Elliptical cosh-Gaussian beams

Using tensor method, a new kind of light beams named elliptical cosh-Gaussian beam (EChGB) is introduced in this paper. An analytical propagation expression for the EChGB passing through axially nonsymmetrical ABCD optical systems is derived by using vector integration. The derived formula is easily reduced to the propagation formula of a fundamental Gaussian beam and that of a cosh-Gaussian beam passing through optical systems. Some numerical simulations are illustrated for the propagation properties of EChGBs through the nonsymmetrical optical transforming systems, and further extensions are pointed out.     

Billiards and Bernoulli schemes

Some two dimensional billiards are Bernoulli flows.     

椭圆傅里叶级数展开法和椭圆光波导的截止频率

与严格马丢（Ｍａｔｈｉｅｕ）函数、有限元法等许多典型方法及一些实验测试的比较表明,本文提出的计算弱导椭圆光波导的椭圆傅里叶级数展开法具有通用、准确、高效、简便的优点。     

Non-paraxial Elliptical Gaussian Beam

By using the methods of Hertz vector and angular spectrum transormation, the exact solution of non-paraxial elliptical Gaussion beam with general astigmatism based on Maxwell′s equations is obtained. We discussed its propagation characteristics. The results show that the orientation of the elliptical beam spot changes continuously as the beam propagates through isotropic media. Splitting or coupling of beam spots may occur for different initial spot size. This is very different from that of paraxial elliptical Gaussian beam.     

Non-paraxial Elliptical Gaussian Beam

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零视距地物长波红外特征场景仿真研究

为仿真地物长波红外场景图像,根据地表温度随时间变化的规律,并结合气象状况、背景材质、热特性参量、热状态等参数,在对太阳辐射、大气长波辐射、大气温度和地表热传导等影响地表温度变化的因素进行分析的基础上,建立了基于热平衡理论和热传导过程的方程。解算出多种常见地表一日之中的温度变化情况,并将其应用于由相同景物可见光纹理图像反演出的相应红外纹理图像中。在考虑景物表面自身发射、反射的辐射计算模型的前提下,生成了具有相似红外纹理细节的地表红外场景。结果表明,该方法可生成接近真实感的红外场景,有效地模拟仿真地物的长波红外特征。     

Elliptical flows in Reggeon theory

A new mechanism for the generation of an azimuthal anisotropy of particles produced in heavy-ion collisions is analyzed. An analysis is performed within Reggeon theory and is general. The resulting effect can be interpreted in terms of the partonic structure of a fast nucleus. This mechanismcan contribute significantly to the observed value of the elliptic flow υ ₂. The dynamics in question differs significantly from a standard mechanism of the collective motion of a hadron medium after a collision.

     

Multifractal Analysis of Inhomogeneous Bernoulli Products

We are interested to the multifractal analysis of inhomogeneous Bernoulli products which are also known as coin tossing measures. We give conditions ensuring the validity of the multifractal formalism for such measures. On another hand, we show that these measures can have a dense set of phase transitions.     

A Poisson random walk is Bernoulli

Particles distributed on the integers in Poisson distribution, each independently taking a random walk, form a stationary Markov chain. The canonical shift in this space is Bernoulli.This research was supported in part by NSF grant MCS 78-07739-A03     

A dimension formula for Bernoulli convolutions

We present a dynamical approach to the study of the singularity of infinitely convolved Bernoulli measuresv , for the golden section. We introducev as the transverse measure of the maximum entropy measure on the repelling set invariant for contracting maps of the square, the fat baker's transformation. Our approach strongly relies on the Markov structure of the underlying dynamical system. Indeed, if =golden mean, the fat baker's transformation has a very simple Markov coding. The ambiguity (of order two) of this coding, which appears when projecting on the line, due to passages for the central, overlapping zone, can be expressed by means of products of matrices (of order two). This product has a Markov distribution inherited by the Markov structure of the map. The dimension of the projected measure is therefore associated to the growth of this product; our dimension formula appears in a natural way as a version of the Furstenberg-Guivarch formula. Our technique provides an explicit dimension formula and, most important, provides a formalism well suited for the multifractal analysis of this measure, as we will show in a forthcoming paper.     

A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core

The electro-elastic interaction between a piezoelectric screw dislocation and an elliptical piezoelectric inhomogeneity, which contains an electrically conductive confocal elliptical rigid core under remote anti-plane shear stresses and in-plane electrical load is dealt with. The analytical solutions to the elastic field and the electric field, the interfacial stress fields of inhomogeneity and matrix under longitudinal shear and the image force acting on the dislocation are derived by means of complex method. The effect of material properties and geometric configurations of the rigid core on interfacial stresses generated by a remote uniform load, rigid core and material electroelastic properties on the image force is discussed.     

