Slow Light Via a Tapered Grating: Transfer Matrix Approach

Reflection properties of a nonuniform apodized Bragg grating connecting a homogeneous medium with a (half-infinite) uniform grating are investigated for system parameters such that the group velocity in the uniform grating is low. In particular a smooth polynomial transition of the index profile to the uniform region is considered. Exact coupled mode equations for local Bloch amplitudes are set up in a transfer matrix formalism. For a linear taper the coupling matrix appears to be singular for parameter values near the edge of the photonic band gap. The polynomial profile removes the singularity in this coupling term.     

Layered Ising models on triangular and honeycomb lattices

We study inhomogeneous Ising models on triangular and honeycomb lattices. The nearest neighbour couplings can have arbitrary strength and sign such that the coupling distribution is translationally invariant in the direction of one lattice axis, i.e. the models have a layered structure. By using a transfer matrix method we derive closed form expressions for the partition functions and free energies. The critical temperatures are calculated. Phase transitions at a finite critical temperature are universally of Ising type. Models with no phase transition may show different behaviour atT=0, which is explicitly shown for fully frustrated models on square, triangular and honeycomb lattices. Finally, generalizations to layered Ising models on more general lattices are discussed.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Geometrical cluster growth models and kinetic gelation

Random percolation, self-avoiding walks or lattice animals can be regarded as static geometrical models where the different possible configurations are completely independent from each other and show no memory effects. These static geometrical models have extensively ben studied in the past. Certain configurations (clusters) were, for technical reasons, sometimes constructed by a growth process where computer time might be interpreted as a measure of time but then one had to make sure that the final result of the growth had the same statistical weight as the configuration of the static model. In nature, however, geometrical clusters (tumors, gels, soot) are usually grown. Thus we review studies of geometrical growth models as such in order to describe some real processes and to compare them with the static models.The growth of a single cluster as well as the growth of a distribution of clusters is of interest. Growth models can be studied as a function of dimensionality and of the specific rules of the growth. One can introduce anisotropy and mobility and even find universality classes in the sense of the theory of phase transitions. Up to now most work has been done with computer simulations but in some cases mean-field type approaches, ε-expansions and transfer matrix calculations on strips are possible. We give a general overview on the subject.The paper begins with an introduction to the field of growth models showing what makes them different from stalic models. Much emphasis is then put on scaling relations and their numerical verification. A principal role in these relations plays the fractal dimension. Then a few models are briefly reviewed and only for some examples we will go into details. These examples are mainly kinetic gelation which is a kinetic generalization of percolation, epidemics which are growth models that produce percolation clusters and aggregation as an example for a model that has no static reference model.     

Characterization of woodwind instrument toneholes with the finite element method

A method is proposed to determine the transfer matrix parameters of a discontinuity in a waveguide with the finite element method (FEM). This is used to characterize open and closed woodwind instrument toneholes and develop expressions for the shunt and series equivalent lengths. Two types of toneholes are characterized: Unflanged toneholes made of thin material, such as found on saxophones and concert flutes, and toneholes drilled through a thick material, such as found on most instruments made of wood. The results are compared with previous tonehole models from the literature. In general, the proposed expressions provide a better fit across a wide range of frequencies and tonehole sizes than previous results. For tall toneholes, the results are in general agreement with previous models. For shorter tonehole heights, some discrepancies from previous results are found that are most important for larger diameter toneholes. Finally, the impact of a main bore taper (conicity) on the characterization of toneholes was investigated and found to be negligible for taper angles common in musical instruments.     

Solution bounds for varying geometry beams

The theory of differential and integral inequalities is applied to obtain upper and lower bounds to the transfer matrix for beams with varying geometry. Various techniques of generating and refining these bounds are investigated. Numerical results indicate that these bounds can be refined to produce numerical agreement of the upper and the lower bound to a given number of significant digits.Proceeding from bounds on the transfer matrix elements a theory is developed for determining upper and lower bounds on the natural frequencies and mode shapes and on the solution state vector for static loading of such beams. This procedure is then extended to the analysis of multispan beams with varying geometry. Numerical results are presented for various configurations.     

