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Second-order consensus in networks of dynamic agents with communication time-delays 被引量:5
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作者 Bo Yang1,2, Huajing Fang3, and Hua Wang4 1. School of Navigation, Wuhan University of Technology, Wuhan 430063, P. R. China 2. Wuhan Second Ship Design and Research Institute, Wuhan 430064, P. R. China +1 位作者 3. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China 4. Department of Aerospace and Mechanical Engineering, Boston University, Boston MA02215, USA 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第1期88-94,共7页
This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employi... This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays. 展开更多
关键词 second-order consensus protocols dynamic networks algebraic graph theory frequency domain analysis com-munication constraints.
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Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps 被引量:4
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作者 PALANISAMY Muthukumar CHINNATHAMBI Rajivganthi 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第5期1033-1048,共16页
The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the po... The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations (jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory. 展开更多
关键词 Approximate controllability Hilbert space Poisson jumps second-order neutral stochas-tic differential equations semigroup theory.
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Second-order interference of two independent and tunable single-mode continuous-wave lasers 被引量:1
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作者 刘建彬 卫栋 +5 位作者 陈辉 周宇 郑淮斌 高宏 李福利 徐卓 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第3期194-199,共6页
The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman's path integral theory. It is concluded that whether the sec... The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman's path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra. 展开更多
关键词 second-order temporal beating two-photon interference Feynman's path integral theory
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Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations
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作者 Shan Shi Zhenlai Han 《Communications on Applied Mathematics and Computation》 2021年第3期497-508,共12页
The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form(r(t)((y(t)+p(t)y(τ(t)))')^(α))'+q(t)yα(σ(t))=0,t≥t_(0),w... The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form(r(t)((y(t)+p(t)y(τ(t)))')^(α))'+q(t)yα(σ(t))=0,t≥t_(0),when∫^(∞)r^(−1/α)(s)ds<∞.We obtain sufficient conditions for the oscillation of the studied equations by the inequality principle and the Riccati transformation.An example is provided to illustrate the results. 展开更多
关键词 Oscillation theory second-order differential equations NEUTRAL Advanced argument Asymptotic behavior
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An R(x)-orthonormal theory for the vibration performance of a non-smooth symmetric composite beam with complex interface 被引量:2
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作者 Chein-Shan Liu Bo-Tong Li 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2019年第1期228-241,I0007,共15页
A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different ... A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces. 展开更多
关键词 SYMMETRIC composite beams R(x)-orthogonality of second-order derivatives of boundary functions R(x)-orthonormal theory Non-smooth/discontinuous interface Sequentially closed-from natural frequencies
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Nonlinear Time-Domain Theory for the Simulation of Moored Floating Body Motion
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作者 Bin Teng Peiwen Cong Ying Gou 《Journal of Marine Science and Application》 CSCD 2018年第3期341-352,共12页
Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular w... Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory. 展开更多
关键词 second-order diffraction theory QTF components TIME-DOMAIN SIMULATION CUMMINS method Response of FLOATING BODIES
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Comparisons of Wave Force Model Effects on the Structural Responses and Fatigue Loads of a Semi-Submersible Floating Wind Turbine
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作者 HAN Yanqing LE Conghuan +1 位作者 ZHANG Puyang XU Shengnan 《Journal of Ocean University of China》 CAS CSCD 2024年第1期69-79,共11页
The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a ... The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses. 展开更多
关键词 floating wind turbine wave force model potential flow theory Morison equation second-order wave forces
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The relative energies of polypeptide conformers predicted by linear scaling second-order M?ller-Plesset perturbation theory
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作者 GUO Yang LI Wei +1 位作者 YUAN DanDan LI ShuHua 《Science China Chemistry》 SCIE EI CAS 2014年第10期1393-1398,共6页
