Noise-induced phase transition in the Vicsek model through eigen microstate methodology

This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.

EIGEN-6C4重力场模型在大高差抽水蓄能电站高程测量中的应用

随着中国清洁能源的大规模开发,抽水蓄能电站得到了快速发展,与传统水电站相比,抽水蓄能电站的水头较高,多为200~800 m。然而,在西部山区等条件恶劣的地区,高程测量手段实施难度极大,且效率低下。根据西北地区多个抽水蓄能电站及常规水电站高程测量成果,利用EGM2008、EIGEN-6C4地球重力场模型对各个电站高程控制测量成果进行拟合计算,并与常规测量成果进行比较。数据表明:EIGEN-6C4地球重力场模型拟合成果具有更好的符合性,尤其是在后期施工控制网高程成果的拟合方面,EIGEN-6C4模型拟合成果更优。因此,该方法可以在保证勘测设计阶段高程控制测量成果精度的同时,降低风险和成本,节约工期,在大高差地形区域具有较高的适用性。

青藏高原东北缘ALOS AW3D30高程模型和EIGEN-6C4自由空气重力异常模型精度分析

利用EGM96全球重力场模型对ALOS AW3D30全球数字高程模型的高程系统进行转换,结合实测GNSS数据,分析ALOS AW3D30模型在青藏高原东北缘地区的精度.利用实测重力数据计算青藏高原东北缘地区的自由空气异常,并与EGIEN-6C4自由空气异常模型进行对比,分析其精度.结果表明:青藏高原东北缘地区ALOS AW3D30模型与264个GNSS测点的差异标准差为3.4 m,该地区ALOS AW3D30精度优于4 m;青藏高原东北缘地区自由空气重力异常整体呈负值,局部为正值,变化范围为-177×10^(-5)~166×10^(-5)m·s^(-2),实测重力异常与模型结果空间分布基本一致,存在局部差异;EIGEN-6C4自由空气重力异常变化范围为-163×10^(-5)~142×10^(-5)m·s^(-2),实测结果与模型结果差异为-119×10^(5)~63×10^(-5)m·s^(-2),平均值为-20×10^(-5)m·s^(-2),差异标准差为29×10^(-5)m·s^(-2),实测结果与模型结果差异较大,青藏高原东北缘地区真实地球重力场应该通过实测获得.最后,本文基于青藏高原东北缘地区的实测重力异常与EGIEN-6C4重力异常模型,利用消去-恢复法,将实测重力异常与模型结果进行融合,提高了青藏高原东北缘地区,尤其是祁连山东缘、海原断裂及周边地区的重力异常精度,可以为区域重力场研究提供参考.

深空组阵Eigen算法及其低信噪比合成性能分析

根据深空组阵信号模型,分析了Eigen最优合成采用的两种准则即最大输出功率和最大信噪比准则。为了快速计算最优权值,给出了两种迭代算法即PM和PMFM算法,同时为了改善微弱信号合成效果,在PMFM算法中引入记忆因子,提出一种可以自适应跟踪信号相位变化的自适应Eigen算法。仿真分析了基于最大输出功率准则的Eigen合成算法和自适应Eigen算法对低信噪比组阵接收信号的合成性能,仿真结果表明自适应Eigen算法不但具有良好的合成效果和自适应特性而且运算量小,具有重要的工程应用价值。

基于EIGEN-CG03C地球重力场模型的GPS高程转换算法研究

针对地形起伏较大地区纯粹采用数值逼近方法进行GPS高程转换精度不高的事实,提出了一种在"移去-拟合-恢复"思路的基础上,综合利用EIGEN-CG03C地球重力场模型和数值逼近算法进行GPS高程转换的方法。通过某隧道实例验证了该方法的有效性和实用性,证实该方法在地形起伏较大的重山区能够达到较高的精度。

EIGEN-GL04C重力场模型的精度分析

本文对GFZ发布的GRACE EIGEN-GL04C重力场模型从球谐系数分析、误差阶方差分析两方面进行了精度评价。研究表明,相较于以往的重力场模型,EIGEN-GL04C重力场模型精度对120阶以下(未包含J2项)的地球中长波部分具有明显的改善。GRACE重力卫星测量已经成为获取地球重力场信息的重要手段。

COMPLETE EIGEN-SOLUTIONS FOR ANTI-PLANE NOTCHES WITH MULTI-MATERIALS BY SUPER-INVERSE ITERATION

Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface conditions. Taking the advantage of the knowledge of the variation forms of the eigen-functions, a series of numerical techniques are proposed to simplify the computation and speed up the convergence rare of the inverse iteration. A number of numerical examples are given to demonstrate the excellent accuracy, efficiency and reliability of the proposed approach.

