 0.2 0.4 0.6 0.8 1.0 x,∂t/ 0.34 Fig. 10. u–x in high density state. 0.32 0 0.2 0.4 0.6 0.8 1.0 Figures7–10 show the different influences of free LC x∂t/ and compulsive LC at the upstream and downstream off-ramp Fig. 7. ρ–x in medium density state. in the medium-/high-density state. In these states, the initial speeds and densities of the two lanes are very close. Therefore, the need for free LC drops down, while the need for compul- 0.70 sive LC remains the same. As vehicles move into the auxiliary 0.66 lane from lane 2 (compulsive LC behavior), their density will decrease largely and their speeds will increase. This leads to
u 0.62 a larger speed/density difference between the two lanes, and then in the downstream off-ramp, the effect of free LC still 0.58 lane 1 lane 2 survives and drives the speed/density of the two lanes close to 0.54 each other. 0 0.2 0.4 0.6 0.8 1.0 x,∂t/ 4.3. Case 3: Non-equilibrium traffic state
Fig. 8. u–x in medium density state. Generally speaking, a second-order differential equation model can simulate the non-equilibrium traffic state well. The high-density state usually exists in congested urban Therefore, we design Case 3 to study our model in a non- traffic, where almost every space available is occupied and the equilibrium state simulation. Take the same settings as the 048901-6 Chin. Phys. B Vol. 25, No. 4 (2016) 048901 free + compulsive LC condition in Case 1, except that the inlet 5. Conclusions boundary condition (16) is changed into In this paper we establish a new second-order contin- n 2π n ρeq,0 uum traffic model with the consideration of both free LC ρ0 = ρeq,0 1 + 0.15sin n , u0 = n ueq,0, (22) Tp ρ0 and compulsive LC behaviors. For the off-ramp problem, we where ρeq,0 and ueq,0 are the constant entrance boundary con- give a form of the source term of compulsive LC, and deter- dition values in Case 1, and Tp is the dimensionless time period mine its value range of the parameter by the empirical data of the sinusoidal function under the assumption of Tp = 2000. taken from an off-ramp at Shanghai. A discretization scheme The simulation results are shown in Figs. 11 and 12. Density for our model is constructed and applied to three numerical and speed curves at x = 0, x = 0.2, x = 0.4, x = 0.6, and x = 1 cases, which show that the proposed model and discretization are drawn in the same figure for comparison. scheme can provide reasonable simulations for various traffic 0.22 states. x=0 The compulsive LC function model is logically derived 0.20 x=0.2 x=0.4 through the inspection of real traffic, however, we are inter- x=0.6 0.18 x=1 ested in looking into how this model can be verified and how lane 2 the parameters could be determined through empirical data in 0.16 the future. ρ In this paper, only one kind of compulsive LC is dis- 0.14 cussed. However, other kinds of compulsive LC behaviors ex- 0.12 ist, such as the keep-right-except-to-pass-rule problem: under lane 1 certain traffic rules, drivers have to change back to the slow 0.10 lane after overtaking the car in front of it by using the quick [24,25] 0.08 lane. Such a situation may be simulated by proposing 0 2 4 6 8 10 t another suitable Φramp,n term in Eq. (8).
