Polynomial invariant measures for maps on the unit interval

A class of polynomial solutions is found for a functional equation which certain invariant measures must satisfy. These solutions exist only for specific values of the parameter of the triangular map on the unit interval. Using this fact, a method is proposed for approximating the invariant measures for the standard quadratic map.     

一维无序扰动周期结构中局域长度的对称等价变换

以一维周期结构光谱对称性为基础，提出了无序扰动周期结构有关局域长度的一个新的变换关系：对称等价变换，并用数值计算加以了验证.该等价变换描述了不同无序度的结构对不同频率光子局域能力之间的等价关系，为无序结构中光子局域性质的进一步研究提供了一个新的工具. 关键词： 局域长度 无序扰动周期结构 对称等价变换     

单水听器波导不变量被动测距

本文主要讨论利用声场干涉现象由单水听器被动测距的可行性及测距性能,为此提出了单水听器波导不变量被动测距方法,通过提取LOFAR图上干涉条纹、使用简正波模型计算波导不变量、频域相关法估计相对速度,最后依据干涉条纹方程得到声源距离估计量。数值仿真和海上实验结果验证了单水听器被动测距的可行性,并具备一定测距性能,在3 dB信噪比环境中,对于7 km处的运动声源,平均测距误差小于5%。本文方法具有设备简单、易于推广至阵列信号处理等特点,为声纳信号处理环境宽容性的提高及环境适配声纳的设计开拓了思路。     

Fractal properties of critical invariant curves

We examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation. The maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed. Our results indicate that the dimension is universal for a given type of singularity and rotation number, and that among all rotation numbers, the golden mean produces the largest dimension.     

基于波导不变量的空中和水下声源分辨方法

波导不变量反映了水下声场多途传播的干涉结构特征。将波导不变量的提取分析应用于空气中声源产生的水下声场,通过数值仿真分析了波导不变量分布随深度的变化,提出了利用小深度接收声场提取的波导不变量分布来分辨空中和水下声源的方法。分析了空气中声速和风速剖面对该方法的影响,指出在实际海上环境条件下,当出现逆温现象或者当接收器在声源下风方向时,该方法是有效的。     

Stochastic climate dynamics: Random attractors and time-dependent invariant measures

This article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one. This unification, via the theory of random dynamical systems (RDS), allows one to consider the detailed geometric structure of the random attractors associated with nonlinear, stochastically perturbed systems. We report on high-resolution numerical studies of two idealized models of fundamental interest for climate dynamics. The first of the two is a stochastically forced version of the classical Lorenz model. The second one is a low-dimensional, nonlinear stochastic model of the El Niño-Southern Oscillation (ENSO). These studies provide a good approximation of the two models’ global random attractors, as well as of the time-dependent invariant measures supported by these attractors; the latter are shown to have an intuitive physical interpretation as random versions of Sinaï-Ruelle-Bowen (SRB) measures.     

Computing the invariant density of bistable noisy maps

A numerical method is presented allowing the computation of the invariant density of a time-discrete bi- or multistable map perturbed by weak noise. It permits the examination of noise-induced transitions between different stable states in the limit of weak but not amplitude-limited noise. The method is tested by comparing the results with computer experiments. For this purpose a new one-parameter family of bistable maps is introduced. It turns out that the numerics are in good agreement with the experiments. The results suggest the conjecture that in the limit of weak but transition-inducing noise the probability of being in one basin of attraction approaches one. A simple example which can be solved in closed form and which illustrates these findings is discussed.     

