A Modified Double Gyre with Ground Truth Hyperbolic Trajectories for Flow Visualization

The model of a Double Gyre flow by Shadden et al. is a standard benchmark data set for the computation of hyperbolic Lagrangian Coherent Structures (LCS) in flow data. While structurally extremely simple, it generates hyperbolic LCS of arbitrary complexity. Unfortunately, the Double Gyre does not come with a well‐defined ground truth: the location of hyperbolic LCS boundaries can only be approximated by numerical methods that usually involve the gradient of the flow map. We present a new benchmark data set that is a small but carefully designed modification of the Double Gyre , which comes with ground truth closed‐form hyperbolic trajectories. This allows for computing hyperbolic LCS boundaries by a simple particle integration without the consideration of the flow map gradient. We use these hyperbolic LCS as a ground truth solution for testing an existing numerical approach for extracting hyperbolic trajectories. In addition, we are able to construct hyperbolic LCS curves that are significantly longer than in existing numerical methods.     

基于视频粒子流和FTLE场的人群运动分割算法

针对复杂视频监控场景中不同运动行为的人群分割,提出了将视频粒子流和有限时间李雅普诺夫指数(FTLE)场相结合的人群运动分割算法。首先利用视频粒子流来表示长周期的粒子运动估计,通过最小化包含粒子外观匹配一致性和粒子间形变的能量函数,来优化每个粒子的轨迹;接着求解粒子流图的空间梯度,并构造FTLE场;最后利用FTLE场中的拉格朗日相干结构把流图分割成运动特性不同的区域。实验结构表明,算法能从拥挤复杂的视频监控场景中有效地分割出不同运动特性的群体,且具有较好的鲁棒性。     

Over Two Decades of Integration‐Based,Geometric Flow Visualization

With ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of flow visualization, which deals with large, time‐dependent, multivariate simulation data sets. In this paper, geometry‐based flow visualization techniques form the focus of discussion. Geometric flow visualization methods place discrete objects in the velocity field whose characteristics reflect the underlying properties of the flow. A great amount of progress has been made in this field over the last two decades. However, a number of challenges remain, including placement, speed of computation and perception. In this survey, we review and classify geometric flow visualization literature according to the most important challenges when considering such a visualization, a central theme being the seeding algorithm upon which they are based. This paper details our investigation into these techniques with discussions on their applicability and their relative merits and drawbacks. The result is an up‐to‐date overview of the current state‐of‐the‐art that highlights both solved and unsolved problems in this rapidly evolving branch of research. It also serves as a concise introduction to the field of flow visualization research.     

Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2-D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle-type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite-time Lyapunov exponent field. The proposed approach is evaluated on both 2-D time-dependent synthetic and vector fields from computational fluid dynamics.     

Toward a Lagrangian Vector Field Topology

In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio‐temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.     

MCFTLE: Monte Carlo Rendering of Finite‐Time Lyapunov Exponent Fields

Traditionally, Lagrangian fields such as finite‐time Lyapunov exponents (FTLE) are precomputed on a discrete grid and are ray casted afterwards. This, however, introduces both grid discretization errors and sampling errors during ray marching. In this work, we apply a progressive, view‐dependent Monte Carlo‐based approach for the visualization of such Lagrangian fields in time‐dependent flows. Our approach avoids grid discretization and ray marching errors completely, is consistent, and has a low memory consumption. The system provides noisy previews that converge over time to an accurate high‐quality visualization. Compared to traditional approaches, the proposed system avoids explicitly predefined fieldline seeding structures, and uses a Monte Carlo sampling strategy named Woodcock tracking to distribute samples along the view ray. An acceleration of this sampling strategy requires local upper bounds for the FTLE values, which we progressively acquire during the rendering. Our approach is tailored for high‐quality visualizations of complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface structures as indicators for Lagrangian coherent structures (LCS). We demonstrate the effectiveness of our approach by using a set of analytic test cases and real‐world numerical simulations.     