EIGEN-6C2重力场模型与中国陆地和岛礁GNSS水准符合性的分析

将我国沿海13个省市的陆地和岛礁上的2 917个GNSS水准点的实测高程异常,分别与EGM2008,EIGEN-6C,EIGEN-6C2,GO_CONS_GCF_2_DIR_R4和GOCO03S这5个重力场模型的不同截断阶次模型高程异常,按照地形类别进行外部精度检验,最后得出了到目前为止EIGEN-6C2重力场模型与我国实测高程异常符合性最好的结论。

EGM2008和EIGEN-6C2模型的精度比较

简要介绍了EGM2008和EIGEN-6C2两种超高阶重力场模型,给出了高程异常模型计算的详细过程,并基于两种重力场模型建立内蒙古地区似大地水准面模型,用空点法和外符合法进行精度分析比较。结果表明,可以用空点法取代外符合法进行精度评定。在内蒙古地区,EIGEN-6C2模型比EGM2008模型的精度提高了3 cm。

基于EIGEN6C2模型的Kaula规则精化

高精度重力场模型精化Kaula规则其要点是将Kaula规则乘上一个与位系数阶数项相关的二阶有理函数,并基于EIGEN6C2重力场模型解算有理函数模型的系数。精化后的Kaula规则与EIGEN6C2模型和EGM2008模型的逼近误差都只是原来Kaula规则的0.26%。因此,精化后的Kaula规则更能正确表示各阶引力位的实际能量,对于重力场模型的解算提供更加合理的约束。

Eigen theory of elastic mechanics for anisotropic solids

Eigen characters of the fundamental equations, equilibrium equation of stress and harmony equation of deformation, of the traditional elastic mechanics under geometrical space were testified by means of the concept of standard space, and the modal equilibrium equation and the modal harmony equation under mechanical space were obtained. Based on them and the modal Hooke’s law, a new system of the fundamental equation of elastic mechanics is given. The advantages of the theory given here are as following: the form of the fundamental equation is in common for both isotropy and anisotropy, both force method and displacement method, both force boundary and displacement boundary; the number of stress functions is equal to that of the anisotropic subspaces, which avoids the man made mistakes; the solution of stress field or strain field is given in form of the modal superimposition, which makes calculation simplified greatly; no matter how complicated the anisotropy of solids may be, the complete solutions can be obtained.

Eigen elastic mechanics and its variation principle

The fundamental equations and the corresponding boundary condition of elastic mechanics under mechanical representation are given by using the conception of eigen space and elastic variation principle. It is proved theoretically that the solution of anisotropic elastic mechanics consists of modal ones, which are obtained respectively from the modal equation of the different subspaces. A simple application is also given.

EIGEN-6c2重力场模型在中国大陆的精度分析

给出重力位模型计算高程异常的严密公式,用中国各地区实测的GPS/水准数据检核了EIGEN-6c2和EGM08模型的精度。结果表明,EIGEN-6c2模型高程异常的精度比EGM08模型提高了2~3 cm,尤其在青藏高原有显著提高,提高18 cm;同时确定出1985国家高程基准与全球高程基准（W0）系统差为26 cm。

EIGEN THEORY OF VISCOELASTIC MECHANICS FOR ANISOTROPIC SOLIDS

Anisotropic viscoelastic mechanics is studied under anisotropicsubspace. It is proved that there also exist the eigen properties forviscoelastic medium. The modal Maxwell's equation, modal dynamicalequation (or modal equilibrium equation) and modal compatibilityequation are ob- tained. Based on them, a new theory of anisotropicviscoelastic mechanics is presented. The advan- tages of the theoryare as follows: 1) the equations are all scalar, and independent ofeach other. The number of equations is equal to that of anisotrpicsubspaces, 2) no matter how complicated the anisotropy of solids maybe, the form of the definite equation and the boundary condition arein com- mon and explicit, 3) there is no distinction between theforce method and the displacement method for statics, that is, theequilibrium equation and the compatibility equation areindistinguishable under the mechanical space, 4) each modal equationhas a definite physical meaning, for example, the modal equations oforder one and order two express the value change and sheardeformation respec- tivley for isotropic solids, 5) there also existthe potential functions which are similar to the stress functions ofelastic mechanics for viscoelastic mechanics, but they are notman-made, 6) the final so- lution of stress or strain is given in theform of modal superimposition, which is suitable to the proxi- matecalculation in engineering.