Fig. 11. (color online) ρ–t in non-equilibrium state. References 1.1 [1] Leclercq L, Chiabaut N, Laval J and Buisson C 2007 Transport. Res. x/ Rec. 1999 79 x/. [2] Laval J A and Leclercq L 2008 Transport. Res. Part B 42 511 x/. x/. [3] Cassidy M J and Rudjanakanoknad J 2005 Transport. Res. Part B 39 1.0 x/ 896 [4] Jin W L 2013 Transport. Res. Part B 57 361 [5] Ahn S and Cassidy M J 2007 17th International Symposium on Trans- lane 1 portation and Traffic Theory (New York: Elsevier) p. 691
u 0.9 [6] Zheng Z, Ahn S, Chen D and Laval J 2011 Transport. Res. Part B 45 1378 [7] Laval J A and Daganzo C F 2006 Transport. Res. Part B 40 251 0.8 [8] Toledo T 2007 Transport Rev. 27 65 [9] Moridpour S, Rose G, Sarvi M 2010 J. Transp. Eng. 136 973 lane 2 [10] Zheng Z 2014 Transport. Res. Part B 60 16 [11] Lighthill M J and Whitham G B 1955 Proc. Royal Soc. A 22 317 0.7 [12] Richards P I 1956 Oper. Res. 4 42 0 2 4 6 8 10 Math. Models Pub. Sys. t [13] Payne H J 1971 28 51 [14] Papageorgiou M, Blosseville J M and Hadj-Salem H 1989 Transport. Res. Part B 23 29 Fig. 12. (color online) u–t in non-equilibrium state. [15] Papageorgiou M, Blosseville J M and Hadj-Salem H 1990 Transport. Res. Part A It can be seen in the figures that as the phase of the fluc- 24 345 [16] Kerner B S and Konhauser¨ P 1993 Phys. Rev. E 48 R2335 tuation at the inlet moves downstream, the amplitude reduces. [17] Zhang H M 2002 Transport. Res. Part B 36 275 This is caused by the free LC, which is in accordance with the [18] Zhu H and Wu Z 2008 Chin. J. Hydro. 23 301 (in Chinese) second case from Ref. [19]. On the other hand, at x = 0.4, [19] Ko H T, Liu X H, Guo M M and Wu Z 2015 Chin. Phys. B 24 098901 x = 0.6, and x = 1 respectively, an overall trend that density [20] Gan Q J and Wen L J 2015 Transport. Res. Rec. 2490 106 [21] Wu Z 1994 Chin. J. Theor. Appl. Mech. 26 149 (in Chinese) drops and speed increases can be seen, with the scenario at [22] Wu Z 2006 Chin. J. Theor. Appl. Mech. 38 785 (in Chinese) x = 0.6 being the most evident. This is caused by the compul- [23] Greenshields B, Bibbins J, Channing W and Miller H 1935 Highway sive LC, which brings down the traffic flow of the road section. research board proceedings 14 [24] http://highwaypal.com/i95/keep-right-except-to-pass-laws-for-i95- This case validates the applicability of our model in the simu- states/ [2014] lation of non-equilibrium traffic near an off-ramp. [25] John C http://www.mit.edu/jfc/right.html [2015] 048901-7 Chinese Physics B
Volume 25 Number 4 April 2016
RAPID COMMUNICATION
047401 Magnetoresistivity and filamentary superconductivity in nickel-doped BaFe2As2 Wei Zhang, Yao-Min Dai, Bing Xu, Run Yang, Jin-Yun Liu, Qiang-Tao Sui, Hui-Qian Luo, Rui Zhang, Xing- Ye Lu, Hao Yang and Xiang-Gang Qiu
GENERAL 040201 Theoretical calculation and experiment of microwave electromagnetic property of Ni(C) nanocapsules Dan-Feng Zhang, Zhi-Feng Hao, Bi Zeng, Yan-Nan Qian, Ying-Xin Huang and Zhen-Da Yang 040202 (2+1)-dimensional dissipation nonlinear Schrodinger¨ equation for envelope Rossby solitary waves and chirp effect Jin-Yuan Li, Nian-Qiao Fang, Ji Zhang, Yu-Long Xue, Xue-Mu Wang and Xiao-Bo Yuan 040203 Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method Shen-Shen Chen, Juan Wang and Qing-Hua Li 040204 New analytical exact solutions of time