煤粉炉内弥散介质辐射传热的综合模拟

本文基于辐射传热计算的DT法和颗粒运动计算的随机轨道法,并结合单颗粒的辐射特性模型,构造了能够详细考虑颗粒燃尽、湍流弥散诸因素对炉内空间局部辐射特性及总体辐射传热影响的弥散介质辐射传热计算模型,并将其耦合到炉内过程的总体数值模型中。采用该程序,比较计算了几种颗粒辐射特性模型对某300MW锅炉炉内温度场的预报结果,结果表明：通常采用的均匀颗粒辐射特性模型会导致温度场的极大误差;由于炉内颗粒浓度的不均匀分布,炉内的温度分布呈现高度非均匀状态,在炉膛轴线上有大面积的高温烟气区存在;考虑残炭存在时,温度分布的不均匀性更显著．     

非均匀随机散射介质层的多次散射和热辐射的分层迭代解

为纳入矢量辐射传输方程的多次散射，将非均匀平行分层分布的随机散射介质划分成多个薄 层，利用各薄层的低阶Mueller矩阵解推导出整层的高阶散射迭代解.用这一方法计算了具有 占空比、粒子大小和温度廓线非均匀分布的平行分层随机密集球形粒子积雪层的极化热辐射 .数值结果与一层均匀随机散射层的离散坐标-特征值方法作了比较，讨论了多次散射和热辐 射与散射层各特征参数的关系，与积雪层微波遥感数据进行了对比. 关键词： VRT方程 平行分层 高阶散射解 迭代解     

One-dimensional Kinetic Ising Model with Nonuniform Coupling Constants

A nonuniform extension of the Glauber model on a one-dimensional lattice with boundaries is investigated. The static behavior of the system is investigated. It is shown that there are cases where the system exhibits a static phase transition, which is a change of behavior of the static profile of the expectation values of the spins near end points.     

An experimental study of acoustoelectric transducers with nonuniform distribution of the piezoelectric coefficient

In this paper, an experimental test of a theoretical model published previously is presented that describes the behavior of an acoustoelectric transducer with a nonuniform distribution of the piezoelectric coefficient within its bulk. Results of this theoretical model are first reviewed. Uniform and nonuniform piezoelectric transducers were fabricated, following a procedure described herein. The receive transfer functions of the transducers were recorded experimentally, and a comparison is made with the theoretical transfer functions predicted by the model, which shows good agreement. The transmit transfer functions of the uniform and nonuniform transducers were also measured and are reported. Numerical calculations of the different transfer functions given by the theoretical model for a uniform transducer associated with different backing materials are also presented, and the results are shown to be equivalent to the results following from the Mason equivalent circuit. Comparisons with experimental results and with Mason's equivalent circuit verified the new theoretical model.     

考虑温度分布效应的非对称RLC树时钟偏差研究

提出了一种RLC互连树零时钟偏差构建方法.给出了RLC互连温度非均匀分布及其延时的解析公式,并推导计算了最优的零时钟偏差点,所提模型同时考虑了互连温度非均匀分布、电感效应及不对称互连结构对零时钟偏差点的影响.针对65 nm工艺节点对所提模型进行了仿真验证,结果显示,相较于同类模型,最大误差不超过1%. 关键词： RLC')" href="#">RLC 温度分布 不对称互连结构 零时钟偏差点     

电偶极子源定位问题的研究

首先得到了封闭形式的电偶极子处于任意位置时电场分布的公式，它是一个线性变换，称其变换矩阵为传递矩阵.并给出了传递矩阵的具体表达式和许多有用的性质，得到了传递矩阵的逆矩阵，导出了利用电场分布来确定单个或者多个偶极子源位置矢量和电偶极矩矢量的公式.对单个偶极子源的计算表明，如果测得两点的电场分布相同，就可以确定偶极子处于它们连线的中点上. 关键词： 电偶极子 传递矩阵 电场分布 定位问题     

Scattering characteristics of conducting cylinder coated with nonuniform magnetized ferrite

An analytical technique, referred to as the scattering matrix method （SMM）, is developed to analyse the scattering of a planar wave from a conductolution for the nonuniform fering cylinder coated with nonuniform magnetized ferrite. The SMM srite coating can be reduced to the expressions for the scattering and penetrated coefficients in four particular cases： nonuniform magnetized ferrite cylinder, uniform magnetized ferrite-coated conducting cylinder, uniform ferrite cylinder as well as homogeneous dielectric-coated conducting cylinder. The resonant condition for the nonuniform ferrite coating is obtained. The distinctive differences in scattering between the nonuniform ferrite coating and the nonuniform dielectric coating are demonstrated. The effects of applied magnetic fields and wave frequencies on the scattering characteristics for two types of the linear profiles are revealed.     

