Some remarks on the Gaussian beam summation method

Summary. Recently, a method using superposition of Gaussian beams has been proposed for the solution of high-frequency wave problems. The method is a potentially useful approach when the more usual techniques of ray theory fail: it gives answers which are finite at caustics, computes a nonzero field in shadow zones, and exhibits critical angle phenomena, including head waves. Subsequent tests by several authors have been encouraging, although some reported solutions show an unexplained dependence on the 'free' complex parameter ε which specifies the initial widths and phases of the Gaussian beams.
We use methods of uniform asymptotic expansions to explain the behaviour of the Gaussian beam method. We show how it computes correctly the entire caustic boundary layer of a caustic of arbitrary complexity, and computes correctly in a region of critical reflection. However, the beam solution for head waves and in edge-diffracted shadow zones are shown to have the correct asymptotic form, but with governing parameters that are explicitly ε-dependent. We also explain the mechanism by which the beam solution degrades when there are strong lateral inhomogeneities. We compare numerically our predictions for some representative, model problems, with exact solutions obtained by other means.     

新四面体理论与磁极倒转

本文以最新修正了的新四面体理论模型来解释地球磁极倒转现象及其规律性。文章简要回顾了依附于收缩说的地球四面体理论的兴衰,接着简述了应归属于脉动说范畴的新四面体理论研究的最新进展——地球多级驻波(式)脉动演化模型。新模型可概括为:地球的形态在演化过程中呈“准球体→负准四面体→准球体→正准四面体→准球体→…”的驻波脉动;在呈每种形体的大阶段中,又包含着次级、更次级的驻波脉动。然后论述了地磁极性倒转的规律性(即多变→固定[正向]→多变→固定[反向] →多变→…)以及新模型对其所做的解释(即固定正向和固定反向阶段分别为负和正准四面体阶段,多变阶段为准球体阶段)。     

水平轴潮流能叶轮尖速比特性分析研究

针对设计尖速比对水平轴潮流能叶轮动力特性的影响问题开展研究工作。基于叶素-动量理论建立叶轮动力特性仿真模型,以叶片数量分别为2、3、4的叶轮为对象,考察设计尖速比对叶轮的功率系数的影响。研究结果表明:设计尖速比越大的叶轮,其最大效率也越高;叶片数量多的叶轮,其功率系数略优于叶片数量少的叶片。结合分析结果,给出了水平轴潮流能叶轮的设计尖速比的选择建议。     

Sustainability evaluation of different systems for sea cucumber (Apostichopus japonicus) farming based on emergy theory

Emergy analysis is effective for analyzing ecological economic systems. However, the accuracy of the approach is af-fected by the diversity of economic level, meteorological and hydrological parameters...     

经济空间场与ESDA结合的公共卫生事件应急策略制定

新型冠状病毒肺炎疫情引起了人们对国家公共卫生事件应对能力的广泛关注。基于波及效应梯度场提出了生产诱发梯度,进一步完善了经济空间场理论,并将其与探索性空间数据分析(exploratory spatial data analysis,ESDA)相结合,对医药制造业波及效应及空间布局进行了研究,制定了有效的公共卫生事件应急策略。经济空间场理论分析结果揭示了产业经济空间中医药制造业与各产业部门之间的波及效应,并由此得到了医药密切相关产业。同时,经济空间场理论与ESDA方法的结合能在区分中国大陆各省空间聚集类型的基础上,评估各省公共卫生事件的应对能力,从而为各省提出相应的应急策略和医药制造业发展建议。该方法综合考虑了产业波及效应和产业空间布局现状,不仅能够促进各省医药制造业的健康合理发展,也有助于增强各省突发公共卫生事件的应对能力。     

Mattig's relation and dynamical distance indicators

We discuss how the redshift (Mattig) method in the Friedmann cosmology relates to dynamical distance indicators based on Newton's gravity (Teerikorpi 2011). It belongs to the class of indicators where the relevant length inside the system is the distance itself (in this case the proper metric distance). As the Friedmann model has a Newtonian analogy, its use to infer distances has instructive similarities to classical dynamical distance indicators. In view of the theoretical exact linear distance‐velocity law, we emphasize that it is conceptually correct to derive the cosmological distance via the route: redshift (primarily observed) → space expansion velocity (not directly observed) → metric distance (physical length in “cm”). Important properties of the proper metric distance are summarized. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

方程误差系统的多新息辨识方法

多新息方法可以用于线性系统和非线性系统的自适应滤波、参数估计、自校正控制、自适应故障检测与诊断等.线性系统包括两种基本类型:方程误差类系统和输出误差类系统.本文将多新息辨识应用到方程误差滑动平均(EEMA)系统(即CARMA系统),研究多新息增广随机梯度算法和多新息增广最小二乘算法,应用到方程误差自回归滑动平均(EEARMA)系统(即CARARMA系统),提出基于分解的多新息广义增广随机梯度算法和基于分解的多新息广义增广最小二乘算法,以及基于滤波的多新息广义增广随机梯度算法和基于滤波的多新息广义增广最小二乘算法.