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Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters 被引量:3
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作者 Long Ma Haibo Min +2 位作者 Shicheng Wang Yuan Liu Zhiguo Liu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第1期232-239,共8页
In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the le... In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations. 展开更多
关键词 Containment control directed network topology multi-agent systems nonlinear second-order systems
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A Theoretical Study of Nonlinear Second-Order Optical Properties of Substituted Silanes 被引量:1
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作者 FENG Ji kang, WANG Hai chuan, WEI Jia you, XIAO Chang yong XU Wen guo and SUN Chia chung (Department of Chemistry and Institute of Theoretical Chemistry, Jilin University, Changchun, 130023) 《Chemical Research in Chinese Universities》 SCIE CAS CSCD 1997年第1期51-60,共10页
On the basis of ZINDO method and according to the sum over states(SOS) expression, the program is devised for the calculation of nonlinear second order optical susceptibilites β ijk and studying how ... On the basis of ZINDO method and according to the sum over states(SOS) expression, the program is devised for the calculation of nonlinear second order optical susceptibilites β ijk and studying how different substituents on the phenyl ring attached to the atom silicon influence on the nonlinear second order optical properties of substituted silane series of molecules. The properties of (CH 3) 3Si? ?has been studied particularly. The effect of the length of silica chains on the calculated values has been studied too. The regularity summarized from the calculated results has been explained micromechanically. 展开更多
关键词 Substituted silanes nonlinear second order optical susceptibility ZINDO SOS
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OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH DAMPING 被引量:1
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作者 罗辉 庄容坤 +3 位作者 郭兴明Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P.R.China 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第4期441-448,共8页
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.... By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results. 展开更多
关键词 second order nonlinear differential equation with damping OSCILLATION Riccati transformation integral averaging technique
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PREPARATION AND SECOND-ORDER OPTICAL NONLINEARITY OF NOVEL PHENOXYSILICON NETWORKS BY SOL-GEL PROCESS 被引量:1
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作者 Xiao Huang Jian Wang Ling-zhi Zhang Zhi-gang Cai Zhao-xi Lianga 《Chinese Journal of Polymer Science》 SCIE CAS CSCD 2001年第1期39-44,共6页
Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H2O and catalyst. All poled polymer network films possess high second-... Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H2O and catalyst. All poled polymer network films possess high second-order nonlinear optical coefficients (d(33)) Of 10(-7)similar to 10(-8) esu. The investigation of NLO temporal stability at room temperature and elevated temperature (120 degreesC) indicated that these films exhibit high d(33) stability because the orientation of the chromophores are locked in the phenoxysilicon organic/inorganic networks. 展开更多
关键词 phenoxysilicon networks sol-gel process azobenzene chromophore stilbene chromophore second order optical nonlinearity
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SECOND ORDER NONLINEAR OPTICAL PROPERTIES OF DICYANOPYRAZINES
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作者 Cheng YE Zhi Ming FENG Yah Jun CHEN Jia Fu WANG Hai Ou DONG (Institute of Chemistry, Academia Sinica, Beijing 100080) Dept. of Chemistry, Branch Campus of Peking University. 《Chinese Chemical Letters》 SCIE CAS CSCD 1991年第10期765-768,共4页
Second order nonlinear optical active 2,3-dichloro-5,6-dicyanopyrazine (DCDCP) and its monoamine-substituted derivatives had been synthesized. Their facile synthesis, high melt point, high incidence af substantial SHG... Second order nonlinear optical active 2,3-dichloro-5,6-dicyanopyrazine (DCDCP) and its monoamine-substituted derivatives had been synthesized. Their facile synthesis, high melt point, high incidence af substantial SHG activity and increased transparency inthe blue and near infrared make this class compounds appealling for further investigation. 展开更多
