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Infinitely many periodic solutions for second-order Hamiltonian systems
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作者 尹翠翠 张福保 黄成山 《Journal of Southeast University(English Edition)》 EI CAS 2009年第4期549-551,共3页
The existence of high energy periodic solutions for the second-order Hamiltonian system -ü(t)+A(t)u(t)=▽F(t,u(t)) with convex and concave nonlinearities is studied, where F(t, u) = F1(t,u)+F2(t,... The existence of high energy periodic solutions for the second-order Hamiltonian system -ü(t)+A(t)u(t)=▽F(t,u(t)) with convex and concave nonlinearities is studied, where F(t, u) = F1(t,u)+F2(t,u). Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory. 展开更多
关键词 variant fountain theorem second-order hamiltonian system infinitely periodic solutions even functional
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Existence and Multiplicity of Periodic solutions for the Non-autonomous Second-order Hamiltonian Systems
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作者 CHEN Yu-song CHANG He-jie 《Chinese Quarterly Journal of Mathematics》 2019年第4期382-396,共15页
In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity the... In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory. 展开更多
关键词 Periodic solution second-order hamiltonian system Saddle Point Theorem Sobolev’s inequality Wirtinger’s inequality
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A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis
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作者 Lu Yang Xuefeng Zhang 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2024年第3期115-126,共12页
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
关键词 second-order auto-regressive filter multi-scale recursive filter sea ice concentration three-dimensional variational data assimilation
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The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition
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作者 Xilai Dai 《Journal of Applied Mathematics and Physics》 2024年第5期1597-1605,共9页
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
关键词 Convergence Rate second-order Regular Variation Condition Fréchet Distribution Extreme Value Index
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Infinitely Many Periodic Solutions for a Class of Second-order Hamiltonian Systems 被引量:4
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作者 Ming-hai YANG Yue-fen CHEN Yan-fang XUE 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第1期231-238,共8页
In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems{ü(t)+A(t)u(t)+▽F(t,u(t))=0,u(0)-u(T)=u^·(0)-u^·(T)=0,where F(t,u) i... In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems{ü(t)+A(t)u(t)+▽F(t,u(t))=0,u(0)-u(T)=u^·(0)-u^·(T)=0,where F(t,u) is even in u,and ▽(t,u) is of sublinear growth at infinity and satisfies the Ahmad-Lazer-Paul condition. 展开更多
关键词 second-order hamiltonian systems periodic solutions Fountain theorem
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Homoclinic orbits for the second-order Hamiltonian systems with obstacle item 被引量:1
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作者 YIN CuiCui & ZHANG FuBao Department of Mathematics, Southeast University, Nanjing 211189, China 《Science China Mathematics》 SCIE 2010年第11期3005-3014,共10页
This paper is concerned with the existence of homoclinic orbits for the second-order Hamiltonian system with obstacle item, ü(t)-A u(t) =▽F (t, u), where F (t, u) is T-periodic in t with ▽F (t, u) = L(t)u + ▽R... This paper is concerned with the existence of homoclinic orbits for the second-order Hamiltonian system with obstacle item, ü(t)-A u(t) =▽F (t, u), where F (t, u) is T-periodic in t with ▽F (t, u) = L(t)u + ▽R(t,u). By using a generalized linking theorem for strongly indefinite functionals, we prove the existence of homoclinic orbits for both the super-quadratic case and the asymptotically linear one. 展开更多
关键词 hamiltonian system HOMOCLINIC ORBITS super-quadratic ASYMPTOTICALLY linear spectrum
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Closed-form steady-state solutions for forced vibration of second-order axially moving systems
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作者 Jingming FAN Bo CHEN Yinghui LI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第10期1701-1720,共20页
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
关键词 Green's function axially moving system closed-form solution second-order model forced vibration Laplace transform
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Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity
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作者 A.V.ROSCA N.C.ROSCA I.POP 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第4期641-652,共12页
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
关键词 three-dimensional(3D)mixed convection flow stagnation point flow first-order slip velocity second-order slip velocity numerical solution stability analysis
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Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs
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作者 Magne Stensland 《Journal of Applied Mathematics and Physics》 2023年第4期1077-1097,共21页
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
关键词 Non-Elementary Functions second-order Nonlinear Autonomous ODE Limit Cycle
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On traceable iterated line graph and hamiltonian path index
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作者 NIU Zhao-hong XIONG Li-ming YANG Wei-hua 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期239-252,共14页
Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characteri... Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph. 展开更多
关键词 iterated line graph TRACEABLE hamiltonian index hamiltonian path index
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Universal Machine Learning Kohn–Sham Hamiltonian for Materials
