Bifurcations with nonuniversal exponents in a lattice model

The bifurcations of a two-dimensional area preserving mapping with a cubic term are studied. This mapping shows a large number of bifurcations where the period becomes a multiple. For a given order of bifurcation exponents are found which depend on the series considered. The exponents calculated numerically are compared with renormalisation calculations for a number of cases.     

基于Vega的红外仿真的优化和评估

借助于三维实时视景仿真软件Vega的红外模块研究了自建模型的红外效应。介绍了红外仿真原理,给出了详细的红外仿真流程,并详细分析了仿真结果。根据项目对仿真精度的要求,提出了优化仿真过程的方法。结合Vega的底层映射机理提出更为精确的长波波段下的辐射量灰度映射关系,同时通过TMM的纹理材质映射关系改进,得到更为符合实际的材质反射率计算公式,并为仿真系统重建了传感器模型,使得仿真模型的辐射量偏差缩小为1.145%~3.358%。此外,初步探讨了仿真系统的校核、验证和确认技术（VV&;A）,并对仿真过程做了全生命周期的可信性评估,为进一步研究仿真系统的可信性评估提供了参考。     

Dynamics of a nonlinear oscillator and a low-amplitude frequency-modulated wave

When the frequency of a small amplitude plane wave is varied slowly over a large enough bandwidth and this wave is incident upon a nonlinear oscillator, the resulting perturbed motion can exhibit stochastic behavior. Applications for the study of this system are wide and varied. We apply Lie-transform perturbation theory and mapping techniques in the analysis of the stochastic transition and the consequent induced diffusion in the oscillator phase space. A constant of the motion to the first order in a perturbation parameter is calculated, a mapping approximation is derived, and diffusion calculations from the mapping are given.     

ANALYTICAL CALCULATION OF BIFURCATION POINTS IN STANDARD MAPPING

For standard mapping, we calculate analytically the values of non-integrable parameter K where the period 1 to 4 orbits variate their stability via tangent bifurcation, period doubling bifurcation and period equal bifurcation.Hence, the analytical stable windows of periodic orbits are given and a complete picture can be seen for the behaviour of bifurcation of periodic motion in standard mapping.     

基于Zernike多项式表示色域边界的色域映射

在彩色图像的跨媒体复制中,由于不同媒体有不同的色域,所以在大多数情况下色域映射是不可避免的。不论采用何种映射算法,色域映射的第一步是确定有关媒体的色域边界。目前大多数的色域边界都是用一组测量的或用其它方法得到的离散数据来表示的。然而,由于这种表示方式是利用一组离散数据来实施色域映射的两个基本处理(即确定任一指定的等色调面平面中色域的边缘线以及确定色域边界与一条映射线的交点),比较复杂和费时,因此希望找到一种色域边界的解析表达式来解决这一问题。简述了不久前提出的一种解析函数色域边界表示方法,并用实例说明了如何利用这种解析表示(Zernike多项式)来实现上述的边缘线确定和交点确定。最后给出了几种映射算法的色域映射完整过程及其结果。     

Image encryption scheme by using iterative random phase encoding in gyrator transform domains

An image encryption is discussed based on the random phase encoding method in gyrator domains. An iterative structure of image encryption is designed for introducing more random phases to encrypt image. These random phase functions are generated by a two-dimensional chaotic mapping with the help of computer. The random phases are utilized for increasing the security of this encryption algorithm. In the chaotic mapping relation, the initial value and expression can serve as the key of algorithm. The mapping relation is considered secretly for storage and transmission in practical application in comparison to traditional algorithms. The angle parameter of gyrator transform is an additional key. Some numerical simulations have been given to validate the performance of the encryption scheme.     

Reciprocal space mapping

This review covers the recent advances in reciprocal space mapping. The experimental techniques as well as the theoretical and conceptual developments are discussed. The advantages of reciprocal space mapping over the conventional single scan X-ray scattering methods become clear from the examples presented. Extracting the additional information from mapping in reciprocal space maps has led to a deeper understanding of materials. Imperfect materials benefit enormously from these methods. Near perfect materials also indicate weak diffuse scattering that can now be interpreted in terms of defects, etc., whereas with single scans the influence is difficult to observe and separate from other features. Reciprocal space maps can be collected with both high and low angular resolution diffractometers, depending on the application, although a combination of resolutions may be necessary. It is also growing in importance in the analysis of materials using specular reflectometry. High-resolution reciprocal space mapping is not restricted to good crystalline quality. Examples of reciprocal space mapping are given for semiconductors, metals, ceramics and biological samples. For semiconductor materials, reciprocal space mapping has now become almost routine in the study of lattice relaxation in thin layers and in the assessment of the “quality” of materials. Combinations of mapping with topography and precision lattice parameter determination are also discussed. The latter part of this review discusses the advantages of three-dimensional reciprocal space mapping, which takes the analysis further. With this method the full three-dimensional shapes in reciprocal space can be studied.     

Inherent limits on optimization and discovery in physical systems

Topological mapping of a large physical system on a graph, and its decomposition using universal measures are proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by motifs, and the ability to reconstruct the full system given approximate representations. The approximate representation of the system most suited for optimization may be different from that which most accurately describes the full system.     

带有对称垂直导体脊的平行板电容器内的电场及其电容量

利用保角变换法研究带有对称垂直导体脊的平行板电容器的电场,给出其电势分布和场强分布函数,通过MATLAB软件绘制电场线和等势线(面)图,并计算其电容量.     