宽带波束形成器的自适应综合

提出一种具有频率不变波束图的宽带基阵设计方法。该方法只需给出参考波束图,无须推导权矢量的表达式,便可由计算机自动完成整个设计任务。其设计过程分为3步:(1)用数值计算的方法计算参考频率下的基阵权矢量。(2)利用自适应模拟法得到其它频率处的基阵权矢量。(3)以各频点处的基阵权矢量作为FIR滤波器的频率响应指标设计FIR滤波器。该方法可应用于任意阵型的阵列,且对各阵元的指向性也没有任何限制,因此本文方法具有重要的工程应用价值。     

Stalactite basin structure of dynamical systems with transient chaos in an invariant manifold

Dynamical systems with invariant manifolds occur in a variety of situations (e.g., identical coupled oscillators, and systems with a symmetry). We consider the case where there is both a nonchaotic attractor (e.g., a periodic orbit) and a nonattracting chaotic set (or chaotic repeller) in the invariant manifold. We consider the character of the basins for the attracting nonchaotic set in the invariant manifold and another attractor not in the invariant manifold. It is found that the boundary separating these basins has an interesting structure: The basin of the attractor not in the invariant manifold is characterized by thin cusp shaped regions ("stalactites") extending down to touch the nonattracting chaotic set in the invariant manifold. We also develop theoretical scalings applicable to these systems, and compare with numerical experiments. (c) 2000 American Institute of Physics.     

Marginal singularities,almost invariant sets,and small perturbations of chaotic dynamical systems

For a class of piecewise monotone locally noncontracting maps f:X-->X with small "traps" Y( varepsilon ) subset, dbl equals X (diam(Y( varepsilon )) infinity conditional probabilities that f(n+1)x in X\Y( varepsilon ) if x,fx,.,f(nx) in X\Y( varepsilon ) and the point x is chosen at random. Also proven is the convergence of &mgr;( varepsilon ) to smooth f-invariant measures as varepsilon -->0. By means of this construction, the numerical phenomenon of the convergence of histograms of trajectories of maps with marginal singularities to densities of nonfinite smooth invariant measures in the computer modeling was investigated.     

Striation-based beamforming for estimating the waveguide invariant with passive sonar

The waveguide invariant summarizes the pattern of constructive and destructive interference between acoustic modes propagating in the ocean waveguide. For many sonar signal-processing schemes, it is essential to know the correct numerical value for the waveguide invariant. While conventional beamforming can estimate the ratio between the waveguide invariant and the range to the source, it cannot unambiguously separate the two terms. In the present work, striation-based beamforming is developed. It is shown that the striation-based beamformer can be used to produce an estimate for the waveguide invariant that is independent of the range. Simulation results are presented.     

Trilinear Lorentz invariant forms

Trilinear invariant forms are described over spaces transforming under the so-called elementary representations ofSL(2,C) obtained from the Gel'fand-Naimark principal series by analytic continuation in the representation parameters (among these are all infinite-dimensional completely irreducible representations). All such forms are described using a manifestly covariant technique. The method is based on a natural one-one correspondence between the invariant forms and invariant separately homogeneous distributions (called kernels of the forms) in three complex two-dimensional non-zero vectors; thus the problem is completely reduced to a problem of distribution theory. The kernels display analyticity properties in the representation parameters; the results on this point are only sketched.     

Hyperbolicity and invariant measures for generalC 2 interval maps satisfying the Misiurewicz condition

In this paper we will show that piecewiseC ² mappingsf on [0,1] orS ¹ satisfying the so-called Misiurewicz conditions are globally expanding (in the sense defined below) and have absolute continuous invariant probability measures of positive entropy. We do not need assumptions on the Schwarzian derivative of these maps. Instead we need the conditions thatf is piecewiseC ², that all critical points off are non-flat, and thatf has no periodic attractors. Our proof gives an algorithm to verify this last condition. Our result implies the result of Misiurewicz in [Mi] (where only maps with negative Schwarzian derivatives are considered). Moreover, as a byproduct, the present paper implies (and simplifies the proof of) the results of Mañé in [Ma], who considers generalC ² maps (without conditions on the Schwarzian derivative), and restricts attention to points whose forward orbit stay away from the critical points. One of the main complications will be that in this paper we want to prove the existence of invariant measures and therefore have to consider points whose iterations come arbitrarily close to critical points. Misiurewicz deals with this problem using an assumption on the Schwarzian derivative of the map. This assumption implies very good control of the non-linearity off ⁿ, even for highn. In order to deal with this non-linearity, without an assumption on the Schwarzian derivative, we use the tools of [M.S.]. It will turn out that the estimates we obtain are so precise that the existence of invariant measures can be proved in a very simple way (in some sense much simpler than in [Mi]). The existence of these invariant measures under such general conditions was already conjectured a decade ago.     