基于粒子纹理融合的流场可视化方法

基于纹理的可视化方法可以描述流场的整体结构，但传统方法计算耗时，生成可视化图像对比度比较低。从加速可视化整体流程出发，提出了一种基于粒子纹理融合的流场可视化方法。此方法首先随机产生一组噪声图像作为初始粒子分布图，然后依次将初始粒子分布图与根据流动而变形的数据网格加权融合得到粒子轨迹图，最后一帧帧彼此相邻的粒子轨迹图组成一个流场的动态显示。该方法具有独立于流场数据、绘制速度快、生成图像对比度高的特点，参数物理意义明显，不同参数选择可得到不同视觉效果的可视化输出结果，能够充分利用现有硬件图形显示加速设备,已经被成功应用于空间晶体生长实验流场数据的可视化，获得了较好的效果。     

Evenly Spaced Streamlines for Surfaces: An Image-Based Approach

We introduce a novel, automatic streamline seeding algorithm for vector fields defined on surfaces in 3D space. The algorithm generates evenly spaced streamlines fast, simply and efficiently for any general surface-based vector field. It is general because it handles large, complex, unstructured, adaptive resolution grids with holes and discontinuities, does not require a parametrization, and can generate both sparse and dense representations of the flow. It is efficient because streamlines are only integrated for visible portions of the surface. It is simple because the image-based approach removes the need to perform streamline tracing on a triangular mesh, a process which is complicated at best. And it is fast because it makes effective, balanced use of both the CPU and the GPU. The key to the algorithm's speed, simplicity and efficiency is its image-based seeding strategy. We demonstrate our algorithm on complex, real-world simulation data sets from computational fluid dynamics and compare it with object-space streamline visualizations.     

Autonomous Particles for Interactive Flow Visualization

We present an interactive approach to analyse flow fields using a new type of particle system, which is composed of autonomous particles exploring the flow. While particles provide a very intuitive way to visualize flows, it is a challenge to capture the important features with such systems. Particles tend to cluster in regions of low velocity and regions of interest are often sparsely populated. To overcome these disadvantages, we propose an automatic adaption of the particle density with respect to local importance measures. These measures are user defined and the systems sensitivity to them can be adjusted interactively. Together with the particle history, these measures define a probability for particles to multiply or die, respectively. There is no communication between the particles and no neighbourhood information has to be maintained. Thus, the particles can be handled in parallel and support a real‐time investigation of flow fields. To enhance the visualization, the particles' properties and selected field measures are also used to specify the systems rendering parameters, such as colour and size. We demonstrate the effectiveness of our approach on different simulated vector fields from technical and medical applications.     

Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.     

State‐dependent switching law design with guaranteed dwell time for switched nonlinear systems

In this article, without the help of predesigned dwell time constraints, a new state‐dependent switching law with guaranteed dwell time for switched nonlinear systems is studied. Some sufficient conditions for asymptotic stability of switched nonlinear systems are derived. Also, all the abovementioned conditions can be transformed to a set of sum of squares (SOS) constraints, which can be checked by using the bilinear SOS methodology. Meanwhile, an improved path following method is provided to solve a bilinear SOS problem. Finally, three simulation examples are given to demonstrate the effectiveness of the obtained results.     

Enhancing the settling time estimation of a class of fixed‐time stable systems

In this paper, we provide a new nonconservative upper bound for the settling time of a class of fixed‐time stable systems. To expose the value and the applicability of this result, we present four main contributions. First, we revisit the well‐known class of fixed‐time stable systems, to show the conservatism of the classical upper estimate of its settling time. Second, we provide the smallest constant that the uniformly upper bounds the settling time of any trajectory of the system under consideration. Third, introducing a slight modification of the previous class of fixed‐time systems, we propose a new predefined‐time convergent algorithm where the least upper bound of the settling time is set a priori as a parameter of the system. At last, we design a class of predefined‐time controllers for first‐ and second‐order systems based on the exposed stability analysis. Simulation results highlight the performance of the proposed scheme regarding settling time estimation compared to existing methods.     

The State of the Art in Flow Visualization: Dense and Texture-Based Techniques

Flow visualization has been a very attractive component of scientific visualization research for a long time. Usually very large multivariate datasets require processing. These datasets often consist of a large number of sample locations and several time steps. The steadily increasing performance of computers has recently become a driving factor for a reemergence in flow visualization research, especially in texture‐based techniques. In this paper, dense, texture‐based flow visualization techniques are discussed. This class of techniques attempts to provide a complete, dense representation of the flow field with high spatio‐temporal coherency. An attempt of categorizing closely related solutions is incorporated and presented. Fundamentals are shortly addressed as well as advantages and disadvantages of the methods.     