fractional KdV KZK equation by Kudryashov methods S Saha Ray 040301 Nonrelativistic Shannon information entropy for Kratzer potential Najafizade S A, Hassanabadi H and Zarrinkamar S 040302 Kraus operator solutions to a fermionic master equation describing a thermal bath and their matrix representation Xiang-Guo Meng, Ji-Suo Wang, Hong-Yi Fan and Cheng-Wei Xia 040303 Deformed photon-added entangled squeezed vacuum and one-photon states: Entanglement, polariza- tion, and nonclassical properties A Karimi and M K Tavassoly 040304 Fidelity between Gaussian mixed states with quantum state quadrature variances Hai-Long Zhang, Chun Zhou, Jian-Hong Shi and Wan-Su Bao 040305 Weakly interacting spinor Bose–Einstein condensates with three-dimensional spin–orbit coupling Shu-Wei Song, Rui Sun, Hong Zhao, Xuan Wang and Bao-Zhong Han 040501 Dynamics of spinor Bose–Einstein condensate subject to dissipation Man-Man Pang and Ya-Jiang Hao 040601 Phase sensitivity of two nonlinear interferometers with inputting entangled coherent states Chao-Ping Wei, Xiao-Yu Hu, Ya-Fei Yu and Zhi-Ming Zhang 040701 Compressed sensing sparse reconstruction for coherent field imaging Bei Cao, Xiu-Juan Luo, Yu Zhang, Hui Liu and Ming-Lai Chen
040702 Preparation and room temperature NO2-sensing performances of porous silicon/V2O5 nanorods Wen-Jun Yan, Ming Hu, Ji-Ran Liang, Deng-Feng Wang, Yu-Long Wei and Yu-Xiang Qin
(Continued on the Bookbinding Inside Back Cover) ATOMIC AND MOLECULAR PHYSICS 043101 Ab initio study on the electronic states and laser cooling of AlCl and AlBr Rong Yang, Bin Tang and Tao Gao 043201 Comment on “Atomic structure calculations for F-like tungsten” by S. Aggarwal [Chin. Phys B 23 (2014) 093203] Kanti M Aggarwal
043202 High-order harmonic generation of the N2 molecule in two-color circularly polarized laser fields Hui Du, Jun Zhang, Shuai Ben, Hui-Ying Zhong, Tong-Tong Xu, Jing Guo and Xue-Shen Liu 043401 Differential cross sections for electron impact excitation of molecular hydrogen using the momentum- space multichannel optical method Yuan-Cheng Wang, Jia Ma and Ya-Jun Zhou
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS 044101 Soliton excitation in the pass band of the transmission line based on modulation Guoying Zhao, Feng Tao and Weizhong Chen 044201 Propagation of Airy Gaussian vortex beams in uniaxial crystals Weihao Yu, Ruihuang Zhao, Fu Deng, Jiayao Huang, Chidao Chen, Xiangbo Yang, Yanping Zhao and Dongmei Deng 044202 The effect of a permanent dipole moment on the polar molecule cavity quantum electrodynamics Jing-Yun Zhao, Li-Guo Qin, Xun-Ming Cai, Qiang Lin and Zhong-Yang Wang 044203 Dynamics of a three-level V-type atom driven by a cavity photon and microwave field Yan-Li Xue, Shi-Deng Zhu, Ju Liu, Ting-Hui Xiao, Bao-Hua Feng and Zhi-Yuan Li 044204 Laser frequency locking based on the normal and abnormal saturated absorption spectroscopy of 87Rb Jian-Hong Wan, Chang Liu and Yan-Hui Wang 044205 Monolithic CEO-stabilization scheme-based frequency comb from an octave-spanning laser Zi-Jiao Yu, Hai-Nian Han, Yang Xie, Hao Teng, Zhao-Hua Wang and Zhi-Yi Wei 044206 A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam Khannous F, Ebrahim A A A and Belafhal A 044207 Spectral distortion of dual-comb spectrometry due to repetition rate fluctuation Hong-Lei Yang, Hao-Yun