Elastic Kirchhoff migration of vectorial wave-fields

Based on Kuo and Dai＇s vectorial wave-field extrapolation equations, we derive new Kirchhoff migration equations by introducing unit vectors which represent the ray directions at the imaging points of the reflected P- and PS converted-waves. Furthermore, using the slope of the events on shot records and a ray racing procedure, mirror-image reflection points are found and the reflection data are smeared along the Fresnel zone. The migration method proposed in this paper solves two troublesome imaging problems caused by limited receiving aperture and migration artifacts resulting from wave propagation at the velocities of non original wave type. The migration method is applied successfully with model data, demonstrating that the new method is effective and correct.

Vectorial Hermite-Laguerre-Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh-Sommerfeld integrals, the free-space propagation expressions for vectorial Hermit-Lagucrre-Gaussian （HLG） beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.

VECTORIAL EKELAND VARIATIONAL PRINCIPLE AND CYCLICALLY ANTIMONOTONE EQUILIBRIUM PROBLEMS

In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle(see Qiu, 2014), we prove a new version of Ekeland variational principle(briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results(no matter scalar-valued case,or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.

Spatial pattern analysis of forest trees based on the vectorial mark

Analysis of spatial patterns to describe the spatial correlation between a tree location and marks(i.e.,structural variables),can reveal stand history,population dynamics,competition and symbiosis.However,most studies of spatial patterns have concentrated on tree location and tree sizes rather than on crown asymmetry especially with direct analysis among marks characterizing facilitation and competition among of trees,and thus cannot reveal the cause of the distributions of tree locations and quantitative marks.To explore the spatial correlation among quantitative and vectorial marks and their implication on population dynamics,we extracted vertical and horizontal marks(tree height and crown projection area)characterizing tree size,and a vectorial mark(crown displacement vector characterizing the crown asymmetry)using an airborne laser scanning point cloud obtained from two forest stands in Oxfordshire,UK.Quantitatively and vectorially marked spatial patterns were developed,with corresponding null models established for a significance test.We analyzed eight types of univariate and bivariate spatial patterns,after first proposing four types.The accuracy of the pattern analysis based on an algorithm-segmented point cloud was compared with that of a truly segmented point cloud.The algorithm-segmented point cloud managed to detect 70–86%of patterns correctly.The eight types of spatial patterns analyzed the spatial distribution of trees,the spatial correlation between tree size and facilitated or competitive interactions of sycamore and other species.These four types of univariate patterns jointly showed that,at smaller scales,the trees tend to be clustered,and taller,with larger crowns due to the detected facilitations among trees in the study area.The four types of bivariate patterns found that at smaller scales there are taller trees and more facilitation among sycamore and other species,while crown size is mostly homogeneous across scales.These results indicate that interspecific facilitation and competition mainly affect tree height in the study area.This work further confirms the connection of tree size with individual facilitation and competition,revealing the potential spatial structure that previously was hard to detect.

A Semi-Vectorial Hybrid Morphological Segmentation of Multicomponent Images Based on Multithreshold Analysis of Multidimensional Compact Histogram

In this work, we propose an original approach of semi-vectorial hybrid morphological segmentation for multicomponent images or multidimensional data by analyzing compact multidimensional histograms based on different orders. Its principle consists first of segment marginally each component of the multicomponent image into different numbers of classes fixed at K. The segmentation of each component of the image uses a scalar segmentation strategy by histogram analysis;we mainly count the methods by searching for peaks or modes of the histogram and those based on a multi-thresholding of the histogram. It is the latter that we have used in this paper, it relies particularly on the multi-thresholding method of OTSU. Then, in the case where i) each component of the image admits exactly K classes, K vector thresholds are constructed by an optimal pairing of which each component of the vector thresholds are those resulting from the marginal segmentations. In addition, the multidimensional compact histogram of the multicomponent image is computed and the attribute tuples or ‘colors’ of the histogram are ordered relative to the threshold vectors to produce (K + 1) intervals in the partial order giving rise to a segmentation of the multidimensional histogram into K classes. The remaining colors of the histogram are assigned to the closest class relative to their center of gravity. ii) In the contrary case, a vectorial spatial matching between the classes of the scalar components of the image is produced to obtain an over-segmentation, then an interclass fusion is performed to obtain a maximum of K classes. Indeed, the relevance of our segmentation method has been highlighted in relation to other methods, such as K-means, using unsupervised and supervised quantitative segmentation evaluation criteria. So the robustness of our method relatively to noise has been tested.

