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Using a H∞ filter assimilation procedure to estimate root zone soil water content

Root zone soil water content impacts plant water availability, land energy and water balances. Because of unknown hydrological model error, observation errors and the statistical characteristics of the errors, the widely used Kalman filter (KF) and its extensions are challenged to retrieve the root zone soil water content using the surface soil water content. If the soil hydraulic parameters are poorly estimated, the KF and its extensions fail to accurately estimate the root zone soil water. The H‐infinity filter (HF) represents a robust version of the KF. The HF is widely used in data assimilation and is superior to the KF, especially when the performance of the model is not well understood. The objective of this study is to study the impact of uncertain soil hydraulic parameters, initial soil moisture content and observation period on the ability of HF assimilation to predict in situ soil water content. In this article, we study seven cases. The results show that the soil hydraulic parameters hold a critical role in the course of assimilation. When the soil hydraulic parameters are poorly estimated, an accurate estimation of root soil water content cannot be retrieved by the HF assimilation approach. When the estimated soil hydraulic parameters are similar to actual values, the soil water content at various depths can be accurately retrieved by the HF assimilation. The HF assimilation is not very sensitive to the initial soil water content, and the impact of the initial soil water content on the assimilation scheme can be eliminated after about 5–7 days. The observation interval is important for soil water profile distribution retrieval with the HF, and the shorter the observation interval, the shorter the time required to achieve actual soil water content. However, the retrieval results are not very accurate at a depth of 100 cm. Also it is complex to determine the weighting coefficient and the error attenuation parameter in the HF assimilation. In this article, the trial‐and‐error method was used to determine the weighting coefficient and the error attenuation parameter. After the first establishment of limited range of the parameters, ‘the best parameter set’ was selected from the range of values. For the soil conditions investigated, the HF assimilation results are better than the open‐loop results. Copyright © 2010 John Wiley & Sons, Ltd.     

A new model for the vibration isolation via pile rows consisting of infinite number of piles

In this study, on the basis of the Floquet transform method, a numerical model for the simulation of the vibration isolation via multiple periodic pile rows with infinite number of piles is established. By means of the fictitious pile method due to Muki and Sternberg, the second kind of Fredholm integral equations for the pile rows are developed by using the fundamental solutions for the half‐space and the compatibility conditions between the piles and half‐space. Employing the Floquet transform method, integral equations for the pile rows in the wavenumber domain are then derived. Solution of the integral equations yields the wavenumber domain solution for the pile rows. The space domain solution can then be retrieved by inversion of the Floquet transform. Numerical results show that the proposed model with the Floquet transform method is in a good agreement with those of the conventional direct superposition method. On the basis of the new model, influences of the spacing between neighboring piles, the Young's modulus of the piles, and the pile length on the vibration isolation effect of the pile rows are investigated. Numerical simulations conducted in this study show that compared with the direct superposition method, the efficiency of the proposed model for simulation of the vibration isolation via pile rows is very high. Copyright © 2012 John Wiley & Sons, Ltd.     

Kepler's Equation and Newton's method

Power series solutions of Kepler's Equation associated with Lagrange, Levi-Civita and Stumpff may be obtained by Newton's method as an algorithm for formal power series.     

双基地激光测风雷达回波信号仿真研究

本文针对传统的体散射模型并未考虑大气不均匀性对信号传输的影响等问题,通过引入垂直非均匀的大气参数改进了模型,并利用其建立了体目标的双基地激光测风雷达方程,仿真了侧向散射回波信号,并与单基地雷达进行了对比分析。研究表明:水平方向上,双基地激光测风雷达的回波信号分布特征与单基地雷达差异较大,其回波信号等值线在近地面为卵形线,随着探测高度的增加,回波信号等值线逐渐变为以主、被动雷达为焦点的椭圆形,并最终趋近于圆形;垂直方向上,双基地激光测风雷达的回波信号随高度衰减剧烈,近地面的回波能量约为10^-10 J,4 km高度的回波能量约为10^-15J,在中低层大气(0~10 km),回波信号中气溶胶散射占比大,在高层大气(10 km以上),分子散射占比大。     

热源强迫的非线性惯性重力内波及其应用

利用动力学分析中的相平面方法,由z坐标系下的非绝热大气运动方程组导出了与非线性惯性重力内波有关的KdV方程,然后利用直接积分法得到两类有天气意义的孤立波解.初步建立了孤立波解与高原低涡的联系,进一步从理论上论证了高原低涡具有与热带气旋类低涡类似的涡眼和暖心结构的特征.     

Describing neutron stars by the relativistic mean field theory

Neutron stars are studied in the framework of the relativistic mean field theory of interacting nucleons, hyperons, and mesons. Within the hadronic freedom, the cores of neutron stars are found to be dominated by hyperons when the density is sufficiently high. The influence of hyperon coupling constants on the transition from a neutron star to a hyperon-dominated strange neutron star is also investigated. It is found that the transition density gets its minimum value when the ratio of hyperon coupling constant to nucleon's takes the value of 0.65, and the calculated maximum mass of the neutron star is 1.4 M which lies within the range of the observational results.     

一类非线性投影方程解的扰动迭代算法及其收敛性

在Hilbert空间中讨论了一类非线性投影方程解的扰动迭代算法及其收敛性分析．