关键词 SHG second order nonlinear OPTICAL PROPERTIES OF DICYANOPYRAZINES NLO
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THE SYNTHESIS OF NEW POLED CROSSLINKED POLYMETHACRYLATES AND THEIR SECOND ORDER NONLINEAR OPTICAL PROPERTIES
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作者 颜星中 陈用烈 +3 位作者 梁兆熙 蔡志岗 杨佩青 罗挺 《Chinese Journal of Polymer Science》 SCIE CAS CSCD 1996年第4期346-354,共9页
Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride ... Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride units, which was obtained by the reaction of 4-nitro-4'-[N-hydroxyethyl, N'-ethyl] amino azobenzene with polymethacryloyl chloride (chromophore content: 25 mol %). During thermal poling process the anhydride reacts with the epoxy group and the resulting crosslinked network structure will stabilize the second harmonic generation in the poled film. The second harmonic generation of the poled film shows a maximum with the variation of composition this is presumed to be due to the effects of the increasing of concentration, orientation order as well as orientation stability of chromophore groups during crosslinking. 展开更多
关键词 second order nonlinear optics poled polymers Disperse Red 1 methacrylate copolymers
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Oscillation Theorems for Second Order Damped Nonlinear Differential Equations
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作者 HEWan-sheng LIWan-tong 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第1期1-9,共9页
Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and ... Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results. 展开更多
关键词 OSCILLATION second order nonlinear differential equation DAMPING
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OSCILLATION THEOREMS FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DAMPING
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作者 陈伯山 《Acta Mathematica Scientia》 SCIE CSCD 1991年第4期409-416,共8页
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p(t) and q(t) are allowed to change sign on [t0,∞).
关键词 OSCILLATION THEOREMS FOR second order nonlinear DIFFERENTIAL EQUATIONS WITH DAMPING
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Asymptotic Calculation of the Wave Trough Exceedance Probabilities in A Nonlinear Sea 被引量:1
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作者 WANG Ying-guang 《China Ocean Engineering》 SCIE EI CSCD 2018年第2期189-195,共7页
This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method... This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures. 展开更多
关键词 wave trough depth second order nonlinear wave model asymptotic method measured data
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A Second Order Difference Scheme with Nonuniform Rectangular Meshes for Nonlinear Parabolic System
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作者 Zheng-su Wan Guang-nan Chen 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2009年第1期159-166,共8页
In this paper, a difference scheme with nonuniform meshes is proposed for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in both spac... In this paper, a difference scheme with nonuniform meshes is proposed for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in both space and time. 展开更多
关键词 second order difference scheme nonuniform meshes nonlinear parabolic system
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Discretization of Nonlinear Non-affine Time Delay Systems Based on Second-order Hold
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作者 Yuan-Liang Zhang 《International Journal of Automation and computing》 EI CSCD 2014年第3期320-327,共8页
When calculating the sampled-date representation of nonlinear systems second-order hold(SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization met... When calculating the sampled-date representation of nonlinear systems second-order hold(SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input.Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method.The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems.The comparison between SOH assumption with first-order hold(FOH) and zero-order hold(ZOH) assumptions is given to show the advantages of the proposed method. 展开更多
关键词 nonlinear system non-affine input DISCRETIZATION Taylor series second-order hold(SOH).