An Infrared Image Synthesis Model for High-Speed Targets

Although a number of infrared models are available for synthesizing the infrared image of static objects, they fail to simulate the infrared signature of targets flying at high speed. This paper presents an infrared image synthesis model for such kind of targets. Within this model, we account for not only all forms of heat transfer inside the targets but also the dynamic interaction between the target's surface and the surrounding air-flow. The heat transfer process between the target's surface and the air-flow is carefully analyzed based on the principles of infrared physics, aerodynamics and heat transfer, and a term due to aerodynamic heating is incorporated into our new model. Experimental results illustrate the potential of the model     

A semiclassical approximation for massive transfer

A semiclassical approximation for the transition matrix for transfer reactions between heavy ions is developed from the distorted-wave Born approximation by means of the three-dimensional WKB approximation. It is designed to be applicable to massive transfer without adopting various assumptions and approximations of previous semiclassical approaches which are reasonable only for few-nucleon transfer. The final expression obtained is of a simple closed form similar to that of the Brink model. It gives a way of seeing the validity of the idea of Brink in massive transfer. Numerical study of illustrative examples indicates promising applicability of the present method to massive transfer.     

非均匀反射体全息窄带带阻滤光片

在实验基础上,利用非均匀耦合波理论得出了介质折射率调制度和空频变化的非均匀模型,利用此模型分析了窄带宽和高光学密度滤光片所应具有的非均匀分布特性,指出了实验工艺上应努力的方向,实验上用重铬酸明胶（DCG）实现了性能优良的高光学密度窄带宽的全息带阻滤光片,峰值波长光学密度为4－5,半宽度小于20nm.     

Static anisotropic fluid spheres in general relativity with nonuniform density

An Ansatz developed by Maharaj and Maartens is used to obtain solutions of Einstein's field equations for static anisotropic fluid spheres with nonuniform density. These solutions are matched with the Schwarzschild exterior solution.     

A fast transfer function algorithm for nonuniform acoustic tubes

A fast algorithm for computing the transfer function for a nonuniform acoustic tube with acoustical losses and branches has been developed. It is based on the derived analytical correlations between the cross-section areas of such a tube and the coefficient of a corresponding autoregressive model with a moving average (ARMA-model). Comparison of transfer functions calculated with the use of the derived correlations with the results of a standard transmission-line method shows the accuracy and efficiency of the developed algorithm.     

Stability of rod-shaped nanoparticles embedded in an elastic matrix

In many biological tissues as well as in some technical materials we find nano-sized rod-shaped particles embedded in a relatively soft matrix. Loss of stability of equilibrium, i.e. buckling, is one of the possible failure modes of such materials. In the present paper different kinds of load transfer between matrix and reinforcing particles, which are typical for rod-shaped nanostructures in biological tissues, are considered with respect to stability of equilibrium. Two regimes of matrix stiffnesses leading to different modes of buckling, and a transition regime in between, have been found: soft matrix materials leading to the so-called ‘flip mode’ (also called ‘tilt mode’) and hard matrix materials resulting in ‘bending mode’ buckling. The transition regime is of particular interest for biological tissues. Numerical and semi-analytical as well as asymptotic concepts are employed leading to results for estimating the critical load intensities both in the form of closed form solutions and diagrams. The analytical solutions are compared with results of finite element analyses. From these comparisons indications are gained for deciding which of the different analytical approaches should be chosen for a particular nanostructure configuration in terms of the associated buckling modes.     

Deformation of Two-Dimensional Nonuniform-Membrane Red Blood Cells Simulated by a Lattice

To study two-dimensional red blood cells deforming in a shear flow with the membrane nonuniform on the rigidity and mass, the membrane is discretized into equilength segments. The fluid inside and outside the red blood cell is simulated by the D2Q9 lattice Boltzmann model and the hydrodynamic forces exerted on the membrane from the inner and outer of the red blood cell are calculated by a stress-integration method. Through the global deviation from the curvature of uniform-membrane, we find that when the membrane is nonuniform on the rigidity, the deviation first decreases with the time increases and implies that the terminal profile of the red blood cell is static. To a red blood cell with the mass nonuniform on the membrane, the deviation becomes more large, and the mass distribution affects the profile of the two sides of the flattened red blood cell in a shear flow.     

Exact solution for the spin-s XXZ quantum chain with non-diagonal twists

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon which a Bethe ansatz calculation can be constructed, in contrast to the well-known case of periodic boundary conditions. In this paper we show how the transfer matrix eigenvalue expression for the spin-s XXZ chain twisted by the charge-conjugation matrix can in fact be obtained. The technique used is the generalization to spin-s of the functional relation method based on “pair propagation through a vertex”. The Bethe ansatz-type equations obtained reduce, in the case of lattice size N = 1, to those recently found for the Hofstadter problem of Bloch electrons on a square lattice in a magnetic field.