蜂窝椭圆反射镜的孔结构设计研究

应用有限方法进行了蜂窝椭圆反射镜的轻量化孔结构设计研究.研究了离散单元尺寸对离散误差的影响,分析了六方形孔形状下孔排布形式和孔尺寸对蜂窝椭圆反射镜的各项性能的影响.结果表明6mm的离散单元尺寸对应着较小的离散误差;孔尺寸对质量、转动惯量和加工变形的影响较大,孔排布形式和孔尺寸对热变形的影响高于对自重变形的影响;80mm孔尺寸的第四种形式是最优的孔结构形式.     

Analysis of Elliptical Thin Ridged Waveguide

Elliptical waveguides and ridged waveguides have found broad applications in many microwave structures. The elliptical waveguide with double infinite thin ridges has been formulated using the mode-matching method. Exact closed-form expressions for eigenvalue problem of all TE and TM modes are presented. Numerical results suggest that the elliptical ridged waveguides have larger bandwidth than that of circular ones. Supported in part by the National Natural Science Foundation of China under Grant 60532010, and in part by the Scientific Research Foundation for the Returned Overseas Chinese Scholars under Grant 04LXJ01.     

A note on Bernoulli polynomials and solitons

Abstract

The dependence on time of the moments of the one-soliton KdV solutions is given by Bernoulli polynomials. Namely, we prove the formula expressing the moments of the one-soliton function sech²(x-t) in terms of the Bernoulli polynomials Bn(x). We also provide an alternative short proof to the Grosset-Veselov formula connecting the one-soliton to the Bernoulli numbers (D?=?d/dx) published recently in this journal.     

On ASEP with Step Bernoulli Initial Condition

This paper extends earlier work on ASEP to the case of step Bernoulli initial condition. The main results are a representation in terms of a Fredholm determinant for the probability distribution of a fixed particle, and asymptotic results which in particular establish KPZ universality for this probability in one regime. (And, as a corollary, for the current fluctuations.)     

The Bernoulli Property for Weakly Hyperbolic Systems

A dynamical system is called partially hyperbolic if it exhibits three invariant directions, one unstable (expanding), one stable (contracting) and one central direction (somewhere in between the other two). We prove that topologically mixing partially hyperbolic diffeomorphisms whose central direction is non-uniformly contracting (negative Lyapunov exponents) almost everywhere have the Bernoulli property: the system is equivalent to an i. i. d. (independently identically distributed) random process. In particular, these systems are mixing: correlations of integrable functions go to zero as time goes to infinity. We also extend this result in two different ways. Firstly, for 3-dimensional diffeomorphisms, if one requires only non-zero (instead of negative) Lyapunov exponents then one still gets a quasi-Bernoulli property. Secondly, if one assumes accessibility (any two points are joined by some path whose legs are stable segments and unstable segments) then it suffices to requires the mostly contracting property on a positive measure subset, to obtain the same conclusions.     

THz自由电子激光椭圆型耦合输出光腔

在对中国工程物理研究院高功率太赫兹（THz）自由电子激光（FEL）装置理论分析和设计的基础上,针对目前THz FEL光腔设计面临的主要难点,提出了椭圆型耦合输出光腔的设计方案,并对椭圆型耦合输出光腔代替传统FEL光腔的优势、光腔品质、耦合效率等进行了分析研究。研究表明,椭圆型耦合光腔的设计更适合目前THz FEL波导光腔的光斑特点,可使光腔输出功率提高33%以上,输出耦合效率即光腔品质可提高30%~70%;随着辐射频率的提高,椭圆孔耦合输出光腔的优势提高更为明显。     

喷气箍缩等离子体X射线椭圆弯晶谱仪研究

为了测量喷气箍缩等离子体X射线的空间分辨光谱,利用椭圆聚焦原理,研制了一种椭圆晶体谱仪.分别利用Si(111)、Mica(002)椭圆晶体作色散元件,离心率均为0.948 0,布喇格角为30～67.5°,光谱信号采用半径为50 mm的半圆形胶片接收,从等离子体源经晶体到胶片的光路长为1 430 mm.在“阳”加速器装置上进行摄谱验证实验,成功获取了氩喷气等离子体X射线的光谱.测量光谱波长与理论值相符,其中Si弯晶获得的光谱分辨率(λ/Δλ＝200～300)低于Mica弯晶获得的光谱分辨率(λ/Δλ＝500～700).实验结果表明,该谱仪适合于喷气箍缩等离子体X射线的光谱学研究.