Generation of diffraction-free vectorial elliptic hollow beams with space-varying inhomogeneous polarizations

Diffraction-free vectorial elliptic hollow beams(vEHBs)are generated by an optical system composed of a short elliptic hollow fiber(EHF)and an axicon.Each beam has a closed elliptic annular intensity profile and space-varying polarization states in its diffraction-free distance of more than 1 m.The generated beams have a counter-clockwise or clockwise periodically-rotated inhomogeneous polarization.And the spin angular momentum(SAM)of the vEHBs is 1ħor-1ħwhich is consistent with the type of dual-mode in the EHF and the periodic polarization rotations of the vEHBs.The vEHBs have potential applications in optically trapping and micromanipulating the micro-or nano-particles,quantum information transmission,and Bose-Einstein condensates,etc.

Far-field divergence of a vectorial plane wave diffracted by a circular aperture from the vectorial structure

Based on the vectorial structure of an electromagnetic wave, the analytical and concise expressions for the TE and TM terms of a veetorial plane wave diffracted by a circular aperture are derived in the far-field. The expressions of the energy flux distributions of the TE term, the TM term and the diffracted plane wave are also presented. The ratios of the power of the TE and TM terms to that of the diffracted plane wave are examined in the far-field. In addition, the far-field divergence angles of the TE term, the TM term and the diffracted plane wave, which are related to the energy flux distribution, are investigated. The different energy flux distributions of the TE and TM terms result in the discrepancy of their divergence angles. The influences of the linearly polarized angle and the radius of the circular aperture on the far-field divergence angles of the TE term, the TM term and the diffracted plane wave are discussed in detail. This research may promote the recognition of the optical propagation through a circular aperture.

Vectorial Bed load Equations and River Width Dynamic Adjustment Modeling

Based on the analysis of forces acting on non-cohesive sediment particle under non-equilibrium con- dition,a vectorial equation of coarse particle movement on arbitrarily riverbed and the mathematical model used to simulate river width adjust are developed,some flume experiments for the time evolution of straight river channel are done.

Nonparaxial propagation of a vectorial apertured off-axis Lorentz beam

Based on the vectorial Ftayleigh-Sommerfeld integral formula and the complex Gaussian expansion of the hardedge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam passing through a rectangular aperture is derived. The unapertured case, the far field expression and the scalar paraxial result are also presented as special cases of the general formulae, respectively. Some numerical examples are also given to show the propagation characteristics of a nonparaxial vectorial off-axis Lorentz beam through a rectangular aperture. It is indicated that the f parameter, the off-axis displacement and the truncation parameter all play an important role in determining nonparaxial propagation behaviour.

A NEW DERIVATION OF THE VECTORIAL EQUATION OF MOTION FOR A TEST PARTICLE IN THE SCHWARZCHILD FIELD

A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field is given which greatly simplifies the procedure given by C. A. Murray[1]

Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.

A Simulation Model for Sexual and Vectorial Transmission of Zika Virus(ZIKV)

Nowadays the Zika virus (ZIKV) has been one of the most studied vector-borne diseases due to the considerable outbreaks that have generated around the world as well as due to the new transmission mechanisms and health complications originated. According to statistics of the INS-Colombia for July 2016, 68% of the population infected by ZIKV (confirmed cases) are pregnant women. Furthermore, the Quindío department belongs to the states with more than 50% of the total infected persons being pregnant women. Taking into account those characteristics, a theoretical model is proposed and analyzed to describe the population dynamics considering the sexual and vectorial transmission of ZIKV, with special emphasis in the consequences of the non-vectorial transmission in the population. The obtained results with simulations through the beta parameter indicate that the probability of sexual transmission between susceptible women and infected men points out the importance of campaigns to inculcate prevention measures for the safe sexual relationships between ZIKV infected population.

