To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregress...To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.展开更多
In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
针对目前基于信道脉冲响应(Channel Impulse Response,CIR)的非视距(None Line of Sight,NLoS)/视距(Line of Sight,LoS)识别方法精度低、泛化能力差的问题,提出了一种多层卷积神经网络(Convolutional Neural Network,CNN)与通道注意力...针对目前基于信道脉冲响应(Channel Impulse Response,CIR)的非视距(None Line of Sight,NLoS)/视距(Line of Sight,LoS)识别方法精度低、泛化能力差的问题,提出了一种多层卷积神经网络(Convolutional Neural Network,CNN)与通道注意力模块(Channel Attention Module,CAM)相结合的NLoS/LoS识别方法。在多层CNN中嵌入CAM提取原始CIR的时域数据特征,利用全局平均池化层代替全连接层进行特征整合并分类输出。使用欧洲地平线2020计划项目eWINE公开的数据集进行不同结构模型和不同识别方法的对比实验,结果表明,所提出的CNN-CAM模型LoS和NLoS召回率分别达到了92.29%与87.71%,准确率达到了90.00%,F1分数达到了90.22%。与现有多种传统识别方法相比,均具有更好的识别效果。展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
Density functional theory (DFT) B3LYP at 6-31G* level is employed to optimize the structures of the molecules bridged through n-vertex bis-substituted carborane (n=5, 6, 7) and combined with finite field (FF) formalis...Density functional theory (DFT) B3LYP at 6-31G* level is employed to optimize the structures of the molecules bridged through n-vertex bis-substituted carborane (n=5, 6, 7) and combined with finite field (FF) formalism to calculate the second-order NLO properties. The results indicate that the structures of n-vertex bis-substituted carborane (n=5, 6, 7) are changed due to bridged donor and acceptor moieties. The distances between two C atoms are becoming longer. And the stability and dipole moment are in- fluenced by changing substituted positions of C atoms. The isomers with the substituents connecting with C atoms of lower coordination number have better stability and larger values of polarizability. One-dimensional structure of the molecules bridged through n-vertex bis-substituted carborane (n=5, 6, 7) is in favor of intramolecular charge-transfer. Meanwhile, the isomer with a larger change of dipole moment has larger value of second-order NLO properties during the charge-transfer process.展开更多
This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is...This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.展开更多
In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are usi...In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.展开更多
This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this met...This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2<sup>nd</sup>-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2<sup>nd</sup>-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.展开更多
This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and par...This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2<sup>nd</sup>-BERRU-PMP, where the attribute “2<sup>nd</sup>” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2<sup>nd</sup>-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.展开更多
This work illustrates the innovative results obtained by applying the recently developed the 2<sup>nd</sup>-order predictive modeling methodology called “2<sup>nd</sup>- BERRU-PM”, where the ...This work illustrates the innovative results obtained by applying the recently developed the 2<sup>nd</sup>-order predictive modeling methodology called “2<sup>nd</sup>- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2<sup>nd</sup>-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2<sup>nd</sup>-order response sensitivities must always be included to quantify the need for including (or not) the 3<sup>rd</sup>- and/or 4<sup>th</sup>-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1<sup>st</sup>- and 2<sup>nd</sup>-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3<sup>rd</sup>- and even 4<sup>th</sup>-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1<sup>st</sup>-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2<sup>nd</sup>-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).展开更多
The second-order nonlinear optical (NLO) properties of 5,10,15-triphenylcorrole (TPC), 5,10,15,20-tetraphenylporphyrin (TPP) and L-amino acid bridged bis-corroles 1,2,3 and 4 have been calculated by using TDHF/P...The second-order nonlinear optical (NLO) properties of 5,10,15-triphenylcorrole (TPC), 5,10,15,20-tetraphenylporphyrin (TPP) and L-amino acid bridged bis-corroles 1,2,3 and 4 have been calculated by using TDHF/PM3 method based on the RHF/6-31G (TPC and TPP) or semiempirical PM3 (1, 2, 3, 4) optimized geometries. Calculation results showed TPC and TPP have C1 and D2h symmetry, respectively when N-H protons are localized on the nitrogen atoms. TPC is the second-order NLO active chromophore due to the cancellation of centrosymmetrical structure and its first hyperpolarizability β increases to 11.524×10^-30 esu. Under electrical dipole approximation, βvalues