MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

Acoustic radiation force on a multilayered sphere in a Gaussian standing field

We develop a model for calculating the radiation force on spherically symmetric multilayered particles based on the acoustic scattering approach.An expression is derived for the radiation force on a multilayered sphere centered on the axis of a Gaussian standing wave propagating in an ideal fluid,The effects of the sound absorption of the materials and sound wave on acoustic radiation force of a multilayered sphere immersed in water are analyzed,with particular emphasis on the shell thickness of every layer,and the width of the Gaussian beam.The results reveal that the existence of particle trapping behavior depends on the choice of the non-dimensional frequency ka,as well as the shell thickness of each layer.This study provides a theoretical basis for the development of acoustical tweezers in a Gaussian standing wave,which may benefit the improvement and development of acoustic control technology,such as trapping,sorting,and assembling a cell,and drug delivery applications.

Acoustic radiation force on a rigid cylinder near rigid corner boundaries exerted by a Gaussian beam field

Acoustic manipulation is one of the well-known technologies of particle control and a top research in acoustic field.Calculation of acoustic radiation force on a particle nearby boundaries is one of the critical tasks,as it approximates realistic applications.Nevertheless,it is quite difficult to solve the problem by theoretical method when the boundary conditions are intricate.In this study,we present a finite element method numerical model for the acoustic radiation force exerting on a rigid cylindrical particle immersed in fluid near a rigid corner.The effects of the boundaries on acoustic radiation force of a rigid cylinder are analyzed with particular emphasis on the non-dimensional frequency and the distance from the center of cylinder to each boundary.The results reveal that these parameters play important roles in acoustic manipulation for particle-nearby complicated rigid boundaries.This study verifies the feasibility of numerical analysis on the issue of acoustic radiation force calculation close to complex boundaries,which may provide a new idea on analyzing the acoustic particle manipulation in confined space.

Polarization singularities in near-field of Gaussian vortex beam diffracted by a circular aperture

Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend on off-axis displacement parameters along the x and y directions, waist width, wavelength, and topological charge of the diffracted Gaussian vortex beam, as well as on propagation distance. The results are illustrated by numerical calculations.

ALMOST SURELY TIME-SPACE INTERMITTENCY FOR THE PARABOLIC ANDERSON MODEL WITH A LOG-CORRELATED GAUSSIAN FIELD

In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.

EXTREMA OF A GAUSSIAN RANDOM FIELD:BERMAN'S SOJOURN TIME METHOD

In this paper we devote ourselves to extending Berman’s sojourn time method,which is thoroughly described in[1-3],to investigate the tail asymptotics of the extrema of a Gaussian random field over[0,T]^(d) with T∈(0,∞).

Non-Gaussian Lagrangian Stochastic Model for Wind Field Simulation in the Surface Layer

Wind field simulation in the surface layer is often used to manage natural resources in terms of air quality,gene flow(through pollen drift),and plant disease transmission(spore dispersion).Although Lagrangian stochastic(LS)models describe stochastic wind behaviors,such models assume that wind velocities follow Gaussian distributions.However,measured surface-layer wind velocities show a strong skewness and kurtosis.This paper presents an improved model,a non-Gaussian LS model,which incorporates controllable non-Gaussian random variables to simulate the targeted non-Gaussian velocity distribution with more accurate skewness and kurtosis.Wind velocity statistics generated by the non-Gaussian model are evaluated by using the field data from the Cooperative Atmospheric Surface Exchange Study,October 1999 experimental dataset and comparing the data with statistics from the original Gaussian model.Results show that the non-Gaussian model improves the wind trajectory simulation by stably producing precise skewness and kurtosis in simulated wind velocities without sacrificing other features of the traditional Gaussian LS model,such as the accuracy in the mean and variance of simulated velocities.This improvement also leads to better accuracy in friction velocity(i.e.,a coupling of three-dimensional velocities).The model can also accommodate various non-Gaussian wind fields and a wide range of skewness–kurtosis combinations.Moreover,improved skewness and kurtosis in the simulated velocity will result in a significantly different dispersion for wind/particle simulations.Thus,the non-Gaussian model is worth applying to wind field simulation in the surface layer.

