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.     

The movement and thermal history of an aluminium particle in a RF plasma generator

In previous studies on plasma-particle interaction, as far as we know, the rf plasma flow and temperature fields are all simulated by the non-self-consistent one-dimensional electromagnetic (1-D EM) field model. In the present paper, the complete self-consistent two-dimensional electromagnetic (2-D EM) field model incorporating the axial Lorentz force component, which is neglected in the 1-D model, is firstly adopted to calculate the aluminium particle trajectory and thermal history in atmospheric rf Ar plasma with the particle evaporation effect included. The crucial effect of reverse flow within the coil region on the particle trajectory is discovered and the results show that the 2-D EM field model must be adopted instead of the 1-D model when the plasma-particle interaction is studied. The effect of carrier gas flux on the particle movement and heating are also studied, resulting in some useful conclusions for both plasma theory and application. recommended by Prof. Wu Chengkang The project supported by the National Natural Science Foundation of China     

斜拉桥塔锚固区光弹性应力分析与等倾线图像处理

本文采用光弹性冻结应力法，对独塔斜拉桥塔锚固区进行了应力分析，给出了有关截面的边界应力分布及主应力迹线，从而为优化工程设计提供了重要的参考依据。本文还提出了一种新的提取等倾线的方法──图像对数增强相减法，实现了等倾线与等差线条纹的分离，同时使条纹得到了细化，提高了处理等倾线的速度与准确度。编制了自动绘制主应力迹线的程序，利用它绘制了桥塔截面的次主应力迹线。     

地铁车站地下拱型结构的光弹性应力分析

本文用三维光弹性法，对地铁车站地下拱型结构进行了实验应力分析并绘出主应力迹线。文中还提出对加压用乳胶气囊进行高温、高压预处理工艺，使乳胶气囊和模型曲面很好地吻合，从而提高了加载的准确度。     

地表温度对颗粒跃移轨迹的影响

为了研究由地表温度变化引起的向上的垂向气流对沙粒跃移运动的影响,本文给出了考虑近地表温度变化和水平来流风场作用下的沙粒的跃移运动。在定量给出不同时刻的近地表温度和垂向风速的基础上,计算了由于太阳辐射所引起的近地表层垂向气流对沙粒跃移运动的影响,发现:垂向风速在午后可达到1.5m/s并使得沙粒跃移轨迹的最大高度和长度分别增加55.56%和73.68%;同时,与不考虑温度效应的情况不同的是,沙粒跃移轨道最大高度将随粒径变化。     

Modeling the Formation of Fluid Banks During Counter-Current Flow in Porous Media

Fluid banks sometimes form during gravity-driven counter-current flow in certain natural reservoir processes. Prediction of flow performance in such systems depends on our understanding of the bank-formation process. Traditional modeling methods using a single capillary pressure curve based on a final saturation distribution have successfully simulated counter-current flow without fluid banks. However, it has been difficult to simulate counter-current flow with fluid banks. In this paper, we describe the successful saturation-history-dependent modeling of counter-current flow experiments that result in fluid banks. The method used to simulate the experiments takes into account hysteresis in capillary pressure and relative permeabilities. Each spatial element in the model follows a distinct trajectory on the capillary pressure versus saturation map, which consists of the capillary hysteresis loop and the associated capillary pressure scanning curves. The new modeling method successfully captured the formation of the fluid banks observed in the experiments, including their development with time. Results show that bank formation is favored where the p_c-versus-saturation slope is low. Experiments documented in the literature that exhibited formation of fluid banks were also successfully simulated.     

Electronic quantum trajectories in a quantum dot

This article gives a quantum‐trajectory demonstration of the observed electric, magnetic, and thermal effects on a quantum dot with circular or elliptic shape. By applying quantum trajectory method to a quantum dot, we reveal the quantum‐mechanical meanings of the classical concepts of backscattering and commensurability, which were used in the literature to explain the peak locations of the magnetoresistance curve. Under the quantum commensurability condition, electronic quantum trajectories in a circular quantum dot are shown to be stationary like a standing wave, whose presence increases the electrical resistance. A hidden quantum effect called magnetic stagnation is discovered and shown to be the main cause of the observed jumps of the magnetoresistance curve. Quantum trajectories in an elliptic quantum dot are found to be chaotic and an index of chaos called Lyapunov exponent is proposed to measure the irregularity of the various quantum trajectories. It is shown that the response of the Lyapunov exponent to the applied magnetic field captures the main features of the experimental magnetoresistance curve. © 2014 Wiley Periodicals, Inc.     

准经典轨线研究Li+HF(ν=0, j=0)→LiF+H反应动力学

基于Aguado等人拟合的APW势能面(PES), 运用准经典轨线(QCT)方法, 对反应Li+HF(ν=0, j=0)→LiF+H的动力学性质进行了计算. 主要研究了不同碰撞能条件下的反应截面、转动取向、产物散射角分布和竞争反应模式等. 结果表明, 该反应存在直接提取型和间接插入型两种反应模式, 在低能量下反应以间接插入反应模式为主, 能量大于200 meV时则以直接提取反应为主.