of bis-corroles 1, 2, 3 and 4 vary from 9.831×10^-30 to 14.221×10^-30 esu, and no much improvement in the first hyperpolarizability was observed as compared to TPC monomer.However, β values of bis-corroles 1, 2, 3 and 4 are improved by about 4 times as compared to their bis-porphyrin counterparts. The analysis of β components indicates that β of this kind of bis-corroles is mainly contributed from its radial component βr. With the variation of amino acid side chains, βHRS, β,βxyz, βr and βa of bis-corroles change remarkably. Chiral L-amino acid bridged bis-corroles 2, 3 and 4 have a right-handed helix structure, and their chiral component βxyz matches βxyz ∝ r^2 ζ/L^4 (helix parameters), showing the second-order chiral NLO response of these bis-corroles could be described by one-electron helical model theory. It was found that the radial component βr of chiral helix bis-corroles also matches βr ∝ r^2 ζ/L^4.展开更多
In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilize...In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.展开更多
In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth ...In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial discretization.In addition,two stabilization terms in different forms are added for the sake of the numerical stability.We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined estimate.By regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete?^(∞)bound of the numerical solution,as a result of the rough error estimate.Subsequently,the refined error estimate is derived to obtain the optimal rate of convergence,following the established?∞bound of the numerical solution.Moreover,the energy stability is also rigorously proved with respect to a modified energy.The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.展开更多
This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different ...This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.展开更多
Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-...Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality (LMI) are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader's states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.展开更多
Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop ...Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.展开更多
A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using...A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.展开更多
基金The National Key Research and Development Program of China under contract No.2023YFC3107701the National Natural Science Foundation of China under contract No.42375143.
文摘To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
文摘针对目前基于信道脉冲响应(Channel Impulse Response,CIR)的非视距(None Line of Sight,NLoS)/视距(Line of Sight,LoS)识别方法精度低、泛化能力差的问题,提出了一种多层卷积神经网络(Convolutional Neural Network,CNN)与通道注意力模块(Channel Attention Module,CAM)相结合的NLoS/LoS识别方法。在多层CNN中嵌入CAM提取原始CIR的时域数据特征,利用全局平均池化层代替全连接层进行特征整合并分类输出。使用欧洲地平线2020计划项目eWINE公开的数据集进行不同结构模型和不同识别方法的对比实验,结果表明,所提出的CNN-CAM模型LoS和NLoS召回率分别达到了92.29%与87.71%,准确率达到了90.00%,F1分数达到了90.22%。与现有多种传统识别方法相比,均具有更好的识别效果。
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金Supported by the Foundation of Jilin Provincial Excellent Youth (Grant No. 20050107)Youth Science Foundation of Northeast Normal University (Grant No. 111494117)
文摘Density functional theory (DFT) B3LYP at 6-31G* level is employed to optimize the structures of the molecules bridged through n-vertex bis-substituted carborane (n=5, 6, 7) and combined with finite field (FF) formalism to calculate the second-order NLO properties. The results indicate that the structures of n-vertex bis-substituted carborane (n=5, 6, 7) are changed due to bridged donor and acceptor moieties. The distances between two C atoms are becoming longer. And the stability and dipole moment are in- fluenced by changing substituted positions of C atoms. The isomers with the substituents connecting with C atoms of lower coordination number have better stability and larger values of polarizability. One-dimensional structure of the molecules bridged through n-vertex bis-substituted carborane (n=5, 6, 7) is in favor of intramolecular charge-transfer. Meanwhile, the isomer with a larger change of dipole moment has larger value of second-order NLO properties during the charge-transfer process.
基金Project supported by the Executive Agency for Higher Education Research Development and Innovation Funding of Romania(No.PN-III-P4-PCE-2021-0993)。
文摘This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.
文摘In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.
文摘This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2<sup>nd</sup>-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2<sup>nd</sup>-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.