We describe an implementation of the cluster-in-molecule (CIM) resolution of the identity (RI) approximation second-order Moller-Plesset perturbation theory (CIM-RI-MP2), with the purpose of extending RI-MP2 cal... We describe an implementation of the cluster-in-molecule (CIM) resolution of the identity (RI) approximation second-order Moller-Plesset perturbation theory (CIM-RI-MP2), with the purpose of extending RI-MP2 calculations to very large systems. For typical conformers of several large polypeptides, we calculated their conformational energy differences with the CIM-RI-MP2 and the generalized energy-based fragmentation MP2 (GEBF-MP2) methods, and compared these results with the density functional theory (DFT) results obtained with several popular functionals. Our calculations show that the conformational energy differences obtained with CIM-RI-MP2 and GEBF-MP2 are very close to each other. In comparison with the GEBF-MP2 and CIM-RI-MP2 relative energies, we found that the DFT functionals (CAM-B3LYP-D3, LC-ωPBE-D3, M05-2X, M06-2X and coB97XD) can give quite accurate conformational energy differences for structurally similar conformers, but provide less-accurate results for structurally very different conformers. 展开更多
关键词 cluster-in-molecule generalized energy-based fragmentation second-order Moller-Plesset perturbation theory resolution of the identity relative energy
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Low-lying electronic states of osmium monoxide OsO
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作者 严汶 邹文利 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第11期24-32,共9页
The ground state of osmium monoxide(OsO) has long been controversial. In this paper, the low-lying Λ–S and ? electronic states of OsO have been comprehensively studied by the high-precision multi-reference calculati... The ground state of osmium monoxide(OsO) has long been controversial. In this paper, the low-lying Λ–S and ? electronic states of OsO have been comprehensively studied by the high-precision multi-reference calculations. The ground state of OsO is unexpectedly the closed-shell1Σ+state with a double bond instead of the previously reported3Φ or5Σ+state;after including the spin–orbit coupling effects, the ground state becomes3Π2. With the help of the theoretical spectroscopic constants and transition dipole moments, the emission spectra in the region of 405 nm–875 nm are assigned.Our results will facilitate the future studies of absorption and emission spectra of OsO. 展开更多
关键词 transition dipole moment multi-reference second-order perturbation theory spin-orbit coupling exacttwo-component
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DFT Studies on Second-order Nonlinear Optical Response of Ir(C∧N)2(pic)Complexes
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作者 WANG Huiying SHEN Zhaobin +2 位作者 YE Jinting WANG Hongqiang QIU Yongqing 《Chemical Research in Chinese Universities》 SCIE CAS CSCD 2019年第2期333-339,共7页
Density flmctional theory(DFT)was employed to calculate the geometrical structures,UV-Vis absorption spectra and second-order nonlinear optical(NLO)properties of a family of iridium(Ⅲ)complexes,which possess of diffe... Density flmctional theory(DFT)was employed to calculate the geometrical structures,UV-Vis absorption spectra and second-order nonlinear optical(NLO)properties of a family of iridium(Ⅲ)complexes,which possess of different cyclometallated ligands(C∧N)and ancillary ligands[pyridme-2-carboxylate(pic)].It was found that the mo-dification of the LUMO energy levels was achieved by changing pic ligands and the energy gaps between the HOMO and LUMO were notably increased or decreased.In addition,the degree of conjugation was significantly changed with the substituent groups varied,which led to that the first hyperpolarizabilityβcould be effectively modulated.Through the analysis of time-dependent DFT(TD-DFT)results,we predicted that these studied complexes withπ→π^*charge transfer was beneficial to the large second-order NLO properties.Therefore,we hope that these studied iridium(III)complexes can be considered as versatile second-order NLO materials. 展开更多
关键词 Density functional theory Iridium(III)complex second-order nonlinear optical(NLO)property
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MULTIPLICITY OF SOLUTIONS TO ASYMPTOTICALLY LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL SYSTEM
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作者 Yucheng Bu(Dept. of Teachers’ Training,Zhenjiang College,Danyang 212300,Jiangsu) 《Annals of Differential Equations》 2011年第3期283-292,共10页
In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Mo... In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory. 展开更多
关键词 second-order ordinary differential systems index theory of linear systems Morse theory multiplicity of solutions
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Full time-domain nonlinear coupled dynamic analysis of a truss spar and its mooring/riser system in irregular wave 被引量:8
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作者 YANG MinDong TENG Bin +3 位作者 XIAO LongFei NING DeZhi SHI ZhongMin QU Yan 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2014年第1期152-165,共14页