Eigen solutions of internal waves over subcritical topography

Diapycnal mixing plays an important role in the ocean circulation.Internal waves are a kind of bridge relating the diapycnal mixing to external sources of mechanical energy.Difficulty in obtaining eigen solutions of internal waves over curved topography is a limitation for further theoretical study on the generation problem and scattering process.In this study,a kind of transform method is put forward to derive the eigen solutions of internal waves over subcritical topography in twodimensional and linear framework.The transform converts the curved topography in physical space to flat bottom in transform space while the governing equation of internal waves is still hyperbolic if proper transform function is selected.Thus,one can obtain eigen solutions of internal waves in the transform space.Several examples of transform functions,which convert the linear slope,the convex slope,and the concave slope to flat bottom,and the corresponding eigen solutions are illustrated.A method,using a polynomial to approximate the transform function and least squares method to estimate the undetermined coefficients in the polynomial,is introduced to calculate the approximate expression of the transform function for the given subcritical topography.

EIGEN THEORY OF VISCOELASTIC DYNAMICS BASED ON THE KELVIN-VOIGT MODEL

Using the eigen theory of solid mechanics, the eigen properties of anisotropic viscoelastic bodies with Kelvin-Voigt model were studied, and the generalized Stokes equation of anisotropic viscoelastic dynamics was obtained, which gives the three-dimensional pattern of viscoelastical waves. The laws of viscoelastical waves of different anisotropical bodies were discussed.Several new conclusiones are given.

DOA ESTIMATION USING A SPARSE LINEAR MODEL BASED ON EIGENVECTORS

To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built.Then based on the FOCal Underdetermined System Solver(FOCUSS) algorithm,a sparse solution finding algorithm to solve the model is developed.Compared with other state-of-the-art methods using a sparse representation,our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources.However,our method has lower computational complexity and performs better in low Signal-to-Noise Ratio(SNR).Lastly,the performance of the proposed method is illustrated by computer simulations.

Solitons in nonlinear systems and eigen-states in quantum wells

We study the relations between solitons of nonlinear Schro¨dinger equation and eigen-states of linear Schro¨dinger equation with some quantum wells. Many different non-degenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for the coupled system with attractive interactions correspond to the identical eigen-states with the ones of the coupled systems with repulsive interactions. Although their energy eigenvalues seem to be different, they can be reduced to identical ones in the same quantum wells. The non-degenerated solitons for multi-component systems can be used to construct much abundant degenerated solitons in more components coupled cases.Meanwhile, we demonstrate that soliton solutions in nonlinear systems can also be used to solve the eigen-problems of quantum wells. As an example, we present the eigenvalue and eigen-state in a complicated quantum well for which the Hamiltonian belongs to the non-Hermitian Hamiltonian having parity–time symmetry. We further present the ground state and the first exited state in an asymmetric quantum double-well from asymmetric solitons. Based on these results, we expect that many nonlinear physical systems can be used to observe the quantum states evolution of quantum wells, such as a water wave tank, nonlinear fiber, Bose–Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another way to understand the stability of solitons in nonlinear Schro¨dinger equation described systems, in contrast to the balance between dispersion and nonlinearity.

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.

基于Eigen和OpenCV的图像算法加速

OpenCV作为一款免费、开源的计算机视觉库已广泛应用于图像处理的各种项目开发中。在算法实现中,高性能的线性代数运算库能提升算法的执行效率和算法实现灵活性。介绍了Eigen线性代数运算库,并在矩阵运算效率上与OpenCV进行了比较。以基于SVD分解的图像压缩算法为例,将Eigen和OpenCV进行联合编程并给出了主要代码。