Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

The electronic spectrum of VCr

The electronic spectrum of VCr has been studied using the complete-active-space self-consistent field complete-active-space second-order perturbation theory approach. Potential-energy curves for 12 electronic states have been computed. Transition energies, with respect to the X² ground state, for some of the calculated electronic states are (with possible experimental values within parentheses) 0.53 eV (0.56) for A²⁺, 1.03 eV (1.14) for A⁴, 1.20 eV (1.14) for B², 1.45 eV (1.51) for B⁴, 1.60 eV (1.51, 1.78) for C², and 1.61 eV (1.63) for A^4–. AcknowledgementsThe research reported in this communication was supported by a grant from the Swedish Natural Science Research Council (NFR). S. Alex and D.G. Leopold are acknowledged for providing results from their negative ion photoelectron spectroscopy on VCr.Contribution to Björn Roos Honorary Issue     

Rate Coefficient for Self-Association Reaction of CF2 Radicals Determined in the Afterglowof Low-Pressure C4F8 Plasmas

We have analyzed decay kinetics of CF₂ radicals in the afterglow of low-pressure, high-density C₄F₈ plasmas. The decay curve of CF₂ density has been approximated by the combination of first- and second-order kinetics. The surface loss probability evaluated from the frequency of the first-order decay process has been on the order of 10^–4. This small surface loss probability has enabled us to observe the second-order decay process. The mechanism of the second-order decay is self-association reaction between CF₂ radicals (CF₂+CF₂C₂F₄). The rate coefficient for this reaction has been evaluated as (2.6–5.3)×10^–14 cm³/s under gas pressures of 2 to 100 mTorr. The rate coefficient was found to be almost independent of the gas pressure and has been in close agreement with known values, which are determined in high gas pressures above 1 Torr.     

云制造平台加工能力分享调度优化研究

云制造平台加工能力分享的调度优化是云制造模式的核心运营问题。为提高云制造平台对参与能力分享企业资源的利用率,解决实际云制造需求环境下企业级制造资源调度问题,达到云制造平台动态实时的要求,以最小化工期和成本为目标函数,构建了基于平台并面向分享的云加工能力调度模型。为快速求解多个云任务订单的最优调度序列,引入任务简易编码和随机权重,设计了改进的二阶粒子群算法,并提出可分享加工能力时间窗的更新策略。最后,通过算例验证云制造平台加工能力调度机制的可行性和有效性。     

基于PSD的微位移测量系统研究

为了提高激光跟踪仪的跟踪精度,改善激光跟踪仪性能,根据测量光斑在PSD上的坐标可实现光斑位移测量的原理,研究了提高微位移测量精度的方法,设计出一种由PSD传感器、ADS8556模数转换器和TMS320F28335数字信号处理器构成的高性能微位移测量系统.该系统在硬件设计中引入二阶有源低通滤波器消除了部分噪声干扰;在软件设计中通过误差补偿和数字滤波进一步提高了数据可靠性.加入抗干扰设计后,获得的二维坐标波动量峰峰值均在6μm以内.实验表明,该系统可获得高精度的光斑坐标,为激光跟踪仪精密跟踪奠定良好基础.     

谱相关的数学关系与物理意义

周期性是自然现象和工程现象的基本特性之一,从复杂多变的、含有噪声的观测数据中发现周期性并测量其参数是信号处理的重要主题.谱相关是分析循环平稳信号二阶周期性的有力工具,本文研究谱相关的周期性解析功能的缘由、过程与特点.首先,梳理了谱相关理论体系中诸多重要概念之间的内在联系,建立了相互之间转换或映射的数学关系图;然后提出了按定义和转换关系逐步求解谱相关的方法.通过单周期信号的分析和每步操作效果与周期的对应关系,诠释了循环自相关、谱相关、无限循环谱和循环频率等重要概念的物理意义.     

线性调频信号低旁瓣脉压窗函数的优化设计

由于线性调频(LFM)信号的幅度谱不是标准的矩形形状,常用的窗函数有时无法将脉压旁瓣降得足够低,因此提出了LFM 信号低旁瓣脉压窗函数的优化设计方法。首先,将频域窗函数的求解表示为一个最优化问题,即在保证设计窗函数下的脉压主瓣与期望主瓣的差别小于给定值的条件下,使设计窗函数下的脉压旁瓣尽可能低;然后,将问题表示为标准二阶锥规划形式并求解。仿真实例表明,设计窗的脉压旁瓣显著低于海明窗的脉压旁瓣,设计窗脉压主瓣的无约束部分有所展宽,两个窗函数下脉压信噪比相同。     

二阶离散隐马尔科夫模型的严格定义及等价性质

隐马氏模型作为一种具有双重随机过程的统计模型,具有可靠的概率统计理论基础和强有力的数学结构,已被广泛应用于语音识别、生物序列分析、金融数据分析等领域.由于传统的一阶隐马氏模型无法表示更远状态距离间的依赖关系,就可能会忽略很多有用的统计特征,故有人提出二阶隐马氏模型的概念,但此概念并不严格.本文给出二阶离散隐马尔科夫模型的严格定义,并研究了二阶离散隐马尔科夫模型的两个等价性质.     

二阶差分方程的奇性边值问题

主要采用上下解方法,研究了一类带有奇性的二阶差分方程的两点边值问题,给出了一系列正解的存在条件.     

带次线性中立项的二阶广义Emden-Fowler微分方程的Philos型振动准则

研究一类带次线性中立项的二阶非线性广义Emden-Fowler时滞微分方程的振动性.利用Riccati变换和不等式技巧,在非正则条件下建立了该类方程多个简便的Philos型和Kamenev型新振动准则.所得定理也适应于包括经典Euler方程等线性非中立型方程,推广和改进了已有文献中的相应结果.最后还给出应用实例展示了所...