四种非矩形截面传感波导中的TE波和TM波

用保角变换将非矩形截面传感波导变换成等效矩形截面波导．给出计算等效矩形截面波导的TE模和TM模、电磁场、临界频率、波导壁电流、功率传输和衰减的公式．并给出4种非矩形传感截面波导数值计算的例子．     

Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

Abstract

In this work we investigate a formal mapping between the dynamical properties of the unidimensional relativistic oscillator and the asymmetrical rigid top at a classical level. We study the relativistic oscillator within Yamaleev's interpretation of Nambu mechanics. Such interpretation is based on the factorisation of the momenta, and as a consequence of this factorisation we are led to a three dimensional phase space. Solutions of the relativistic oscillator are given in terms of the Jacobian elliptic functions and hence we establish a correspondence of these solutions in terms of well known quantities from the rigid body theory. We also study some mechanical restrictions that appear in the mathematical development of the mapping. In particular, we find a lower bound for the relativistic frequency in order to make the mapping self-consistent and physically legitimate.     

Exact periodic wave solutions to the coupled Schrödinger-KdV equation and DS equations

The exact solutions for the coupled non-linear partial differential equations are studied by means of the mapping method proposed recently by the author. Taking the coupled Schrödinger-KdV equation and DS equations as examples, abundant periodic wave solutions in terms of Jacobi elliptic functions are obtained. Under the limit conditions, soliton wave solutions are given.     

Application of the schwarz-christoffel mapping to planar gravity: static solutions

Point-like masses on a given initial domain of the complex plane are interacting globally under gravity and as a consequence the initial domain is mapped into a final domain which encodes all effects of localized sources . The mapping between the two domains is a truncated beta function which so far has not been fully investigated. In this paper we propose to know more about the final domain and so we start from the remark that when the masses are put on the real axis of the upper half plane, the mapping in question is the Schwarz-Christoffel mapping (SCM), a popular and useful tool in computational geometry. The linking of planar gravity with the SCM will allow us to use all what we know from this mapping to get answer for certain static solutions in planar gravity. Among the problems we will study we mention: masses distributed on the real axis of the full complex plane, masses distributed on a circle, the dust string either closed or infinite open. Strings with tensions are however not linked to SCM as these mappings do not involve the concept of tension.     

Renormalization for stochastic layers

Chirikov's standard mapping for stochastic layers is derived in a simpler and more general way. A one-parameter renormalization transformation yields, analytically, many universal quantities defined in a previous renormalization theory. Expressions are given for the width of stochastic layers that correct several previous estimates.     

Chaotic dynamics of a bouncing ball

A detailed study of a mapping on a two-dimensional manifold is made. The mapping describes a system subject to periodic forcing, in particular an imperfectly elastic ball bouncing on a vibrating platform. Quasiperiodic motion on a one-dimensional manifold is proven, and observed numerically, at low forcing, while at higher forcing Smale horseshoes are present. We examine the evolution of the attracting set with changing parameter. Spatial structure is oganised by fixed points of the mapping and sudden changes occur by crises. A new type of chaos, in which a trajectory alternates between two distinct chaotic regions, is described and explained in terms of manifold collisions. Throughout we are concerned to examine the behaviour of Lyapunov exponents. Typical behaviour of Lyapunov exponents in the quasiperiodic regime under the influence of external noise is discussed. At higher forcing a certain symmetry of the attractor allows an analytic expression for the exponents to be given.     

Reduced models and noncommutative gauge theories

A brief review of the relation between reduced models and noncommutative Yang-Mills (NCYM) theory is given. The twisted Eguchi-Kawai model, the mapping onto NCYM, the Morita equivalence, the fundamental matter, the Wilson loops in NCYM, and the D-brane interpretation are considered.     

Modern developments in particle image velocimetry

This paper summarises the development of particle image velocimetry (PIV) over the last decade and describes its applications as an effective measuring technique for mapping complex flow fields. A review of work in the field is given. Current aerodynamic and hydrodynamic investigation by the authors exploiting the method are described and used as illustration.     

托卡马克的快速Mapping方法

本文介绍一种托卡马克等离子体实验装置的快速Mapping方法。它用于揭示由外加线圈产生的径向场与托卡马克磁场共振产生的磁岛和随机场结构。说明了它在TEXT上的应用及其结果。 关键词：     

A note on singular lagrangian submanifolds

Classification of singular lagrangian submanifolds which appear as images of a regular one under a symplectic relation, is considered from the point of view of standard singularity theory. The classification is carried out in small dimensions and restricted to special types of symplectic objects. Normal forms for singular pullbacks and pushforwards are given using an appropriate symplectic equivalence group. It is shown that the general classification problem reduces to the classification problem for appropriate mapping diagrams. An approach to the classical theories of phase transition is given based on the geometry of singular lagrangian images. The variational open swallowtails and regularly intersecting pairs of holonomic components are resolved using an appropriate reduction relation. Examples are given of singularities encountered in physics.     

Structure of two-dimensional sandpile. I. Height probabilities

The height probabilities of the two-dimensional Abelian sandpile model are the fractionial numbers of lattice sites having heights 1, 2, 3, 4. A combinatorial method for evaluation of these quantities is proposed. The method is based on mapping the set of allowed sandpile configurations onto the set of spanning trees covering a given lattice. Exact analytical expressions for all probabilities are obtained.