Non-perturbative positive Lyapunov exponent of Schrödinger equations and its applications to skew-shift mapping

We first study the discrete Schrödinger equations with analytic potentials given by a class of transformations. It is shown that if the coupling number is large, then the Lyapunov exponent equals approximately to the logarithm of this coupling number. When the transformation becomes the skew-shift mapping, we prove that the Lyapunov exponent is weak Hölder continuous, and the spectrum satisfies Anderson Localization and contains large intervals. Moreover, all of these conclusions are non-perturbative.     

金属导体电阻温度系数实验数据处理方法的比较

基于金属导体电阻温度系数实验数据的特点,我们采用三种不同的数据处理方法:逐差法、最小二乘法和Origin绘图,对实验数据进行了分析处理,并且将三种方法在处理实验数据时的特点做了对比分析。根据我们的分析发现,将Origin应用到大学物理实验教学的数据处理中,不仅能够简单、快捷地完成数据的统计、分析和曲线拟合,而且有利于帮助学生掌握物理规律,更好地提高物理实验教学的效果。     

Differential infrared thermography for boundary layer transition detection on pitching rotor blade models

Differential infrared thermography (DIT) was investigated and applied for the detection of unsteady boundary layer transition locations on a pitching airfoil and on a rotating blade under cyclic pitch. DIT is based on image intensity differences between two successively recorded infrared images. The images were recorded with a high framing rate infrared camera. A pitching NACA0012 airfoil served as the first test object. The recorded images were used in order to investigate and to further improve evaluation strategies for periodically moving boundary layer transition lines. The measurement results are compared with the results of unsteady CFD simulations based on the DLR-TAU code. DIT was then used for the first time for the optical measurement of unsteady transition locations on helicopter rotor blade models under cyclic pitch and rotation. Image de-rotation for tracking the blade was employed using a rotating mirror to increase exposure time without causing motion blur. The paper describes the challenges that occurred during the recording and evaluation of the data in detail. However, the results were found to be encouraging to further improve the method toward the measurement of unsteady boundary layer transition lines on helicopter rotor models in forward flight.     

Engineered Anisotropic Fluids of Rare-Earth Nanomaterials

The self-assembly of inorganic nanoparticles into well-ordered structures in the absence of solvents is generally hindered by van der Waals forces, leading to random aggregates between them. To address the problem, we functionalized rigid rare-earth (RE) nanoparticles with a layer of flexible polymers by electrostatic complexation. Consequently, an ordered and solvent-free liquid crystal (LC) state of RE nanoparticles was realized. The RE nanomaterials including nanospheres, nanorods, nanodiscs, microprisms, and nanowires all show a typical nematic LC phase with one-dimensional orientational order, while their microstructures strongly depend on the particles’ shape and size. Interestingly, the solvent-free thermotropic LCs possess an extremely wide temperature range from −40 °C to 200 °C. The intrinsic ordering and fluidity endow anisotropic luminescence properties in the system of shearing-aligned RE LCs, offering potential applications in anisotropic optical micro-devices.     

在线社交网络控制实验的现状与展望

在线社交网络已发展成为一个独特的电子生态系统，其应用深刻影响着人们生活的方方面面。由于在线社交网络特性复杂，分析在线社交网络形成和变化中的规律成为当前计算机科学、社会学和物理学的一项挑战。传统上，在线社交网络实证研究主要采用计算机辅助的被动数据获取和分析方式。近年来，在真实大规模在线社交网络上直接进行控制实验从而主动获取数据并开展分析研究的方式广受关注。评述了这一领域的研究进展，包括：社交网络控制实验的主要研究模式；控制实验方法在社交网络结构、信息传播、行为和心理学等领域取得的主要成果以及主要实验工具的适用条件和局限性。最后，展望了人工智能技术在社交网络控制实验中的应用潜力，分析了智能算法对降低实验成本和提高实验效率的作用。