Wei and Yan Li 044208 Frequency-stabilized Yb:fiber comb with a tapered single-mode fiber Yang Xie, Hai-Nian Han, Long Zhang, Zi-Jiao Yu, Zheng Zhu, Lei Hou, Li-Hui Pang and Zhi-Yi Wei 044209 Modulation of terahertz generation in dual-color filaments by an external electric field and preformed plasma Min Li, An-Yuan Li, Bo-Qu He, Shuai Yuan and He-Ping Zeng 044210 Strip silicon waveguide for code synchronization in all-optical analog-to-digital conversion based on a lumped time-delay compensation scheme Sha Li, Zhi-Guo Shi, Zhe Kang, Chong-Xiu Yu and Jian-Ping Wang
(Continued on the Bookbinding Inside Back Cover) 044211 Planar waveguides in neodymium-doped calcium niobium gallium garnet crystals produced by proton implantation Chun-Xiao Liu, Meng Chen, Li-Li Fu, Rui-Lin Zheng, Hai-Tao Guo, Zhi-Guang Zhou, Wei-Nan Li, She-Bao Lin and Wei Wei 044301 Study of the temperature rise induced by a focusing transducer with a wide aperture angle on biological tissue containing ribs Xin Wang, Jiexing Lin, Xiaozhou Liu, Jiehui Liu and Xiufen Gong 044302 Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide Wen-Yu Luo, Xiao-Lin Yu, Xue-Feng Yang and Ren-He Zhang
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
045101 Initiation of vacuum breakdown and failure mechanism of the carbon nanotube during thermal field emission Dan Cai, Lie Liu, Jin-Chuan Ju, Xue-Long Zhao, Hong-Yu Zhou and Xiao Wang 045201 Numerical analysis of the optimized performance of the electron cyclotron wave system in a HL-2M tokamak Jing-Chun Li, Xue-Yu Gong, Jia-Qi Dong, Jun Wang and Lan Yin 045202 Surface diffuse discharge mechanism of well-aligned atmospheric pressure microplasma arrays Ren-Wu Zhou, Ru-Sen Zhou, Jin-Xing Zhuang, Jiang-Wei Li, Mao-Dong Chen, Xian-Hui Zhang, Dong-Ping Liu, Kostya (Ken) Ostrikov and Si-Ze Yang 045203 Electrical and optical characteristics of the radio frequency surface dielectric barrier discharge plasma actuation Wei-Long Wang, Hui-Min Song, Jun Li, Min Jia, Yun Wu and Di Jin 045204 Characteristics of droplets ejected from liquid glycerol doped with carbon in laser ablation propulsion Zhi-Yuan Zheng, Si-Qi Zhang, Tian Liang, Lu Gao, Hua Gao and Zi-Li Zhang
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES
046101 Microstructure and lateral conductivity control of hydrogenated nanocrystalline silicon oxide and its application in a-Si:H/a-SiGe:H tandem solar cells Tian-Tian Li, Tie Yang, Jia Fang, De-Kun Zhang, Jian Sun, Chang-Chun Wei, Sheng-Zhi Xu, Guang-Cai Wang, Cai-Chi Liu, Ying Zhao and Xiao-Dan Zhang 046102 Pressure-induced solidifications of liquid sulfur below and above 휆-transition Fei Tang, Lin-Ji Zhang, Feng-Liang Liu, Fei Sun, Wen-Ge Yang, Jun-Long Wang, Xiu-Ru Liu and Ru Shen 046103 Convenient synthesis of stable silver quantum dots with enhanced photoluminescence emission by laser fragmentation Shuang Li and Ming Chen 046104 Radiation-induced 1/푓 noise degradation of PNP bipolar junction transistors at different dose rates Qi-Feng Zhao, Yi-Qi Zhuang, Jun-Lin Bao and Wei Hu