Application of invariant grey scale features for analysis of porous minerals

Three-dimensional (3D) texture analysis can be used to differentiate similar materials which have a complex structural nature that is not easily reduced to geometric primitives. A method which extends the concept of invariant grey scale features to non-structured 3D textures is introduced and applied to the study of five processed mineral carbon materials which are characteristically similar but derive from different industrial sources. X-ray microtomography (XRMT) was used to obtain 3D tomographic data with isotropic voxel spacing of 9.8 microm. These data were used to construct invariant features for 3D texture measurement via Monte Carlo based sampling routines and integrals of grey scale relational kernel functions. The procedure produced multi-component texture vectors, which were successfully tested against texture samples as a classification-recognition tool. Identification accuracies ranging from 69% to approximately 84% were achieved for the five material sources examined. This result provides a sound basis for quantitative analysis of these materials which to date have proved very difficult to examine using traditional image analysis tools because of their complex natural structure.     

A method for visualization of invariant sets of dynamical systems based on the ergodic partition

We provide an algorithm for visualization of invariant sets of dynamical systems with a smooth invariant measure. The algorithm is based on a constructive proof of the ergodic partition theorem for automorphisms of compact metric spaces. The ergodic partition of a compact metric space A, under the dynamics of a continuous automorphism T, is shown to be the product of measurable partitions of the space induced by the time averages of a set of functions on A. The numerical algorithm consists of computing the time averages of a chosen set of functions and partitioning the phase space into their level sets. The method is applied to the three-dimensional ABC map for which the dynamics was visualized by other methods in Feingold et al. [J. Stat. Phys. 50, 529 (1988)]. (c) 1999 American Institute of Physics.     

On the singularity structure of invariant curves of symplectic mappings

We study invariant curves in standard-like maps conjugate to rigid rotation with complex frequencies. The main goal is to study the analyticity domain of the functions defined perturbatively by Lindstedt perturbation expansions. We argue, based on infinite-dimensional bifurcation theory that the boundary of analyticity should typically consist of branch points of order two and we verify it in some examples using nonperturbative numerical methods. We show that this nature of the singularities of the analyticity domain can explain previously reported numerical results and also suggests other numerical methods. (c) 1995 American Institute of Physics.     

Obtaining gauge invariant actions via symplectic embedding formalism

The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non‐invariant ones. Both are named also as first‐ and second‐class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non‐invariant theories. Once established, this kind of mapping between first‐class (gauge invariant) and second‐class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non‐invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non‐Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non‐Abelian systems.     

基于不变系数的光照不变最小二乘匹配

最小二乘匹配(LSM)对全局灰度和几何畸变有较好的适应性,得到了广泛应用和重视。但是该方法存在计算量大,难以实时应用,以及不能适应局部光照变化等问题。提出了不变系数光照不变最小二乘匹配,通过固定法方程式系数,大幅减少了单位迭代计算量。在实际中,由于成像场景和光照条件的复杂性,传统的以整体灰度变换模型近似图像间灰度变化往往会存在较大误差,由于真实灰度畸变模型不易获取和计算,该问题一直没有得到很好解决。提出了用光照不变描述替换原始灰度描述的方法,实现了对局部灰度畸变的适应,并将最小二乘匹配的迭代维数由8维降为6维,进一步提升了计算速度。理论分析和真实数据实验表明,该方法较之传统方法计算速度提升6.18倍;几何变化和局部光照变化仿真实验证明了此方法对局部光照变化有较好的适应性。     

An invariant imbedding formulation of coupled-wave theory

An alternative formulation of coupled-wave theory adapted to numerical analyses is developed, using the method of invariant imbedding. Solutions of the coupled-wave equations are represented in terms of a reflectance matrix and a transmission matrix (rather than the transition matrix of the more classical approach).