Planetary theories with the aid of the expansions of elliptic functions

For coplanar circular orbits, the mutual perturbations between two bodies can be expressed in term of the argument of Jacobian elliptic functions instead of the difference of the mean longitudes. For a given pair of planets, such a change of time variable improves the convergence of the developments. At the first order of planetary masses an integration of Lagrange's equations for the osculating elements is performed. When compared to classical developments the results are reduced by an important factor. The method is then extended to the mutual perturbations of Jupiter and Saturn, at any order of planetary masses, either with Fourier series with two arguments, or with one argument solely, taking advantage of the close commensurability of the mean motions.     

Performance of various similarity functions for nondimensional wind and temperature profiles in the surface layer in stable conditions

The linear functions for non-dimensional wind and temperature profiles are commonly used to describe the surface layer fluxes in atmospheric models. However, their applicability is limited to smaller values of the stability parameter z/L (where z is the height above ground and L is the Obukhov length) i.e. z/L < 1.0. These linear functions have been modified (Webb 1970, Quart. J. Roy. Meteor. Soc. 96, 67–90; Clarke 1970, Quart. J. Roy. Meteor. Soc. 96, 91–114; Hicks 1976, Quart. J. Roy. Meteor. Soc. 102, 535–551; Beljaars and Holtslag 1991, J. Appl. Meteorol. 30, 327–341; Cheng and Brutsaert 2005, Boundary-Layer Meteorol. 114, 519–538) over the years for calculating fluxes when z/L > 1.0 under strongly stable conditions. In view of this, the objective of the present study is to analyze the performance of these similarity functions to compute surface fluxes in stable conditions.The meteorological observations from the Cooperative Atmosphere-Surface Exchange Study (CASES-99) experiment are utilized for computing the surface fluxes in stable conditions. The computed fluxes are found to be reasonably close to those observed. The ratio of observed to computed fluxes reveals that the computed fluxes are close to the observations for all the similarity functions for z/L < 1.0 whereas the computed values show relatively a large scatter from observations for z/L > 1.0. The computed values of u and heat flux do not show significant differences from those observed at 99% confidence limit. The performance of all the similarity functions considered here is found to be comparable to each other in strongly stable conditions.     

Gap Filling and Quality Assessment of CO2 and Water Vapour Fluxes above an Urban Area with Radial Basis Function Neural Networks

Vertical turbulent fluxes of water vapour, carbon dioxide, and sensible heat were measured from 16 August to the 28 September 2006 near the city centre of Münster in north-west Germany. In comparison to results of measurements above homogeneous ecosystem sites, the CO₂ fluxes above the urban investigation area showed more peaks and higher variances during the course of a day, probably caused by traffic and other varying, anthropogenic sources. The main goal of this study is the introduction and establishment of a new gap filling procedure using radial basis function (RBF) neural networks, which is also applicable under complex environmental conditions. We applied adapted RBF neural networks within a combined modular expert system of neural networks as an innovative approach to fill data gaps in micrometeorological flux time series. We found that RBF networks are superior to multi-layer perceptron (MLP) neural networks in the reproduction of the highly variable turbulent fluxes. In addition, we enhanced the methodology in the field of quality assessment for eddy covariance data. An RBF neural network mapping system was used to identify conditions of a turbulence regime that allows reliable quantification of turbulent fluxes through finding an acceptable minimum of the friction velocity. For the data analysed in this study, the minimum acceptable friction velocity was found to be 0.15 m s⁻¹. The obtained CO₂ fluxes, measured on a tower at 65 m a.g.l., reached average values of 12 μmol m⁻² s⁻¹ and fell to nighttime minimum values of 3 μmol m ⁻² s⁻¹. Mean daily CO₂ emissions of 21 g CO₂ m⁻²d ⁻¹ were obtained during our 6-week experiment. Hence, the city centre of Münster appeared to be a significant source of CO₂. The half-hourly average values of water vapour fluxes ranged between 0.062 and 0.989 mmol m⁻² s⁻¹and showed lower variances than the simultaneously measured fluxes of CO₂.     

Analysis of the three-dimensional stellar velocity field using vector spherical functions

We apply vector spherical functions to problems of stellar kinematics. Using these functions allows all of the systematic components in the stellar velocity field to be revealed without being attached to a specific physical model. Comparison of the theoretical decomposition coefficients of the equations for a particular kinematical model with observational data can provide precise information about whether the model is compatible with the observations and can reveal systematic components that are not described by this model. The formalism of vector spherical functions is particularly well suited for analyzing the present and future (e.g., GAIA) catalogs containing all three velocity vector components: the propermotions in both coordinates and the radial velocity. We show that there are systematic components in the proper motions of Hipparcos stars that cannot be interpreted in terms of the linear Ogorodnikov-Milne model. The same result is also confirmed by an analysis of the radial velocities for these stars.     