Approximation Properties of Vectorial Exponential Functions

This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,and Applications”.With respect to classical Finite Elements Methods,Trefftz methods are unconventional methods because of the way the basis functions are generated.Trefftz discontinuous Galerkin(TDG)methods have recently shown potential for numerical approximation of transport equations[6,26]with vectorial exponential modes.This paper focuses on a proof of the approximation properties of these exponential solutions.We show that vectorial exponential functions can achieve high order convergence.The fundamental part of the proof consists in proving that a certain rectangular matrix has maximal rank.

Two-Dimensional Manifolds with Computation V-Function of ODE Systems

The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.

超表面的矢量光场调控

矢量光场由于其独特的光场分布特性,在许多领域都得到了广泛且深入的研究与应用。传统光场调控手段受限于材料的光学特性及物理尺寸,难以实现灵活高效的动态操控功能。超表面凭借其亚波长结构设计所带来的额外自由度,突破了上述局限,使得对矢量光场的振幅、相位、偏振态乃至传播方向等的独立调控成为可能。本文结合国内外矢量光场领域的基础理论及最新进展,系统地阐述了矢量光场的基本原理及其数学模型,重点介绍了目前超表面生成矢量光场的方法,以及这种矢量光场在聚焦、轨道角动量检测、高精度定位等方面应用的具体案例与创新成果。

矢量全息技术的研究进展与应用

全息技术能够记录和重建物光波的全部信息,自问世发展至今已经取得了显著的进步。近年来,矢量全息的出现为这一领域带来新的发展。矢量全息技术不仅继承了传统标量全息技术记录振幅和相位的能力,还额外引入了对偏振维度的调控,因此能够显著提高记录信息的密度,并在多个领域得以广泛应用。本文旨在从偏振调控的角度深入探讨矢量全息技术。首先介绍了标量全息技术和矢量全息技术的概念,并比较了二者的优缺点,重点阐述了矢量全息技术的优势;然后详细地介绍了矢量全息技术的两种偏振态调控方式,包括对入射光和出射光偏振态的调控;同时阐述了矢量全息技术在三维显示和加密领域的应用;最后总结了矢量全息技术目前面临的挑战,并展望了其未来的发展趋势。

基于四元数矩阵分解算法的多分量地震数据矢量重建研究

与单分量纯纵波勘探相似,多波多分量地震勘探在数据采集时也会遭遇地震道缺失和不规则采样问题,也需要进行数据规则化重建.然而,对多分量地震数据重建而言,目前普遍采用单分量重建方法逐个分量进行重建,这种标量化做法忽略了各分量之间的非线性关系,破坏了地震波场的矢量结构特征.本文将四元数理论与矩阵分解降秩算法相结合,提出一种基于四元数矩阵分解降秩算法的多分量地震数据矢量规则化重建方法,并将其应用于三分量三维不规则缺失地震道的矢量联合重建.与现有单分量重建方法相比,本文方法能够实现三分量数据的联合重建,且在重建时能有效保持各分量间的非线性正交结构特征,保护波场的矢量特性,此外,该方法是一种非SVD分解类算法,计算成本低.最后,模型数据和实际资料验证了本文方法的有效性和先进性.