(Continued on the Bookbinding Inside Back Cover) 046105 Large scale silver nanowires network fabricated by MeV hydrogen (H+) ion beam irradiation Honey S, Naseem S, Ishaq A, Maaza M, Bhatti M T and Wan D 046106 Channeling of fast ions through the bent carbon nanotubes: The extended two-fluid hydrodynamic model Lazar Karbunar, Duskoˇ Borka, Ivan Radovic´ and Zoran L Miskoviˇ c´ 046301 Complete low-frequency bandgap in a two-dimensional phononic crystal with spindle-shaped inclusions Ting Wang, Hui Wang, Mei-Ping Sheng and Qing-Hua Qin 046401 Structure phase transformation and equation of state of cerium metal under pressures up to 51 GPa Ce Ma, Zuo-Yong Dou, Hong-Yang Zhu, Guang-Yan Fu, Xiao Tan, Bin Bai, Peng-Cheng Zhang and Qi-Liang Cui
046801 Optoelectronic properties of SnO2 thin films sprayed at different deposition times Allag Abdelkrim, Saadˆ Rahmane, Ouahab Abdelouahab, Attouche Hafida and Kouidri Nabila
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTI- CAL PROPERTIES
047101 Investigations of mechanical, electronic, and magnetic properties of non-magnetic MgTe and ferro-
magnetic Mg0.75푇 푀0.25Te (푇 푀 = Fe, Co, Ni): An ab-initio calculation Mahmood Q, Alay-e-Abbas S M, Mahmood I, Asif Mahmood and Noor N A 047102 Fabrications and characterizations of high performance 1.2 kV, 3.3 kV, and 5.0 kV class 4H–SiC power SBDs Qing-Wen Song, Xiao-Yan Tang, Hao Yuan, Yue-Hu Wang, Yi-Meng Zhang, Hui Guo, Ren-Xu Jia, Hong- Liang Lv, Yi-Men Zhang and Yu-Ming Zhang
047201 Inverted polymer solar cells with employing of electrochemical-anodizing synthesized TiO2 nanotubes Mehdi Ahmadi, Sajjad Rashidi Dafeh and Hamed Fatehy 047301 Design of terahertz beam splitter based on surface plasmon resonance transition Xiang Liu and Dong-Xiao Yang 047302 Excitonic transitions in Be-doped GaAs/AlAs multiple quantum well Wei-Min Zheng, Su-Mei Li, Wei-Yan Cong, Ai-Fang Wang, Bin Li and Hai-Bei Huang 047303 Dirac operator on the sphere with attached wires E. N Grishanov, D A Eremin, D A Ivanov and I Yu Popov
047304 Study on electrical defects level in single layer two-dimensional Ta2O5 Dahai Li, Xiongfei Song, Linfeng Hu, Ziyi Wang, Rongjun Zhang, Liangyao Chen, David Wei Zhang and Peng Zhou 047305 An analytical model for nanowire junctionless SOI FinFETs with considering three-dimensional cou- pling effect Fan-Yu Liu, Heng-Zhu Liu, Bi-Wei Liu and Yu-Feng Guo 047306 Numerical simulation of the magnetoresistance effect controlled by electric field in p–n junction Pan Yang, Wen-Jie Chen, Jiao Wang, Zhao-Wen Yan, Jian-Li Qiao, Tong Xiao, Xin Wang, Zheng-Peng Pang and Jian-Hong Yang
(Continued on the Bookbinding Inside Back Cover) 047501 Effects of Mg substitution on the structural and magnetic properties of Co0.5Ni0.5−푥Mg푥Fe2O4 nanopar- ticle ferrites R M Rosnan, Z Othaman, R Hussin, Ali A Ati, Alireza Samavati, Shadab Dabagh and Samad Zare
047502 Spin-cluster glass state in U(Ga0.95Mn0.05)3 Dong-Hua Xie, Wen Zhang, Yi Liu, Wei Feng, Yun Zhang, Shi-Yong Tan, Xie-Gang Zhu, Qiu-Yun Chen, Qin Liu, Bing-Kai Yuan and Xin-Chun Lai 047503 Study of magnetization reversal and anisotropy of single crystalline ultrathin Fe/MgO (001) film by magneto-optic Kerr effect Miao-Ling Zhang, Jun Ye, Rui Liu, Shu Mi, Yong Xie, Hao-Liang Liu, Chris Van Haesendonck and Zi-Yu Chen
047601 Magnetic transition behavior of perovskite manganites Nd0.5Sr0.3Ca0.2MnO3 polycrystalline Ru Xing, Su-Lei Wan, Wen-Qing Wang, Lin Zheng, Xiang Jin, Min Zhou, Yi Lu and Jian-Jun Zhao 047801 Apparent directional spectral emissivity determination of semitransparent materials Chun-Yang Niu, Hong Qi, Ya-Tao Ren and Li-Ming Ruan 3+ 047802 Effect of co-doped metal caions on the properties of Y2O3:Eu phosphors synthesized by gel- combustion method Hui Shi, Xi-Yan Zhang, Wei-Li Dong, Xiao-Yun Mi, Neng-Li Wang, Yan Li and Hong-Wei Liu
