Note on Kepler's problem with variable angular momentum

Based on the equations of planar motion with drag used in point dynamics, a simple derivation is presented that shows how a constant Keplerian (elliptical) orbit can be obtained with a non-central force field and variable angular momentum.     

GNSS控制网坐标移动转换的三次曲面拟合法

针对2000国家大地坐标到海南独立坐标系需要保密参数的局限性,该文利用三次曲面拟合坐标移动转换法进行2000国家大地坐标系到海南独立坐标转换,解决了在没有海南独立坐标系参数的情况下无法进行坐标转换的困扰,确保参数保密性。测试比较结果表明,三次曲面拟合法移动坐标转换法能够提高坐标转换精度。     

An Explicit High Resolution Scheme for Nonlinear Shallow Water Equations

The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe＇ s flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws （MUSCL） variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.     

The scaling of the meridional overturning with the meridional temperature gradient in idealised general circulation models

The scaling law linking the strength of the meridional overturning to the surface meridional temperature gradient is re-examined in two ocean general circulation models at coarse resolution in an idealised single-hemisphere setting. Two sets of results are presented, where the surface meridional temperature gradient is decreased either by increasing the northernmost temperature and keeping the equator temperature fixed, or by decreasing the equator temperature and keeping the northernmost temperature fixed. The maximum of the meridional overturning first increases and then decreases when the northernmost temperature is gradually increased, whereas the maximum overturning decreases monotonically when the equator temperature is decreased. No scaling law can be derived when the northernmost temperature is increased, whereas a 2/3 power law is found when the temperature is decreased at the equator. The behaviour of the overturning is strongly influenced by the vigour and, particularly, the spatial patterns of convection, which vary substantially between the two sets and which control the horizontal and vertical density gradients at high latitudes.     

Declining Union Contract Coverage and Increasing Income Inequality in U.S. Metropolitan Areas

We focus on the association between the institutional factor of union contract coverage rates among workers and the variation in income inequality across a set of sixty-four metropolitan areas of the United States for the years 1990, 2000, and 2010. We use market variables of relative skills and relative education and demographic variables of race and gender as controls in our regression models. We also specify a set of models that substitute right-to-work status for union contract coverage rates. Our primary finding is that union contract coverage rates are temporally consistent and significant negative covariates of income inequality, as measured by Gini coefficients, across the metropolitan areas. Further, metropolitan areas in right-to-work states have consistently and significantly higher levels of inequality than expected given the control variable effects. Our interpretation of the primary finding is that issues of labor power and class play a clearly important role in contributing to income inequality in the set of metropolitan areas used in the analysis.     

Scaling Variances of Scalars in a Convective Boundary Layer Under Different Entrainment Regimes

For the presentation and analysis of atmospheric boundary-layer (ABL) data, scales are used to non-dimensionalise the observed quantities and independent variables. Usually, the ABL height, surface sensible heat flux and surface scalar flux are used. This works well, so long as the absolute values of the entrainment ratio for both the scalar and temperature are similar. The entrainment ratio for temperature naturally ranges from −0.4 to −0.1. However, the entrainment ratio for passive scalars can vary widely in magnitude and sign. Then the entrainment flux becomes relevant as well. The only customary scalar scale that takes into account both the surface flux and the entrainment flux is the bulk scalar scale, but this scale is not well-behaved for large negative entrainment ratios and for an entrainment ratio equal to −1. We derive a new scalar scale, using previously published large-eddy simulation results for the convective ABL. The scale is derived under the constraint that scaled scalar variance profiles are similar at those heights where the variance producing mechanisms are identical (i.e., either near the entrainment layer or near the surface). The new scale takes into account that scalar variance in the ABL is not only related to the surface flux of that scalar, but to the scalar entrainment flux as well. Furthermore, it takes into account that the production of variance by the entrainment flux is an order of magnitude larger than the production of variance by the surface flux (per unit flux). Other desirable features of the new scale are that it is always positive (which is relevant when scaling standard deviations) and that the scaled variances are always of order 1–10.     

尺度推绎研究中的几点基本问题

尺度推绎作为将一个尺度上的信息推绎到另一个尺度上的过程,具有尺度依赖性、模型非线性和研究的复杂性等特征,其理论基础主要有等级理论、分形理论等,其研究的关键问题表现为尺度选择与信息提取问题、尺度域与特征尺度问题、模型问题等方面。针对相邻尺度推绎和跨尺度推绎两种情况,还介绍了不同情况下尺度推绎研究的基本思路。尺度推绎作为现代地学、生态学等学科研究的重要问题之一,其发展需要多学科的交流和理论与技术的创新。     

薄冲积层下开采地表动态移动规律与特征

位于采煤影响区的高压线、输气输油管道、河道等设施对地表动态移动极为敏感。以甘肃某煤矿在金沙河下开采为背景,通过现场地表移动监测,获得薄冲积层条件下综放开采地表动态移动变形规律。研究表明：薄冲积层下综放开采地表具有下沉移动起始期很短、活跃期较长等特点。地表移动活跃期位于工作面前方110 m至工作面后方400 m范围内,历时185 d,期间地表点下沉量可达到该点总下沉量的90.7%;地表移动剧烈期在工作面后方50 m至150 m范围内,但剧烈扰动时间相对较短,历时约60 d。基于测点下沉曲线为S型分布、下沉速度曲线类似为正态分布特点,建立了考虑开采时间和工作面推进速度因素的地表下沉及下沉速度动态模型,并追踪刻画出地表测点往复式下沉与水平运动的轨迹。薄冲积层下开采,地表裂缝更易平行于工作面走向方向发育,并且随工作面的推进,地表裂缝具有前移和密集区向工作面外侧小范围扩大的时空特征。     

对浙江地质找矿的几点思考

本文根据矿床分布的分形丛集性、亲缘性，矿床密度分布律和储量分布律。对浙江地质找矿提出了一些新认识，并指出有待进一步研究的关键问题。