Mode-field half-widths of Gaussian approximation for the fundamental mode of two kinds of optical waveguides

This paper analyzes the characteristic of matching efficiency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half-width of Caussian approximation for the fundamental mode should be defined according to the maximal matching efficiency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching efficiency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed.

Multivariate stationary non-Gaussian process simulation for wind pressure fields

Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be characterized as a stationary non-Gaussian field. This paper reviews several simulation algorithms related to the Spectral Representation Method （SRM） and the Static Transformation Method （STM）. Polynomial and Exponential transformation functions （PSTM and ESTM） are discussed. Deficiencies in current algorithms, with respect to accuracy, stability and efficiency, are analyzed, and the algorithms are improved for better practical application. In order to verify the improved algorithm, wind pressure fields on a large-span roof are simulated and compared with wind tunnel data. The simulation results fit well with the wind tunnel data, and the algorithm accuracy, stability and efficiency are shown to be better than those of current algorithms.

Log Gaussian Cox场手部指节的图像偏移特征学习与识别

针对手部指节图像结构特征模糊与建模困难的问题,以Log Gaussian Cox随机场为图像建模基础,给出了随机图像上偏移特征的抽取与学习方法,实现了手部图像中指节的识别。在缺乏Cox过程图像模型先验假设的条件下,结合随机图像的水平集分解,得到了图像偏移表示的逼近结果。在图像灰度分布非参数密度核估计基础上,利用非线性各向异性滤波对偏移特征进行增强,建立了偏移测度特征的Bayesian估计。提出了不同偏移参数下偏移特征的模型学习与融合算法,获得了指节图像特征的融合表示,并在手部指节图像数据库中比较了不同分层偏移模型下的识别结果,给出了批量识别ROC曲线统计规律。结果表明,识别方法具有较为稳定的正确分类能力,具有可行性。

基于Gaussian-MRF的DTI图像的正则化

为了对DTI图像进行正则化,采用了Gaussian-MRF模型。正则化方法根据Bayes准则对图像灰度值进行最大后验(MAP)估计,估计采用模拟退火方法进行,退火温度采用指数冷却进度表。通过对不同加权梯度下的同一层图像(一共7幅)同时进行正则化实验,结果表明该方法能够改善图像的噪声性能。把本正则化方法的结果与对张量场直接进行正则化的结果进行比较,表明采用本方法能够更加有效地减小噪声影响。通过把指数冷却进度表和对数冷却进度表的结果进行比较,表明采用指数温度能够在更短的时间内获得更好的正则化效果。

小级数Ince-Gaussian光束光强模式分析

研究了因斯-高斯(IG)光束级数m较小时,分立光瓣模式的光强分布。通过数值模拟,对IG奇偶模式以及奇偶模式线性叠加生成的PIG分立光瓣模式的光强进行了分析。分析结果表明:m较小时,PIG分立光瓣模式光瓣的空间位置介于奇偶模式之间,但是光瓣的光强分布变化较为明显。同一模式光瓣角向椭圆变量越接近于椭圆长轴,其光强比重越大。在统一总光强后,相同阶数与级数的不同模式光瓣总光强与角向椭圆变量差为一个三次函数的关系。对于偶模椭圆长轴上的光瓣,随着该模式通过PIG^(π/2)模式转化为奇模,该光瓣上的光强分布逐渐由弥散向着逆时针方向集中。

外场中一种钻石型等级晶格上Gaussian模型的临界性质

利用重正化群变换方法，在一种特殊钻石型等级晶格上研究了有外场存在时Gaussian模型的临界性质。结果表明：与一般的钻石型等级晶格上的结果相比，在临界点上，格点近邻相互作用参量和外磁场都具有相同的形式，但临界指数不相同，这表明这两种晶格的铁磁性质属于不同的普适类。

