The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

Evolution of Local Structural Ordering and Chemical Distribution upon Delithiation of a Rock Salt–Structured Li1.3Ta0.3Mn0.4O2 Cathode

Lithium‐rich disordered rock‐salt oxides have attracted great interest owing to their promising performance as Li‐ion battery cathodes. While experimental and theoretical efforts are critical in advancing this class of materials, a fundamental understanding of key property changes upon Li extraction is largely missing. In the present study, single‐crystal synthesis of a new disordered rock‐salt cathode material, Li_1.3Ta_0.3Mn_0.4O₂ (LTMO), and its use as a model compound to investigate Li concentration–driven evolution of local cationic ordering, charge compensation, and chemical distribution are reported. Through the combined use of 2D and 3D X‐ray nanotomography, it is shown that Li removal accompanied by oxygen oxidation is correlated with the development of morphological defects such as particle cracking. Chemical heterogeneity, quantified by subparticle level distribution of Mn valence state, is minimal during Mn redox, which drastically increases upon the formation of cracks during oxygen redox. Density functional theory and bond valence sum mismatch calculations reveal the presence of local short‐range ordering in the pristine oxide, which gradually disappears along with the extraction of Li. The study suggests that with cycling the transformation into true cation–disordered state can be expected, which likely impacts the voltage profile and obtainable energy density of the oxide cathodes.     

Path to achieving molecular dispersion in a dense reactive mixture

A uniform dispersion of reactants is necessary to achieve a complete reaction involving multicomponents. In this study, we have examined the role of plasticizer in the reaction of two seemingly unlikely reactants: a highly crystalline hexamethylenetetramine (HMTA) and a strongly hydrogen bonded phenol formaldehyde resin. By combining information from NMR, infrared spectroscopy and differential scanning calorimetry, we were able to determine the role of specific intermolecular interactions necessary for the plasticizer to dissolve the highly crystalline HMTA and to plasticize the phenol formaldehyde resin in this crosslinking reaction. The presence of the plasticizer increased the segmental mobility, disrupted the hydrogen bonded matrix, and freed the hydroxyl units, which further increased the solubility of the HMTA. Both the endothermic and exothermic transitions are accounted for in the calorimetric data obtained. For the first time, it is possible to obtain the effective molar ratio of each component needed to complete the crosslinking reaction efficiently. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1519–1526     

Handover and Uplink Power Control Performance in the 3.84 Mcps TDD mode of UTRA Network

In this article we consider the performance of the 3.84 Mcpstime-division duplex (TDD) mode of UTRA (Universal TerrestrialRadio Access) network. We emphasize two of the radio resourcemanagement algorithms, handover and uplink power control, whoserole in the overall system performance is studied extensively.First, a handover algorithm used in WCDMA (Wideband Code DivisionMultiple Access) standard is considered in a TDD-mode operation.This gives rise to a careful setting of different handoverparameters, and the evaluation of the effects to the systemperformance. Secondly, the specified uplink power controlalgorithm is considered. Since it is based on several user-mademeasurements which may involve both random and systematic errors acareful study about the suitability of the power control scheme iscarried out.     

五种恒虚警方法性能分析

比较了五种恒虚警方法在各种杂波背景下的检测性能,得出CMLD-CFAR是工程上可以实现且检测性能比较好的一种恒虚警处理方法.     

移动机器人路径规划方法研究

移动机器人技术研究中的一个重要领域是路径规划技术，它分为基于模型的环境已知的全局路径规划和基于传感器的环境未知的局部路径规划。综述了移动机器人路径规划技术的发展现状指出了各种方法的优点与不足，最后对移动机器人路径规划技术的发展趋势进行了展望。     

高性能调度技术中应用程序调度模型设计--地理空间信息网格调度技术的研究

地理空间信息网格调度技术，要比传统的高性能计算中的调度技术复杂，原因是如果将全部网格资源作为一个应用程序的调度和执行目标，必将导致通信延迟、成本昂贵、执行低效等。为此，综合考虑应用程序特性、机器特性等，研究设计了地理空间信息网格高性能调度技术中的应用程序调度模型，包括地理空间信息网格应用程序分析；资源特性分析；应用程序分解；性能预测；资源调度；机器选择；任务映射；任务调度；任务调度器和调度器管理模块。以实现为不同的应用程序匹配不同的计算资源，提高计算资源的利用率和应用程序的执行效率。     

通信性能评估的仿真实验研究

研究了流量控制和差错控制对通信性能的综合影响，着重分析了停止-等待协议和连续ARQ协议的优缺点，讨论了信道利用率和帧长的关系。介绍了几种多点接人技术的基本原理，如CSMA和CSMA／CD，并给出了各自相应的性能仿真曲线。所设计的通信性能评估实验，仿真界面形象丰富，与实验知识点紧密结合，可以大大提高实验教学的效率和质量。     

小波变换在光谱特征提取方面的应用

人们在处理高光谱图像时一般要对一些典型地物进行光谱分析、特征波段的提取,以便提取出最大量的有效信息,剔除无用或冗余的信息,然后再进行分类识别.采用小波变换的分析方法,选用合适的小波进行分解,根据分解后的高频分量中包含的重要信息,利用局部相邻的正负极值点找出对应于原始光谱曲线上每个吸收带的左右边界;利用局部过零点,即可比较精确的提取出各个吸收带的中心波长.该方法比传统的光谱特征提取方法更简洁、有效,实验证明为一种比较理想的光谱特征提取方法.     

基于有限状态的全周期序列混沌映射的研究

在有限长度的数字计算机中，混沌迭代序列是一个有限周期序列，其相关性能远远低于理想序列。基于skew tent映射，提出一种离散化的有限状态混沌映射，它允许精确的数值计算，没有舍入误差，通过选择合适的参数，映射能产生全周期长度的序列。仿真实验表明，归一化的序列平均周期对计算机精度不敏感，生成的二进制序列具有良好的相关性能。