Applications of Lodrigues Matrix in 3D Coordinate Transformation

Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: ① the traditional rotation angles θ , φ ,ψ are substituted with a , b, c which are three re-spective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.     

一类带阻尼项Duffing型方程周期解的存在性

考虑带有阻尼项的Duffing型方程的边值问题,在Banach空间上运用Leray-Schauder度理论证明其周期解的存在性。     

中尺度大气波动的波谱和谱函数——数学模型和计算方法

作者得到了准二维Boussinesq方程组，并用其研究了中尺度大气波动的波谱和谱函数。在一定条件下对该方程组线性化并取标准模后，可将其初边值问题转化为矩阵的广义特征值问题来进行数值求解，这样就可知原问题波谱和谱函数的性质。当无基本流且取地转参数、层结参数为常数时，可求得其波谱和谱函数的解析解。此时该模式中仅包含有一对重力惯性内波模态，且各模态均是简谐波；模态越高，垂直波数越大则波动传播得越慢，所有的模态均为离散谱，并存在聚点。对此作者用数值解作了验算，结果表明，该数值求解方案合理可行，对不太高的模态其精度也令人满意。在无基本流然而考虑层结的垂直变化后，则一般无法求取解析解，为此进行了数值求解。这时该模式仍仅包含有一对重力惯性内波的离散谱模态，不过由于层结参数的变化，各模态结构与简谐波出现了偏差。     

MCZT在气枪震源信号频谱分析中的应用

气枪震源信号是短时非平稳信号,采用频谱细化算法能提高频谱分析的准确性。首先进行了改进线性调频Z变换(MCZT)和FFT两种频谱分析算法的误差仿真计算,然后进行气枪震源的水下子波信号和地震波信号的对比计算。结果表明MCZT计算误差较小、计算时间较少,能有效提高气枪震源信号频率和幅度特征提取的准确性,是气枪震源信号频谱特征分析的一个有效方法。     

Spatio-temporal characteristics of small-scale wave–current ripples on the Ameland ebb-tidal delta

Ebb-tidal deltas are highly dynamic environments affected by both waves and currents that approach the coast under various angles. Among other bedforms of various scales, these hydrodynamics create small-scale bedforms (ripples), which increase the bed roughness and will therefore affect hydrodynamics and sediment transport. In morphodynamic models, sediment transport predictions depend on the roughness height, but the accuracy of these predictors has not been tested for field conditions with strongly mixed (wave–current dominated) forcing. In this study, small-scale bedforms were observed in the field with a 3D Profiling Sonar at five locations on the Ameland ebb-tidal delta, the Netherlands. Hydrodynamic conditions ranged from wave dominated to current dominated, but were mixed most of the time. Small-scale ripples were found on all studied parts of the delta, superimposed on megaripples. Even though a large range of hydrodynamic conditions was encountered, the spatio-temporal variations in small-scale ripple dimensions were relatively small (height 0.015 m, length 0.11 m). Also, the ripples were always highly three-dimensional. These small dimensions are probably caused by the fact that the bed consists of relatively fine sediment. Five bedform height predictors were tested, but they all overestimated the ripple heights, partly because they were not created for small grain sizes. Furthermore, the predictors all have a strong dependence on wave- and current-related velocities, whereas the ripple heights measured here were only related to the near-bed orbital velocity. Therefore, ripple heights and lengths in wave–current-dominated, fine-grained coastal areas ( mm) may be best estimated by constant values rather than values dependent on the hydrodynamics. In the case of the Ameland ebb-tidal delta, these values were found to be m and m. ©2019 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

双轴压缩条件下绿片岩的蠕变规律研究

在锦屏二级水电站辅助洞绿片岩的双轴压缩蠕变试验结果的基础上,研究了应力路径对双轴压缩蠕变变形的影响。结果表明:当侧向应力相同时,随着轴向应力的增加,轴向稳态蠕变阶段的变形速率逐渐增加;当轴向应力相同时,随着侧向应力的增加,轴向稳态蠕变阶段的变形速率逐渐减小。     

非线性惯性重力内波的特征及天气意义

对大气非线性惯笥重力内波方程组,利用相平面分析法导出了相应的ＫｄＶ方程。采用直接积分法求出两类有意义的孤立波解,讨论了波解的基本特征,并着重分析了一类奇异孤立波与某些天气系统（如青藏高原５００ｈＰａ低涡）的可能联系。     

甘肃河西走廊沙尘暴与赤道中,东太平洋海温之间的遥相关分析

春、夏季甘肃河西走廊沙尘暴发生次数与赤道中、东太平洋海温之间遥相关分析结果表明：春、夏季河西走廊沙尘暴发生次数与前二年赤道中、东太平洋海温的负相关最好,时间过远或过近,相关性反而较差。利用前期的赤道中、东太平洋海温可以较好地预报出河西走廊春季沙尘暴发生的多寡。     

工业测量系统在多波束天线安装检测中的应用

根据多波束天线测量和检测的实际情况 ,主要介绍了多波束天线的数学模型、解算方法、测量方案的设计以及调整量的计算等问题。最后对实测结果进行了分析。