Simulation of unsteady two-phase flows using a parallel Eulerian–Lagrangian approach

The present study details the implementation of a time accurate method for the tracking of particles being acted upon by a continuous gas phase and gravity. The Lagrangian particle tracking approach was implemented within the framework of a parallel, incompressible, unstructured, node-centered finite-volume flow solver. The paper gives a method for selecting time steps for individual particles such that interactions with the continuum phase are updated at particle locations nearest the continuum-phase nodes while constraining the particle from passing beyond boundaries of the relevant adjacent cell. An implementation of this technique for three-dimensional nonuniform multi-element unstructured grids is given in the context of domain decomposition for implementation on distributed-memory parallel computers. Results of simulations with and without particle–particle collisions compare favorably with experimental validation results.     

A study of microwave imaging for a metallic cylinder

This article presents the studies of time‐domain inverse scattering for a metallic cylinder which based on the finite‐difference time‐domain (FDTD) method and the dynamic differential evolution (DDE). For this study, the FDTD is used for the analysis of the forward scattering part, while for the DDE is applied for the reconstruction of the two‐dimensional metallic cylinder. For the forward scattering, the FDTD method is used to calculate the scattered E fields. Based on the scattering fields, these inverse scattering problems are transformed into optimization problem. By comparing the simulated scattered fields and the calculated scattered fields, the shape and location of the metallic cylinder are reconstructed. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In addition, the effects of Gaussian noise on the reconstruction results are investigated. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE , 2012.     

可重入混合流水车间调度的拉格朗日松弛算法

为了有效提升多重入车间的生产效率,考虑了实际生产中检查和修复过程对于逐层制造的可重入生产系统的重要性,提出了基于拉格朗日松弛算法的可重入混合流水车间的调度方法.首先进行了问题域的描述,并在此基础上以最小化加权完成时间为调度目标,建立数学规划模型.针对该调度问题提出了基于松弛机器能力约束的拉格朗日松弛算法,使松弛问题分解成工件级子问题,并使用动态规划方法建立递归公式,求解工件级子问题.随后,使用次梯度算法求解拉格朗日对偶问题.最后,对各种不同问题规模进行了仿真实验,结果表明,所提出的调度算法能够在合理的时间内获得满意的近优解.     

Delay‐distribution‐dependent robust stability of uncertain systems with time‐varying delay

By employing the information of the probability distribution of the time delay, this paper investigates the problem of robust stability for uncertain systems with time‐varying delay satisfying some probabilistic properties. Different from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delay is random and its probability distribution is known a priori. In terms of the probability distribution of the delay, a new type of system model with stochastic parameter matrices is proposed. Based on the new system model, sufficient conditions for the exponential mean square stability of the original system are derived by using the Lyapunov functional method and the linear matrix inequality (LMI) technique. The derived criteria, which are expressed in terms of a set of LMIs, are delay‐distribution‐dependent, that is, the solvability of the criteria depends on not only the variation range of the delay but also the probability distribution of it. Finally, three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer

This paper studies coordinated control of multiple Lagrangian systems with parametric uncertainties subject to external disturbances by proposing a fully distributed continuous control law based on the improved self‐tuning adaptive observer inspired by non‐identifier‐based high‐gain adaptive control technique. Under this distributed continuous control law, a group of Lagrangian systems are driven to the convex hull spanned by multiple heterogenous dynamic leaders, which can be any combination of step signals of arbitrary unknown magnitudes, ramp signals of arbitrary unknown slopes, and sinusoidal signals of arbitrary unknown amplitudes, initial phases, and any unknown frequencies. It is also worth to mention that this control law we propose, depending neither on any information of leader systems for uninformed followers, nor on external disturbances, even independent of neighbors' velocity, can achieve asymptotic tracking of multiple leaders without any additional condition instead of ensuring the ultimate boundedness of the containment error as in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

基于李雅普诺夫指数的离散混沌系统的控制研究

讨论了通过改变离散混沌系统的李雅普诺夫指数对离散混沌系统进行控制的一种方法。离散混沌系统的李雅普诺夫指数可按需要配置为负值，从而使系统收敛到任意的期望点上，仿真和实验结果表明，该控制方法是有效的，可以实现系统的快速稳定。