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY
048101 Field emission properties of a-C and a-C:H films deposited on silicon surfaces modified with nickel nanoparticles Jin-Long Jiang, Yu-Bao Wang, Qiong Wang, Hao Huang, Zhi-Qiang Wei and Jun-Ying Hao 048102 Graphene/polyaniline composite sponge of three-dimensional porous network structure as supercapaci- tor electrode Jiu-Xing Jiang, Xu-Zhi Zhang, Zhen-Hua Wang and Jian-Jun Xu 048103 Effects of catalyst height on diamond crystal morphology under high pressure and high temperature Ya-Dong Li, Xiao-Peng Jia, Bing-Min Yan, Ning Chen, Chao Fang, Yong Li and Hong-An Ma 048104 Subsurface defect characterization and laser-induced damage performance of fused silica optics polished with colloidal silica and ceria Xiang He, Gang Wang, Heng Zhao and Ping Ma 048105 Aluminum incorporation efficiencies in 퐴- and 퐶-plane AlGaN grown by MOVPE Dong-Yue Han, Hui-Jie Li, Gui-Juan Zhao, Hong-Yuan Wei, Shao-Yan Yang and Lian-Shan Wang 048201 Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics Naruemon Rueangkham and Charin Modchang 048401 Effects of Shannon entropy and electric field on polaron in RbCl triangular quantum dot M Tiotsop, A J Fotue, S C Kenfack, N Issofa, H Fotsin and L C Fai 048402 Analysis and experiments of self-injection magnetron Yi Zhang, Wen-Jun Ye, Ping Yuan, Huan-Cheng Zhu, Yang Yang and Ka-Ma Huang
(Continued on the Bookbinding Inside Back Cover) 048501 Extraction of temperature dependences of small-signal model parameters in SiGe HBT HICUM model Ya-Bin Sun, Jun Fu, Yu-Dong Wang, Wei Zhou, Wei Zhang and Zhi-Hong Liu 048502 Ultra-low specific on-resistance high-voltage vertical double diffusion metal–oxide–semiconductor field- effect transistor with continuous electron accumulation layer Da Ma, Xiao-Rong Luo, Jie Wei, Qiao Tan, Kun Zhou and Jun-Feng Wu 048503 Damage effect and mechanism of the GaAs pseudomorphic high electron mobility transistor induced by the electromagnetic pulse Xiao-Wen Xi, Chang-Chun Chai, Gang Zhao, Yin-Tang Yang, Xin-Hai Yu and Yang Liu 048504 Damage effect and mechanism of the GaAs high electron mobility transistor induced by high power microwave Yang Liu, Chang-Chun Chai, Yin-Tang Yang, Jing Sun and Zhi-Peng Li 048505 Comparison of blue–green response between transmission-mode GaAsP- and GaAs-based photocath- odes grown by molecular beam epitaxy Gang-Cheng Jiao, Zheng-Tang Liu, Hui Guo and Yi-Jun Zhang 048701 X-ray absorption near-edge structure study on the configuration of Cu2+/histidine complexes at different pH values Mei-Juan Yu, Yu Wang and Wei Xu 048901 A new traffic model on compulsive lane-changing caused by off-ramp Xiao-He Liu, Hung-Tang Ko, Ming-Min Guo and Zheng Wu 048902 Pedestrian evacuation at the subway station under fire Xiao-Xia Yang, Hai-Rong Dong, Xiu-Ming Yao and Xu-Bin Sun
GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS
049401 Effect of supply voltage and body-biasing on single-event transient pulse quenching in bulk fin field- effect-transistor process Jun-Ting Yu, Shu-Ming Chen, Jian-Jun Chen, Peng-Cheng Huang and Rui-Qiang Song