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作者 钟阳 于宏宇 +3 位作者 杨吉辉 郭星宇 向红军 龚新高 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第7期95-110,共16页
While density functional theory(DFT)serves as a prevalent computational approach in electronic structure calculations,its computational demands and scalability limitations persist.Recently,leveraging neural networks t... While density functional theory(DFT)serves as a prevalent computational approach in electronic structure calculations,its computational demands and scalability limitations persist.Recently,leveraging neural networks to parameterize the Kohn-Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations.Despite advancements,challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist.Addressing these hurdles,this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project.We demonstrate its generality in predicting electronic structures across the whole periodic table,including complex multi-elemental systems,solid-state electrolytes,Moir´e twisted bilayer heterostructure,and metal-organic frameworks.Moreover,we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets,identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands.By offering a reliable efficient framework for computing electronic properties,this universal Hamiltonian model lays the groundwork for advancements in diverse fields,such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible. 展开更多
关键词 hamiltonian utilize TWISTED
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Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions
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作者 孙志强 侯国林 +1 位作者 乔艳芬 刘金存 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第1期581-590,共10页
A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o... A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method. 展开更多
关键词 hamiltonian system symplectic elasticity QUASICRYSTALS analytic solution state function
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Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2023年第2期236-266,共31页
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
关键词 second-order Predictive Modeling Data Assimilation Data Adjustment Uncertainty Quantification Reduced Predicted Uncertainties
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Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2023年第2期267-294,共28页
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
关键词 second-order Predictive Modeling Data Assimilation Data Adjustment Uncertainty Quantification Reduced Predicted Uncertainties
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Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark
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作者 Ruixian Fang Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2023年第2期295-322,共28页
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
关键词 second-order Predictive Modeling OECD/NEA Reactor Physics Benchmark Data Assimilation Best-Estimate Results Uncertainty Quantification Reduced Predicted Uncertainties
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An Eight Component Integrable Hamiltonian Hierarchy from a Reduced Seventh-Order Matrix Spectral Problem
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作者 Savitha Muthanna Wen-Xiu Ma 《Journal of Applied Mathematics and Physics》 2024年第6期2102-2111,共10页
We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and the... We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed. 展开更多
关键词 Matrix Spectral Problem Zero Curvature Equation Lax Pair Integrable Hierarchy NLS Equations mKdV Equations hamiltonian Structure Lie Bracke
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Second-Order Raman Scattering from n- and p-Type 4H-SiC
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作者 高欣 孙国胜 +4 位作者 李晋闽 王雷 赵万顺 张永新 曾一平 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2004年第12期1555-1560,共6页
The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigne... The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density. 展开更多
关键词 H-SiC second-order Raman cutoff frequency
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Anti-periodic solutions to a class of second-order evolution equations
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作者 张莉娜 薛星美 《Journal of Southeast University(English Edition)》 EI CAS 2003年第4期432-436,共5页
In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operato... In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations. 展开更多
关键词 maximal monotone operator anti-periodic solution poincare inequality second-order evolution equations
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分数阶Hamiltonian系统的可解性
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作者 薛婷婷 《云南大学学报(自然科学版)》 CAS CSCD 北大核心 2023年第6期1179-1188,共10页
研究一类分数阶Hamiltonian系统解的存在性.考虑含有参数的势函数W(t,u)满足新的超线性和次线性组合条件W(t,u)=W_(1)(t,u)+μW_(2)(t,u),μ>0.当|u|→∞时,W_(1)(t,u)满足更一般的超线性增长条件,代替Ambrosetti-Rabinowitz条件;W_(... 研究一类分数阶Hamiltonian系统解的存在性.考虑含有参数的势函数W(t,u)满足新的超线性和次线性组合条件W(t,u)=W_(1)(t,u)+μW_(2)(t,u),μ>0.当|u|→∞时,W_(1)(t,u)满足更一般的超线性增长条件,代替Ambrosetti-Rabinowitz条件;W_(2)(t,u)满足更一般的次线性增长条件.这部分需要建立新的紧嵌入定理,用于验证序列的紧性.利用临界点理论,得到上述系统2个解存在结果. 展开更多
关键词 分数阶微分方程 hamiltonian系统 变分方法 解的存在性.
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Anti-interference beam pattern design based on second-order cone programming optimization 被引量:1
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作者 戴文舒 鲍凯凯 +1 位作者 王萍 王黎明 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2016年第3期255-260,共6页
When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be op... When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization (SOCP) algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming. 展开更多
关键词 anti-interference beam pattern second-order cone programming optimization (SOCP) weak signal detection
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