The mathematical modelling of rotating capillary tubes for holey-fibre manufacture

Understanding and controlling the manufacturing process of producing (“drawing”) microstructured optical fibres (“holey fibres”) is of paramount importance in obtaining optimal control of the final fibre geometry and identifying industrially useful production regimes. The high cost of the manufacturing process and the challenge of ensuring reproducible final fibre geometries renders theoretical approaches invaluable. In this study the fluid dynamics of capillary drawing is examined using an extensional-flow asymptotic approach based on the small aspect ratio of the capillary. The key focus of the study is the additional effects that may be introduced by adding fibre rotation to the manufacturing process. Predictions are made concerning the effects of rotation, and a variety of asymptotic limits are examined in order to gain an understanding of the physics involved. Drawing regimes that are useful from a practical point of view are identified and the role of fibre rotation, both as a control measure (that may be used to influence the final geometry of a capillary) and as a means of reducing unwanted effects (such as fibre birefringence and polarisation model dispersion), is discussed.     

FISHER'S INFORMATION MATRIX FOR SEASONAL AUTOREGRESSIVE-MOVING AVERAGE MODELS

Abstract. Two procedures are described for obtaining Fisher's information matrix of a multiplicative seasonal autoregressive-moving average process. They can be useful in determining the asymptotic covariance matrix of Gaussian maximum likelihood estimators of the parameters. Components of the information matrix are expressed in the first procedure as integrals of rational functions. The second procedure makes use of the autocorrelation function of several autoregressive processes.     

矿井瞬变电磁矩形回线源瞬变电磁响应研究

为研究均匀全空间介质中任意点（除发射框边）处矩形回线源瞬变电磁响应,从全空间磁偶极子的切向电场和水平圆形回线发射框中心磁场出发,采用互易原理和积分法推导了全空间任意点处的瞬变响应。通过对全空间瞬变场磁场Bz及其时间导数?Bz/?t的核函数Y(ω)和Y’(ω)特征的研究,将全程瞬变响应分为早期、中期和晚期。Y(ω)的早期和晚期阶段,其内层误差函数采用渐近展开式,外层积分采用直接多项式积分;中期阶段,内层误差函数采用有理契比雪夫展开式,外层积分采用龙贝格积分。Y’(ω)的晚期和非对角区域的早期采用误差函数渐近展开式;Y’(ω)的中期和对角区域的早期采用龙贝格积分。采用理论模型计算验证了公式的精度。结果表明,该算法求取的数值解,其Bz核函数Y(ω)的相对误差可以控制在1×10-6%以内;而?Bz/?t的核函数Y’(ω)的相对误差可以控制在1×10-4%以内。早期阶段,Bz和?Bz/?t在发射框内部的极值中心沿着与短边呈45°夹角方向向发射框内部移动,并且短边处的两个极值中心先行合并,然后再沿长边方向合并;?Bz/?t极值向发射框内部和发射框外部移动的速度大于Bz相应的移动速度。     

Fast computation of wideband RCS using characteristic basis function method and asymptotic waveform evaluation technique

The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering problems. As the number of unknowns increases, the size of Method Of Moments (MOM) impedance matrix grows very rapidly, so it is a prohibitive task for the computation of wideband Radar Cross Section (RCS) from electrically large object or multi-objects using the traditional AWE technique that needs to solve directly matrix inversion. In this paper, an AWE technique based on the Characteristic Basis Function (CBF) method, which can reduce the matrix size to a manageable size for direct matrix inversion, is proposed to analyze electromagnetic scattering from multi-objects over a given frequency band. Numerical examples are presented to illustrate the computational accuracy and efficiency of the proposed method.     

Tests for change—points based on recursive u—statistics

Tests for change—points for the location as well as regression models are often based on cumulative sums of recursive residuals. These recursive residuals are also employed in the sequential detection problem. In the context of general estimable parameters (funtionals of the underlying distribution functions), such recursive residuals may be defined in terms of recursive U—statistics. A class of tests for the change—points based on recursive U—statistics has been considered. Along with some invariance principles for recursive U—statistics, asymptotic properties of the proposed tests are studied.     

On asymptotically Risk-effivient sequential versions of generalized U-statistics

Sequential point estimation of means of generalized U-statistics is considered. Based on a well defined stopping rule, the proposed sequential (estimation) procedure is shown to be asymptotically (first order) risk-efficient. Asymptotic distributions of sequential generalized U-statistics and the allied stopping times are also studied.     

ASYMPTOTIC PROPERTY STUDY OF THE LEAST SQUARE ESTIMATES OF 2-D EXPONENTIAL SIGNALS VIA COMPLEX SIGNAL PROCESSING APPROACH

By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.     

FACILITATED TRANSPORT OF CARBON DIOXIDE: A REVIEW

The effect of reversible chemical reaction upon the diffusion of carbon dioxide in thin liquid film membranes is reviewed. Particular emphasis is placed upon the hydration reaction of CO₂ and catalysis thereof. Theoretical analysis is developed for equilibrium, near-equilibrium and near-diffusion regimes. The important effects of weak acid buffers, proteins and amines upon CO₂ transport are also discussed, as well as the significance of diffusion potentials, particularly in the case of protein systems. Results of experimental investigations of facilitated CO₂ transport are reviewed, as well as general aspects of CO₂ transport in biological systems and absorbers.     

DIFFUSION AND REACTION WITH A LIMITED AMOUNT OF REACTANT

The rotational motion of a rigid particle is considered. The method of Green's functions is used which reduces the governing equation to a Fredholm's integral equation of the first kind. Numerical and analytical solutions are obtained with any stress singularities taken explicitly into account.