Mechanical deformations of a liquid crystal elastomer at director angles between 0° and 90°: Deducing an empirical model encompassing anisotropic nonlinearity

Despite the wealth of studies reporting mechanical properties of liquid crystal elastomers (LCEs), no theory can currently describe their complete mechanical anisotropy and nonlinearity. Here, we present the first comprehensive study of mechanical anisotropy in an all‐acrylate LCE via tensile tests that simultaneously track liquid crystal (LC) director rotation. We then use an empirical approach to gain a deeper insight into the LCE's mechanical responses at values of strain, up to 1.5, for initial director orientations between 0° and 90°. Using a method analogous to time–temperature superposition, we create master curves for the LCE's mechanical response and use these to deduce a model that accurately predicts the load curve of the LCE for stresses applied at angles between 15° and 70° relative to the initial LC director. This LCE has been shown to exhibit auxetic behavior for deformations perpendicular to the director. Interestingly, our empirical model predicts that the LCE will further demonstrate auxetic behavior when stressed at angles between 54° and 90° to the director. Our approach could be extended to any LCE; so it represents a significant step forward toward models that would aid the further development of LCE theory and the design and modeling of LCE‐based technologies. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1367–1377     

Phase transition in the one-dimensional pair-hopping model with unusual one-electron hopping

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction.     

Detecting nonclassicality of light via Lieb's concavity

Nonclassical light states are important for both conceptual and practical reasons: they are basic ingredients in testing and exploring quantum foundations, and are crucial resources in quantum technologies. Various useful criteria have been developed to detect nonclassicality in the literature, and several meaningful measures of nonclassicality have been introduced and measured experimentally. In this work, by use of a non-Hermitian generalization of the Wigner-Yanase-Dyson skew information and playing with operator ordering in evaluating average photon number, we develop a novel family of criteria for detecting nonclassicality of light based on Lieb's concavity, which is a deep and powerful result concerning interaction between quantum states and observables. We elucidate the information-theoretic as well as the physical meaning of the criteria, and illustrate their effectiveness in capturing and quantifying nonclassicality of various important light states.     

基于时序多光谱影像的干旱草原区开采扰动信息提取方法

露天开采会彻底改变原有土地利用景观格局，直接破坏当地生态环境，甚至会影响附近居民的生产和生活，因此越来越多的学者开始关注开采扰动。先前有关利用时序多光谱影像提取开采扰动的研究区集中于扰动形式单一的森林区。而我国露天煤矿大多集中于草原区，且我国东北部的草原矿区因其脆弱的生态环境以及其他多种扰动形式的存在，使得开采扰动识别更加困难。为明确我国东北部生态脆弱区草原露采场的开采扰动，以胜利矿区为例，利用1986年-2017年27期Landsat多光谱遥感影像，基于归一化植被指数NDVI（normalized difference vegetation index）的长时间序列轨迹变化特征（为了去除物候、云和阴影等对时序多光谱影像的影响，利用BISE-WT滤波器对原始NDVI时间序列进行滤波处理, 有效地去除时序NDVI数据中的噪声并同时保留有效信息），经过样本点训练，获得CV阈值（变异系数coefficient of variation）和Max阈值（植被阈值），构建CV-Max扰动识别模型，提取研究区的扰动分布。并利用植被阈值，分析NDVI时序轨迹，获得扰动年际信息，重构扰动历史地图；进而通过分析研究区典型地物的光谱特征，构建裸煤提取规则，以此来提取研究区的裸煤分布；最后通过构建裸煤及扰动区两者间的拓扑关系，进行空间拓扑叠置分析，从而获得开采扰动信息。经过精度验证，开采扰动的提取精度达到93.17%（Kappa系数=0.85），扰动年际信息提取精度达到83.35%（Kappa系数=0.81）。结果表明：在研究期间，空间上，开采扰动面积占研究区总面积的8.90%；时间上，开采扰动的发生集中于2000年-2009年，期间开采扰动像元占开采扰动总像元的76.70%；1988年-1998年矿区属于土地损毁初始期，2000年-2005年矿区属于土地损毁加速期，2006年-2009年矿区属于土地损毁高峰期，2010年-2017年开采扰动像元占比趋势比较平缓且持续处于较低水平，矿区土地损毁范围基本稳定。所提出的针对我国东北部生态脆弱性草原矿区，基于时序多光谱影像，利用植被指数NDVI和裸煤光谱特征提取开采扰动信息的方法是可行的，该研究结果可为干旱、半干旱草原露天矿区的可持续发展提供数据和理论方法支撑。     

On a Lyapunov-type inequality and the zeros of a certain Mittag–Leffler function

In this work, a Lyapunov-type inequality is obtained for the case when one is dealing with a fractional differential boundary value problem. We then use that result to obtain an interval where a certain Mittag–Leffler function has no real zeros.     

Estimator of a change point in single index models

This paper considers the problem of change point in single index models. In order to obtain asymptotically valid confidence intervals for the estimation of the change point, the convergence rate and asymptotic distribution of the change point estimate is studied. Some simulation results are presented which show that the numerical performance of our estimator is satisfactory.     

地球化学模拟在高放废物地质处置中的应用与发展

随着核能事业的发展,高放废物的处理和处置问题日益突出.其中,研究高放废物在环境介质中的吸附、扩散和迁移行为是获取放射性核素对周围环境和人群健康影响的基础参数的最重要和最直接的途径.近年来,人们利用已有的实验数据及核素的基础热力学和动力学数据,附以相应的数学模型,建立了一些地球化学模拟软件,用于分析核素在地质介质中可能发生的连续性和长期性变化.目前,国内外常用的地球化学模拟软件有十多种.本文从热力学平衡计算原理、种态分布计算方法和表面配位模型假设等几个方面对地球化学模拟软件进行了简要介绍,对近年来地球化学模拟软件在核素种态分布计算和表面配位模型模拟两方面的应用进行了举例分析,并以Ca-U-CO3配合物为例,说明完备的热力学数据对地球化学模拟软件发展的重要性,以期促进我国地球化学模型的应用和发展.     

C_(2~6)烯烃在H-ZSM-5分子筛周期性模型上吸附的理论研究

采用密度泛函理论中的PBE-D方法研究了C2~6直链烯烃以及丁烯异构体在H-ZSM-5分子筛周期性模型上的吸附行为。结果表明,对于C2~6直链烯烃,随着碳数的增加,烯烃的吸附能以-12 kJ/mol的常数线性增大,体系中色散校正能ED以-13 kJ/mol的常数线性增大,而不考虑范德华力的能量E*随碳数增加变化不大,只在C5和C6时由于空间阻力凸显而减小。ED显著大于E*,说明烯烃在分子筛孔道中吸附时范德华力起主要作用,且碳数增加其影响增大。丁烯异构体吸附能大小顺序为:反式-2-丁烯顺式-2-丁烯正丁烯异丁烯。正丁烯的3种异构体ED相近且都比正丁烯的大,3种异构体的吸附能差异由E*不同引起。差分电荷密度分析表明,烯烃双键与酸性中心之间有电子聚集,且聚集程度与π配位作用相一致,而且酸性中心H原子有质子化趋向,O原子及其周围电子增加。     

关于高等代数题解的五种方法

介绍处理高等代数习题的标准形式化方法、公理化方法、模型转换方法、形式统一性方法和形态联想方法,并给出实例加以说明.