基于事件触发机制的船舶补给同步抗干扰控制

[目的]针对多变海洋环境下补给船与被补给船补给作业同步航行控制问题,考虑风浪流引起的海洋环境干扰、船间效应导致的干扰、两船软连接相互作用,提出事件触发下基于干扰估计和补偿的同步抗干扰控制方法。[方法]将补给船受到的干扰建模为一阶马尔科夫过程,描述风浪流引起的海洋环境干扰和未建模动态,将船间效应导致的干扰和两船软连接相互作用等均集中为未建模动态,构造干扰观测器在线估计时变未知有界干扰,在控制设计中利用干扰在线估计值对干扰进行补偿,抵消干扰和不确定性对航行补给控制的影响,设计辅助动态系统来减少推进器控制饱和的影响,引入事件触发机制降低推进器执行频率以避免其过度磨损。[结果]仿真结果表明,本文提出的事件触发机制存在大于0的最小采样间隔且不会在有限时间内发生无限次触发。该控制器可实现补给船与被补给船同步航行,保证控制系统所有信号全局一致最终有界。[结论]仿真结果验证了事件触发干扰估计和补偿控制的有效性。

湖北省嗜人按蚊分布、生态与传疟作用研究

目的 :查明湖北省嗜人按蚊分布范围、生态习性与传疟作用。方法 :全省定点和扩大范围调查嗜人按蚊分布 ,以卵块和成蚊形态鉴定蚊种 ,观察嗜人按蚊成蚊的生态及传疟能量。结果 :全省调查 4 2个县 (市区场 ) 2 87个乡镇 1151个村 ,捕获按蚊 574 4 8只 ,鉴定 4 6 130只 ,其中嗜人按蚊 396 7只 ,中华按蚊 4 2 0 14只 ,八代按蚊 149只 ,在 19个县 (市区场 ) 10 4个乡镇 6 96个村发现有嗜人按蚊分布。范围人口约 1456万 ,面积 4 .6万km2 。嗜人按蚊夜间活动高峰在 0～ 2时 ,白天主要栖息在人房 ,其次为牛房及猪栏 ,构成比依次为 84 .4 0 %、10 .30 %、9.2 5% ,少数栖息于室外。该蚊吸人血指数为 0 .86 8。传疟能量 5～ 11月平均为 0 .0 6 6 7,比同域中华按蚊 (0 .0 0 15)高 4 4 .4 7倍。结论 :嗜人按蚊分布在大洪山麓与桐柏山之间的低山、丘陵、岗地及江汉平原结合部 。

河南省信阳市嗜人按蚊传疟作用研究

目的 调查嗜人按蚊的传疟作用 ,为嗜人按蚊分布区媒介监测和制订合理的防治措施提供依据。 方法 在河南省信阳市二十里河村选择 5个自然村作为观察点 ,采用寄生虫学和昆虫学方法进行调查 ,估算嗜人按蚊的媒介能量和临界叮人率。 结果 1999年 7～ 8月 ,居民带虫发病率为 7.4% ,原虫率为 2 .0 % ,IFAT抗体阳性率为 8.4%。嗜人按蚊密度组成在人房内占优势 ,平均叮人率为 4.9388/(人 /夜 ) ,人血指数为 0 .785 7,媒介能量为 5 .5 2 96 ,是中华按蚊的 6 .2倍。嗜人按蚊临界叮人率为 0 .2 40 7(人 /夜 ) ,而实际叮人率是它的 2 0倍。结论 嗜人按蚊是当地疟疾传播的主要媒介。提示临界叮人率在媒介监测中具有应用的意义。目的 调查嗜人按蚊的传疟作用 ,为嗜人按蚊分布区媒介监测和制订合理的防治措施提供依据。 方法 在河南省信阳市二十里河村选择 5个自然村作为观察点 ,采用寄生虫学和昆虫学方法进行调查 ,估算嗜人按蚊的媒介能量和临界叮人率。 结果 1999年 7～ 8月 ,居民带虫发病率为 7.4% ,原虫率为 2 .0 % ,IFAT抗体阳性率为 8.4%。嗜人按蚊密度组成在人房内占优势 ,平均叮人率为 4.9388/ (人 /夜 ) ,人血指数为 0 .785 7,媒介能量为 5 .5 2 96 ,是中华按蚊的 6 .2倍。