Fault detection by reflected surface waves based on ambient noise interferometry

Detecting subsurface fault structure is important for evaluating potential earthquake risks associated with active faults. In this study, we propose a new method to detect faults using reflected surface waves observed in ambient noise cross correlation functions. Ambient noise tomography using direct surface waves obtained from ambient noise interferometry has been widely used to characterize active fault zones. In cases where a strong velocity contrast exists across the fault interface, fault-reflected surface waves are expected. We test this idea using a linear array deployed in the Suqian segment of Tanlu fault zone in Eastern China. The fault-reflected surface waves can be clearly seen in the cross-correlation functions of the ambient noise data, and the spatial position of the fault on the surface is close to the stations where the reflected signals first appear. Potentially reflected surface waves could also be used to infer the dip angle, fault zone thickness and the degree of velocity contrast across the fault by comparing synthetic and observed waveforms.     

Analytical evaluation of the relativistic thermodynamic functions using binomial expansion theorem and incomplete Gamma functions

A simple evaluation algorithm for calculation of the fermions and bosons relativistic thermodynamic functions with high accuracy is presented. This method is based on the use of the binomial expansion theorems and incomplete Gamma functions. The importance of this result is that it enables a series analytical formula to determine the thermodynamic functions of fermions and bosons in cases of degeneracy and relativity. The formulas obtained are numerically stable for ψ < 0. Examples of comparative calculations are given. Numerical results verify the effectiveness of the present approach and they are in good agreement with literature.     

Sediment cascades and the entangled relationship between human impact and natural dynamics at the pre-pottery Neolithic site of Göbekli Tepe,Anatolia

This study presents a meta-analysis of radiocarbon ages for the environs of Göbekli Tepe – one of the oldest monumental structures worldwide – using cumulative probability functions to diachronically assess phases of geomorphodynamic activity as controlled by natural or anthropogenic drivers. We employ sediment cascades as a heuristic framework to study the complex responses of the geomorphological system to various triggers at local to supra-regional scales. Possible triggers include climatic variability as documented by supra-regional hydroclimatic proxy data, regional demographic trends, and local to regional socioeconomic developments such as the emergence of sedentism or the introduction and dispersal of livestock herding. Our results show that phases of intensified geomorphodynamic activity occurred between ca. 7.4–7.0 and 5.8–3.3 ka BP. These phases roughly coincide with phases of population growth in southern Turkey and climatic variations in Turkey and the Levant. The phase between ca. 5.8–3.3 ka BP also corresponds to the time when organized agriculture and the seeder plough were introduced. Also, the identified phases are in agreement with the general trend of varying geomorphodynamic activity in the Eastern Mediterranean as driven by human impact and climatic change. However, neither the Younger Dryas–Holocene transition nor the development of herding during the Pre-Pottery Neolithic left a clear signature. We demonstrate how the different depositional environments in the studied landscape compartments vary with respect to their spatiotemporal coverage and discuss challenges when trying to understand processes that once shaped landscapes of past societies. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd     

基于生态位理论的东北三省政府干预强度与市场化水平格局演变研究

以“政府干预强度”和“市场化水平”为研究对象,通过对其生态系统的剖析,构建相应的评价指标体系及其生态位模型,并选取东北三省地级市为评价对象,对其“强政府弱市场”格局和演变趋势进行分析。定量分析的主要结论为：东北三省普遍存在“强政府弱市场”现状,其中黑龙江省最为突出,其次为吉林省、辽宁省;东北三省“强政府弱市场”格局出现多次波动,仅2003~2005年降幅较高,说明2003年“东北振兴战略”影响效果的持续性较短;东北各地市“强政府弱市场”格局具有明显的区域溢出效应,格局较明显的区域主要集中在离中心城市或沿海口岸较远的黑龙江省北部以及辽宁省、吉林省的部分内陆城市。     

高阶非线性系统自适应模糊有限时间状态约束控制

针对一类具有状态约束的非严格反馈高阶非线性系统,研究一种自适应模糊有限时间跟踪控制问题.首先,利用模糊逻辑系统逼近不确定性非线性函数,在此基础上,采用障碍Lyapunov函数,解决状态约束问题,通过障碍加幂积分方法和反步递推技术,提出了一种有限时间控制设计方法.在有限时间Lyapunov稳定意义下,严格证明闭环系统半全局实际有限时间稳定且系统的状态不超出给定的约束边界,并实现了有限时间跟踪控制目标.最后,仿真研究进一步验证了所提出控制方法的有效性.     

狭长区域下基于正交法的GPS高程拟合研究

将GPS点大地高直接转换成正常高,越来越广泛地应用于建立高程控制网的实践中。而要保证GPS点高程精度的关键是高程异常拟合模型选择的合理性。文中介绍了在狭长带状区域下利用正交函数法拟合GPS点高程的数学模型。并利用试验数据进行比对分析。结果表明,文中提出的方法计算具有算法稳定,成果合理的特点。