A new full time-domain nonlinear coupled method has been established and then applied to predict the responses of a Truss Spar in irregular wave. For the coupled analysis, a second-order time-domain approach is develo... A new full time-domain nonlinear coupled method has been established and then applied to predict the responses of a Truss Spar in irregular wave. For the coupled analysis, a second-order time-domain approach is developed to calculate the wave forces, and a finite element model based on rod theory is established in three dimensions in a global coordinate system. In nu- merical implementation, the higher-order boundary element method (HOBEM) is employed to solve the velocity potential, and the 4th-order Adams-Bashforth-Moultn scheme is used to update the second-order wave surface. In deriving convergent solu- tions, the hull displacements and mooring tensions are kept consistent at the fairlead and the motion equations of platform and mooring-lines/risers are solved simultaneously using Newmark-fl integration scheme including Newton-Raphson iteration. Both the coupled quasi-static analysis and the coupled dynamic analysis are performed. The numerical simulation results are also compared with the model test results, and they coincide very well as a whole. The slow-drift responses can be clearly ob- served in the time histories of displacements and mooring tensions. Some important characteristics of the coupled responses are concluded. 展开更多
关键词 coupled method full time-domain second-order truss spar rod theory irregular wave
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Theoretical Study on the Mechanism of the Cycloaddition Reaction between Methylidenesilene and Ethylene 被引量:2
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作者 卢秀慧 于海彬 +1 位作者 徐曰华 武卫荣 《Chinese Journal of Chemistry》 SCIE CAS CSCD 2006年第3期307-310,共4页
The mechanism of a cycloaddition reaction between singlet methylidenesilene and ethylene has been investigated with MP2/6-31G^* and B3LYP/6-31G^* methods, including geometry optimization and vibrational analysis for... The mechanism of a cycloaddition reaction between singlet methylidenesilene and ethylene has been investigated with MP2/6-31G^* and B3LYP/6-31G^* methods, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. Energies of the involved conformers were calculated by CCSD(T)//MP2/6-31G* and CCSD(T)//B3LYP/6-31 G* methods, respectively. The results show that the dominant reaction pathway of the cycloaddition reaction is that a complex intermediate is firstly formed between the two reactants through a barrier-free exothermic reaction of 13.3 kJ/mol, and the complex is then isomefized to a four-membered ring product P2,1 via a transition state TS2.1 with a barrier of 32.0 kJ/mol. 展开更多
关键词 methylidenesilene cycloaddition reaction potential energy surface second-order Moller-Plesset perturbation and density functional theory
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Theoretical Study on the Mechanism of the Cycloaddition Reaction between Alkylidene Carbene and Ethylene 被引量:1
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作者 卢秀慧 翟利民 武卫荣 《Chinese Journal of Chemistry》 SCIE CAS CSCD 2004年第1期24-27,共4页
The mechanism of cycloaddition reaction between singlet alkylidene carbene and ethylene has been investigated with second-order Moller-Plesset perturbation theory (MP2). By using 6–31G* basis, geometry optimization, ... The mechanism of cycloaddition reaction between singlet alkylidene carbene and ethylene has been investigated with second-order Moller-Plesset perturbation theory (MP2). By using 6–31G* basis, geometry optimization, vibrational analysis and energetics have been calculated for the involved stationary points on the potential energy surface. The results show that the title reaction has two major competition channels. An energy-rich intermediate (INT) is firstly formed between alkylidene carbene and ethylene through a barrier-free exothermic reaction of 63.62 kJ/mol, and the intermediate then isomerizes to a three-membered ring product (Pl) and a four-membered ring product (P2) via transition state TS1 and TS2, in which energy barriers are 47.00 and 51.02 kl/mol. respectively. PI is the main product. 展开更多
关键词 alkylidene carbene cycloaddition reaction second-order Moller-Plesset perturbation theory potential energy surface
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Asymptotic expansions of complete Kahler-Einstein metrics with finite volume on quasi-projective manifolds 被引量:1
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作者 Xumin Jiang Yalong Shi 《Science China Mathematics》 SCIE CSCD 2022年第9期1953-1974,共22页
We give an elementary proof to the asymptotic expansion formula of Rochon and Zhang(2012)for the unique complete Kahler-Einstein metric of Cheng and Yau(1980),Kobayashi(1984),Tian and Yau(1987)and Bando(1990)on quasi-... We give an elementary proof to the asymptotic expansion formula of Rochon and Zhang(2012)for the unique complete Kahler-Einstein metric of Cheng and Yau(1980),Kobayashi(1984),Tian and Yau(1987)and Bando(1990)on quasi-projective manifolds.The main tools are the solution formula for second-order ordinary differential equations(ODEs)with constant coefficients and spectral theory for the Laplacian operator on a closed manifold. 展开更多
关键词 asymptotic expansions Kahler-Einstein metric quasi-projective manifolds complex Monge-Ampère equations second-order ODE Schauder estimates spectral theory
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