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基于积分滑模的二阶系统任意预设时间编队控制
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作者 程雯 过榴晓 《计算机工程》 CAS CSCD 北大核心 2024年第11期163-172,共10页
在通信过程中,智能体受各种未知干扰信号的影响,导致系统性能降低。针对二阶非线性多智能体系统,研究了在有向通信拓扑结构下实现任意预设时间编队期望的问题。首先,结合预设时间机制与积分滑模控制策略,设计一种新的编队控制协议,该控... 在通信过程中,智能体受各种未知干扰信号的影响,导致系统性能降低。针对二阶非线性多智能体系统,研究了在有向通信拓扑结构下实现任意预设时间编队期望的问题。首先,结合预设时间机制与积分滑模控制策略,设计一种新的编队控制协议,该控制协议能够确保二阶多智能体系统在任意预设时间内实现到达段和滑动段2个阶段的收敛,引入的积分滑模控制项有效降低了系统的稳态误差,并提高其在预设时间控制下的鲁棒稳定性;其次,利用李雅普诺夫方法与代数图论知识,分析得出二阶系统在该控制方法下达到预设时间编队期望的充分条件,并证明了包含预设时变函数控制协议的有界性。仿真实验结果验证所设计控制方法的有效性与可行性,即给定任意初值,带干扰项的二阶系统均可在任意预设时间内快速准确地达到稳定状态。 展开更多
关键词 滑模控制 任意预设时间控制 编队控制 二阶非线性系统 多智能体
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多传感器非线性系统序贯观测融合二阶扩展卡尔曼滤波器
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作者 姜吉鹏 孙书利 《黑龙江大学工程学报(中英俄文)》 2024年第1期27-39,共13页
对多传感器非线性系统提出了一种序贯观测融合二阶扩展卡尔曼滤波(Second-order Extended Kalman Filter,SOEKF)算法。该算法的中心思想是根据传感器观测数据到达融合中心的先后次序依次进行处理。研究表明,提出的序贯观测融合SOEKF算... 对多传感器非线性系统提出了一种序贯观测融合二阶扩展卡尔曼滤波(Second-order Extended Kalman Filter,SOEKF)算法。该算法的中心思想是根据传感器观测数据到达融合中心的先后次序依次进行处理。研究表明,提出的序贯观测融合SOEKF算法比集中式观测融合EKF算法具有更高的精度;与集中式观测融合SOEKF算法精度相当,且具有更低的计算复杂度。目标跟踪系统的仿真验证了算法的有效性。 展开更多
关键词 多传感器信息融合 序贯观测融合 非线性系统 二阶扩展卡尔曼滤波器
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大失准角条件下制导炮弹组合导航方法研究
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作者 卢宝峰 梅春波 +1 位作者 杨鹏翔 张昊 《弹箭与制导学报》 北大核心 2024年第5期115-120,共6页
制导炮弹多采用发射后上电空中对准的方式实现导航初始信息的获取,初始姿态信息中滚转角的获取难度远高于俯仰角和偏航角。针对空中对准中滚转角信息获取难度较高的问题,提出了一种适用于大初始滚转角误差的组合导航方法,旨在省略滚转... 制导炮弹多采用发射后上电空中对准的方式实现导航初始信息的获取,初始姿态信息中滚转角的获取难度远高于俯仰角和偏航角。针对空中对准中滚转角信息获取难度较高的问题,提出了一种适用于大初始滚转角误差的组合导航方法,旨在省略滚转角对准过程和压缩空中对准时间。通过在组合导航状态向量中引入四元数误差,将状态方程的强非线性误差模型转换为了二阶非线性模型,降低了系统的复杂度。在此基础上,采用二阶扩展卡尔曼滤波方法实现惯性导航系统各项误差的估计,并基于四元数模1约束设计了优化的量测更新方法。各量级初始滚转角误差下的半实物仿真结果表明:所设计方法可适应大初始滚转角误差情况,7 s内滚转角误差可由180°收敛至10°内;各量级初始滚转角误差下收敛位置稳定一致,有效的提升了组合导航的适应性。 展开更多
关键词 组合导航系统 二阶非线性 大失准角 扩展卡尔曼滤波
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Quasiperiodic Solutions for Nonlinear Differential Equations of Second Order with Symmetry 被引量:2
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作者 Liu Bin Department of Mathematics Peking University Beijing,100871 China You Jiangong Department of Mathematics Nanjing University Nanjing,210008 China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1994年第3期231-242,共12页
In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the... In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions. 展开更多
关键词 TH Quasiperiodic Solutions for nonlinear Differential Equations of second order with Symmetry MATH
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THE SINGULAR SECOND ORDER NONLINEAR EIGENVALUE PROBLEM WITH INFINITELY MANY POSITIVE SOLUTIONS 被引量:6
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作者 姚庆六 《Annals of Differential Equations》 2001年第3期268-274,共7页
In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of c... In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of cone expansion-compression type we give several sufficient conditions. 展开更多
关键词 second order nonlinear eigenvalue problem infinitely many po-sitive solutions singular coefficient Krasnosel'skii fixed point theorem
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OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR NEUTRAL PERTURBED DYNAMIC EQUATIONS ON TIME SCALES 被引量:1
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作者 Xiuping Yu 1,Hongyu Yang 2,Jianmei Zhang 1,Chengmin Hou 3 1.Dept.of Math.and Physics,Hebei Institute of Architecture and Civil Engineering,Zhangjiakou 075024,Hebei 2.Dept.of Mechanic and Engineering,Zhangjiakou Vocational Technology Institute,Zhangjiakou 075031,Hebei 3.Dept.of Math.,Yanbian University,Yanji 133002,Jilin, 《Annals of Differential Equations》 2012年第4期460-464,共5页
In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example tha... In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example that dwells upon the sharp conditions of our result is also included. 展开更多
关键词 OSCILLATION NEUTRAL second order nonlinear dynamic equation time scale