基于几何相位超表面的Ince-Gaussian矢量涡旋光场聚焦

为了实现电介质超表面的聚焦功能和对光场相位的调控,采用几何相位调制原理设计微元结构及空间分布,以SiO_(2)为基底、亚波长TiO_(2)椭圆柱的六边形晶胞为基本结构,设计了一种相位突变呈抛物线梯度分布的聚焦超表面,适用于480nm~580nm波段。基于此结构进行了理论分析和实验验证,发现该结构对线偏振光聚焦,其归一化后的半峰全宽约为428nm,而对矢量光聚焦约为258nm,获得了更出色的聚焦效果。研究了3阶和4阶Ince-Gaussian矢量光场通过该超表面后的聚焦特性,得到了聚焦场能保持入射矢量光场的基本空间结构,但中心结构信息会有损失的结果,即Ince-Gaussian矢量涡旋光场由于涡旋相位的存在,聚焦后会呈现破缺的空间结构。结果表明,超表面结构和入射光场矢量结构之间的匹配程度是影响聚焦特性的重要因素。该研究为理解复杂矢量光场的超表面聚焦机理提供了参考。

Ince-Gaussian矢量光场束腰位置对紧聚焦特性影响的研究

为了获得Ince-Gasussian矢量光场束腰位置对紧聚焦特性的影响规律,采用正交偏振的奇偶模式叠加理论和Richards-Wolf矢量衍射积分理论,对不同束腰位置的Ince-Gaussian矢量光场紧聚焦特性进行了研究。结果表明,在高数值孔径聚焦条件下,入射Ince-Gaussian矢量场的束腰距离透镜位置zi在一定瑞利长度zR范围内(zi<0.5zR)改变时,其聚焦场的横向场结构即光强与偏振态分布,依然可以保持稳定;通过聚焦场相位结构分析,给出了在束腰距离透镜位置zi超过一定瑞利长度zR范围(zi>0.5zR)时,影响横向场结构不稳定的原因;聚焦场纵向偏振分量作为聚焦场的一个自由度,被证明可以用来构建更加丰富的矢量结构光场。此研究结果对复杂结构矢量光场在光学微操控与光信息存储方面的研究有重要参考价值。

Abnormality Degree Detection Method Using Negative Potential Field Group Detectors

Online monitoring methods have been widely used in many major devices, however the normal and abnormal states of equipment are estimated mainly based on the monitoring results whether monitored parameters exceed the setting thresholds. Using these monitoring methods may cause serious false positive or false negative results. In order to precisely monitor the state of equipment, the problem of abnormality degree detection without fault sample is studied with a new detection method called negative potential field group detectors（NPFG-detectors）. This method achieves the quantitative expression of abnormality degree and provides the better detection results compared with other methods. In the process of Iris data set simulation, the new algorithm obtains the successful results in abnormal detection. The detection rates for 3 types of Iris data set respectively reach 100%, 91.6%, and 95.24% with 50% training samples. The problem of Bearing abnormality degree detection via an abnormality degree curve is successfully solved.

Correct Classification Rates in Multi-Category Discriminant Analysis of Spatial Gaussian Data

This paper discusses the problem of classifying a multivariate Gaussian random field observation into one of the several categories specified by different parametric mean models. Investigation is conducted on the classifier based on plug-in Bayes classification rule (PBCR) formed by replacing unknown parameters in Bayes classification rule (BCR) with category parameters estimators. This is the extension of the previous one from the two category cases to the multi-category case. The novel closed-form expressions for the Bayes classification probability and actual correct classification rate associated with PBCR are derived. These correct classification rates are suggested as performance measures for the classifications procedure. An empirical study has been carried out to analyze the dependence of derived classification rates on category parameters.

Coherence vortices of partially coherent beams in the far field

Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator~ zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre-Gaussian beams.

Theoretical Study of Electromagnetic Wave Propagation: Gaussian Bean Method

In this work, we present the study of electromagnetic wave propagation through a medium with a variable dielectric function using the concept of Gaussian Beam. First of all, we start with wave equation with which we obtain the solution in terms of the electric field and intensity distributions approximate to Gaussian Function, . With this, we analyze the dependency of r on Gaussian beam distribution spread, the distant from the axis at which the intensity of the beam distribution begins to fall at a given estimate of its peak value. The influence of the optimum beam waist wo and the beam spread on the intensity distribution will also be analyzed.