混合层中柱状粒子运动的研究

本文在直接数值模拟混合层流场的基础上,求解柱状粒子运动方程而得到粒子运动轨迹,说明粒子在混合层中的不同区域,其运动轨迹也不同,有的呈现波状轨迹,有的呈现环状轨迹,有的是混合轨迹。粒子的混合程度与St数有关。文中结论对工程应用有指导意义。     

等变集压缩场的零点指标公式

本文在紧致李群作用下的Ｂａｎａｃｈ空间中，讨论了等变严格集压缩场的正则零点轨道的指标计算问题，推广了（１），（２）的结果。     

Finite-time disturbance observer-based trajectory tracking control for quadrotor unmanned aerial vehicle with obstacle avoidance

This paper investigates the problem of trajectory tracking control for quadrotor unmanned aerial vehicle (UAV) in the presence of dynamic obstacles and external disturbance forces/torques. More specifically, two new sliding mode disturbance observers are firstly designed to estimate the external disturbances, in which the observation errors can converge to zero in finite time. Furthermore, utilizing the observation information, a new sliding mode surface-like variable-based position tracking control scheme and a novel nonsingular terminal sliding mode-based attitude synchronization control scheme are developed to drive the UAV tracking the reference trajectory with obstacle avoiding. Moreover, the tracking errors of the close-loop control system can converge to zero within finite time by the analyses of Lyapunov methodology. Finally, the numerical simulation results are presented to illustrate the effectiveness of the proposed control schemes.     

Dynamic Optical Vortex Trajectory Guided by the Symmetric Pearcey Gaussian Vortex Beam in the Uniformly Moving Parabolic Potential

This paper analytically and numerically proposes the propagation dynamics of the symmetric Pearcey Gaussian vortex beam (SPGVB) in the uniformly moving parabolic potential. The optical vortex located in the initial plane produces a vortex channel in the presence of the uniformly moving parabolic potential, called the vortex trajectory. The vortex trajectory can be manipulated dynamically by configuring different combinations of the parameters, and the optical intensity and the focal position can also be affected. Moreover, the spatial dynamic vortex trajectory is derived analytically, and the 2D on-axis and off-axis vortex scenarios are also presented. Our work expands the methods of the vortex trajectory manipulation and may broaden more practical potential applications in the particle manipulation.     

Controlling the Trajectory of Swallowtail Gaussian Beams in Dynamic Parabolic Potentials

The propagation dynamics of finite-energy Swallowtail beams in a dynamic parabolic potential, including uniformly moving, accelerating, and oscillating potentials, are investigated. The strong influence of dynamic potentials on the propagation trajectory of Swallowtail beams is demonstrated and various effective manipulations of the beams, including trajectory control, are validated. The intensity and the focal position can also be affected. In addition, the extension to 2D scenarios is also presented. The results theoretically provide more diverse manipulation possibilities for Swallowtail beams, and thus may broaden their potential applications in trajectory and particle manipulation.     

FAST OPTIMIZATION METHOD OF REENTRY TRAJECTORY CONSIDERING AERODYNAMIC PARAMETER PERTURBATION

针对传统再入轨迹优化方法收敛速度慢、对初值敏感程度高等的局限性,提出了一种基于序列凸优化的再入轨迹快速求解方法.该方法以倾侧角的变化率作为控制量,改进了现有凸化策略,考虑到抑制数值优化过程中由于数值离散方式带来的锯齿化现象,采用 B 样条曲线离散控制量,同时为避免算法在初始猜想值附近出现伪不可行的问题,增加额外虚拟控制量,通过一种"回溯直线"搜索的方法,提高算法的稳定性、快速性和寻优结果的光滑性.为研究飞行器再入过程中的气动参数扰动问题,采用采样点少、易于实现,计算效率高的广义混沌多项式理论研究方法,建立了基于广义混沌多项式和凸优化相结合的再入轨迹鲁棒优化模型,该模型在优化过程中考虑气动参数扰动对寻优结果的影响作用,避免了传统轨迹与制导律的复杂迭代设计环节,可有效降低优化轨迹对气动参数扰动的敏感程度,在气动参数不确定条件的干扰下,依然可以保证飞行器顺利安全的完成飞行任务.最后,以美国某可重复使用飞行器的再入任务为例,验证了基于序列凸优化的再入轨迹优化方法的快速性以及鲁棒优化模型对气动参数扰动的抗干扰性能力,表明了该方法具有一定的工程应用性.     

Two‐dimensional reactive scattering with transmitted quantum trajectories

A simple and easy‐to‐implement method is presented for the study of time‐dependent reaction dynamics by propagating an ensemble of transmitted quantum trajectories. During the trajectory evolution, reflected trajectories are gradually removed and all the remaining trajectories represent the transmitted subensemble. The removal process of reflected trajectories avoids numerical instabilities arising from node formation in the reactant region, and allows stable long‐time propagation of transmitted trajectories. This method is applied to a two‐dimensional model chemical reaction. Excellent computational results are obtained for the time‐dependent reaction probabilities evaluated by the time integration of the probability flux. © 2014 Wiley Periodicals, Inc.     

Eliminating counterexamples: A Grade 8 student’s learning trajectory for contrapositive proving

This study uses a teaching experiment and retrospective analysis to develop a learning trajectory for improving a Grade 8 student’s ability to construct, critique, and validate contrapositive arguments. The study is predicated on the hypothesis that adolescents perform poorly on contrapositive reasoning tasks because they lack sufficient ways of justifying contrapositive argumentation as a viable mode of argumentation. By studying a student’s actions and comments as she develops, critiques, and validates not-the-conclusion-implies-the-conditions-are-impossible arguments for conditional claims, a promising learning trajectory for contrapositive argumentation is developed. The student’s learning trajectory demonstrates how a conception of contrapositive proving as eliminating counterexamples can be useful in developing, critiquing, and validating contrapositive arguments.     

Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.