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Calculations on the Nonlinear Second-Order Optical Polarizabilities for Series of Donor-C_(60) Molecules
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作者 刘孝娟 封继康 +1 位作者 任爱民 周新 《Chinese Journal of Chemistry》 SCIE CAS CSCD 2003年第6期610-616,共7页
The equilibrium geometries and UV visible spectra of a series of donor C 60 molecules were obtained by means of the AM1 and INDO/CI method, on the basis of accurate geometric and electronic structures. The nonl... The equilibrium geometries and UV visible spectra of a series of donor C 60 molecules were obtained by means of the AM1 and INDO/CI method, on the basis of accurate geometric and electronic structures. The nonlinear second order optical polarizabilities were calculated using the method INDO/SDCI combined with the Sum Over States (SOS) expression. The calculated β ( λ =1 34 μm) values are 28 81, 48 56, 57 33, 66 99, 70 85, 85 84, and 142 14 (×10 -30 esu) for the molecules A, B, C, D, E, F and G, respectively. The frontier orbitals were plot for the representative molecules in order to exhibit the intramolecular charge transfer. The results indicate that introduction of thienylethylene can enhancethe NLO response and the dimethyl^aniline substituted di^thienyl^ethylene C 60 (molecule G) possesses the largest NLO second order optical polarizability. The large β values can be attributed to the charge transfer between the substituents and C 60 , as well as within the three dimensional conjugated sphere of C 60 . 展开更多
关键词 INDO/SDCI nonlinear second order polarizability SOS expression
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Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations
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作者 Lijun Yi Zhongqing Wang 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2014年第2期149-178,共30页
In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algori... In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algorithm for the singleinterval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy ofthe proposed methods. 展开更多
关键词 Legendre-Gauss spectral collocation method second order nonlinear delay differential equations error analysis
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Modulation of the Second Order Nonlinear Optical Properties of Helical Graphene Nanoribbons Through Introducing Azulene Defects or/and BN Units
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作者 ZHENG Xuelian LIU Ling +3 位作者 YANG Cuicui HE Yuanyuan CHEN Jiu TIAN Wei Quan 《Chemical Research in Chinese Universities》 SCIE CAS CSCD 2022年第4期974-984,共11页
The current study has obtained excellent potential nonlinear optical(NLO)materials by combining density functional theory methods with sum-over-states model to predict the second order NLO properties of helical graphe... The current study has obtained excellent potential nonlinear optical(NLO)materials by combining density functional theory methods with sum-over-states model to predict the second order NLO properties of helical graphene nanoribbons(HGNs)through introducing azulene defects or/and BN units.The introduction of these functional groups deforms the pristine HGN(compression or tension)and enhances obviously the static first hyperpolarizability(〈β0〉)of system by up to two orders of magnitude.The tensor components along the helical axis of HGNs play a dominant role in the total〈β0〉.The azulene defects and the BN units polarize the pristine HGN to different degrees,and the azulenes and contiguous benzenes are involved in the major electron excitations with significant contributions to〈β0〉but the BN units are not.The BN-doped chiral HGNs have good kinetic stability and strong second order NLO properties(6.84×10^(5)×10^(−30) esu),and can be a potential candidate of high-performance second order NLO materials.The predicted two-dimensional second order NLO spectra provide useful information for further exploration of those helicenes for electro-optic applications. 展开更多
关键词 Helical graphene nanoribbon Azulene defect BN-doping second order nonlinear optical(NLO)property Sum-over-states model
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