Extracting flow structures from tracer data

A method of visualizing structures in closed chaotic flows out of homogenous particle distributions is presented in the example of models of a meandering jet. To this end, the system will be leaked or opened up by defining a region of the flow, so that a particle is considered to be escaped if it leaves this region. By applying this method to an ensemble of nonescaped tracers, we are able to characterize mixing processes by visualizing the converging and stretching filamentations (stable and unstable manifolds) in the flow without using additional mathematical tools. The possibility of applying the algorithm to analyze buoy data, and a comparison with the finite time manifolds are discussed.     

Super-resolution enhancement of UAV images based on fractional calculus and POCS

Abstract

A super-resolution enhancement algorithm was proposed based on the combination of fractional calculus and Projection onto Convex Sets (POCS) for unmanned aerial vehicles (UAVs) images. The representative problems of UAV images including motion blur, fisheye effect distortion, overexposed, and so on can be improved by the proposed algorithm. The fractional calculus operator is used to enhance the high-resolution and low-resolution reference frames for POCS. The affine transformation parameters between low-resolution images and reference frame are calculated by Scale Invariant Feature Transform (SIFT) for matching. The point spread function of POCS is simulated by a fractional integral filter instead of Gaussian filter for more clarity of texture and detail. The objective indices and subjective effect are compared between the proposed and other methods. The experimental results indicate that the proposed method outperforms other algorithms in most cases, especially in the structure and detail clarity of the reconstructed images.     

The Collision Manifold of the Collinear One-Bumper Two-Body Problem

We present a special model which is a caricature of the collinear three-body problem. Near triple-collision behavior for the model is governed by the collision manifold. We study the bifurcations of the dynamics on this manifold as we vary the ratio of masses. Both analytic and numerical results are presented.This revised version was published online in October 2005 with corrections to the Cover Date.     

Low Energy Transfer to the Moon

In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less Vthan a standard Hohmann transfer. In this paper, we apply the dynamical systems techniques developed in our earlier work to reproduce systematically a Hiten-like mission. We approximate the Sun–Earth–Moon-spacecraft 4-body system as two 3-body systems. Using the invariant manifold structures of the Lagrange points of the 3-body systems, we are able to construct low energy transfer trajectories from the Earth which execute ballistic capture at the Moon. The techniques used in the design and construction of this trajectory may be applied in many situations.     

地形图点状符号自动识别中不变性特征参数的提取

特征参数的抽取,是实现地形图中点状符号自动识别的关键。本文根据点状符号在扫描图中可能出现的旋转、缩放等情况,归纳和总结出了４种易于计算的不变性特征,并给出了这些特征的提取方法和部分实验结果。这４种特征参数是:复杂度——用以描述符号外围的复杂程度;扁率——用以反映符号的扁平程度;比重——符号的黑色部分在其整个覆盖区域中所占的比例;偏心率——用以反映符号重心与符号的几何中心的偏离程度。这４种特征参数具有旋转不变性和大小不变性,且便于提取、容易计算。     

Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.     

运用SI-Harris算子提取遥感图像点特征

推导了SI-Harris算子(尺度不变Harris算子)的理论公式,并将其应用于遥感图像的点特征提取。重点对Harris算子与SI-Harris算子在不同空间分辨率遥感图像上的点特征提取进行实验比较,利用"重复率"指标对实验结果进行定量评价。实验表明:SI-Harris算子"重复率"较Harris算子有明显提升,可用于不同空间分辨率遥感图像的点特征提取,进而可服务于不同空间分辨率遥感图像的匹配。     

Escapes and Recurrence in a Simple Hamiltonian System

Many physical systems can be modeled as scattering problems. For example, the motions of stars escaping from a galaxy can be described using a potential with two or more escape routes. Each escape route is crossed by an unstable Lyapunov orbit. The region between the two Lyapunov orbits is where the particle interacts with the system. We study a simple dynamical system with escapes using a suitably selected surface of section. The surface of section is partitioned in different escape regions which are defined by the intersections of the asymptotic manifolds of the Lyapunov orbits with the surface of section. The asymptotic curves of the other unstable periodic orbits form spirals around various escape regions. These manifolds, together with the manifolds of the Lyapunov orbits, govern the transport between different parts of the phase space. We study in detail the form of the asymptotic manifolds of a central unstable periodic orbit, the form of the escape regions and the infinite spirals of the asymptotic manifolds around the escape regions. We compute the escape rate for different values of the energy. In particular, we give the percentage of orbits that escape after a finite number of iterations. In a system with escapes one cannot define a Poincaré recurrence time, because the available phase space is infinite. However, for certain domains inside the lobes of the asymptotic manifolds there is a finite minimum recurrence time. We find the minimum recurrence time as a function of the energy.This revised version was published online in October 2005 with corrections to the Cover Date.     

一种基于局部判别正切空间排列的高光谱遥感影像降维方法

提出一种基于局部判别正切空间排列(local discriminative tangent space alignment,LDTSA)的高光谱影像降维方法。LDTSA源于局部正切空间排列(LTSA)中的排列机制,在一个局域块内利用线性局部正切平面对类内样本的流形结构建模,同时还考虑到类间判别信息以最大化判别边界。利用多幅高光谱数据进行降维和分类试验。结果表明,LDTSA主要有三个优点:①在小样本问题上性能稳定;②在降维过程中保持类别间的判别信息;③有效挖掘数据集的几何流形结构。     

On the relationship between Lyapunov times and macroscopic instability times

On the basis of the general theory of Hamiltonian systems, we consider the relationship between Lyapunov times and macroscopic diffusion times. We find out that there are two regimes: the Nekhoroshev regime and the resonant overlapping regime. In the first case the diffusion time is exponentially long with respect to Lyapunov times. In the second case, the relationship is polynomial although we do not find any theoretical reason for the existence of a universal power law. We show numerical evidences which confirm our theoretical considerations.