文摘This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2<sup>nd</sup>-BERRU-PMP, where the attribute “2<sup>nd</sup>” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2<sup>nd</sup>-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.
文摘This work illustrates the innovative results obtained by applying the recently developed the 2<sup>nd</sup>-order predictive modeling methodology called “2<sup>nd</sup>- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2<sup>nd</sup>-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2<sup>nd</sup>-order response sensitivities must always be included to quantify the need for including (or not) the 3<sup>rd</sup>- and/or 4<sup>th</sup>-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1<sup>st</sup>- and 2<sup>nd</sup>-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3<sup>rd</sup>- and even 4<sup>th</sup>-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1<sup>st</sup>-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2<sup>nd</sup>-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).
基金Supported by the NNSFC (20476034), Research Grants Council of Hongkong and SRF for ROCS, State Education Ministry
文摘The second-order nonlinear optical (NLO) properties of 5,10,15-triphenylcorrole (TPC), 5,10,15,20-tetraphenylporphyrin (TPP) and L-amino acid bridged bis-corroles 1,2,3 and 4 have been calculated by using TDHF/PM3 method based on the RHF/6-31G (TPC and TPP) or semiempirical PM3 (1, 2, 3, 4) optimized geometries. Calculation results showed TPC and TPP have C1 and D2h symmetry, respectively when N-H protons are localized on the nitrogen atoms. TPC is the second-order NLO active chromophore due to the cancellation of centrosymmetrical structure and its first hyperpolarizability β increases to 11.524×10^-30 esu. Under electrical dipole approximation, βvalues of bis-corroles 1, 2, 3 and 4 vary from 9.831×10^-30 to 14.221×10^-30 esu, and no much improvement in the first hyperpolarizability was observed as compared to TPC monomer.However, β values of bis-corroles 1, 2, 3 and 4 are improved by about 4 times as compared to their bis-porphyrin counterparts. The analysis of β components indicates that β of this kind of bis-corroles is mainly contributed from its radial component βr. With the variation of amino acid side chains, βHRS, β,βxyz, βr and βa of bis-corroles change remarkably. Chiral L-amino acid bridged bis-corroles 2, 3 and 4 have a right-handed helix structure, and their chiral component βxyz matches βxyz ∝ r^2 ζ/L^4 (helix parameters), showing the second-order chiral NLO response of these bis-corroles could be described by one-electron helical model theory. It was found that the radial component βr of chiral helix bis-corroles also matches βr ∝ r^2 ζ/L^4.
基金supported by National Natural Science Foundation of China (No.60504007)the PhD Programs Foundation of Ministry of Educationof China (No.20070286040)the Scientific Research Foundation of Graduate School of Southeast University
文摘In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.
基金supported by the Chinese Academy of Sciences(CAS)Academy of Mathematics and Systems Science(AMSS)the Hong Kong Polytechnic University(PolyU)Joint Laboratory of Applied Mathematics+4 种基金supported by the Hong Kong Research Council General Research Fund(Grant No.15300821)the Hong Kong Polytechnic University Grants(Grant Nos.1-BD8N,4-ZZMK and 1-ZVWW)supported by the Hong Kong Research Council Research Fellow Scheme(Grant No.RFS2021-5S03)General Research Fund(Grant No.15302919)supported by US National Science Foundation(Grant No.DMS-2012269)。
文摘In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial discretization.In addition,two stabilization terms in different forms are added for the sake of the numerical stability.We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined estimate.By regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete?^(∞)bound of the numerical solution,as a result of the rough error estimate.Subsequently,the refined error estimate is derived to obtain the optimal rate of convergence,following the established?∞bound of the numerical solution.Moreover,the energy stability is also rigorously proved with respect to a modified energy.The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70571059)
文摘This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.
基金supported by the Fundamental Research Funds for the Central Universities(JUSRP11020)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20090093120006)
文摘Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality (LMI) are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader's states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.
文摘Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.
基金The project sponsored by the Foundation for Doctorate Thesis of Tsinghua Universitythe National Key Project in 1999-2004 sponsored by the Ministry of Science and Technology of China
文摘A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.