Formal Integrals and Nekhoroshev Stability in a Mapping Model for the Trojan Asteroids

A symplectic mapping model for the co-orbital motion (Sándor et al., 2002, Cel. Mech. Dyn. Astr. 84, 355) in the circular restricted three body problem is used to derive Nekhoroshev stability estimates for the Sun–Jupiter Trojans. Following a brief review of the analytical part of Nekhoroshev theory, a direct method is developed to construct formal integrals of motion in symplectic mappings without use of a normal form. Precise estimates are given for the region of effective stability based on the optimization of the size of the remainder of the formal series. The stability region found for t=10¹⁰ yrs corresponds to a libration amplitude D_p=10.6°. About 30% of asteroids with accurately known proper elements (Milani, 1993, Cel. Mech. Dyn. Astron. 57, 59), at low eccentricities and inclinations, are included within this region. This represents an improvement with respect to previous estimates given in the literature. The improvement is due partly to the choice of better variables, but also to the use of a mapping model, which is a simplification of the circular restricted three body problem.     

The summer maximum in total ozone over northwest Europe

Station records of ozone observations have been critically reviewed to investigate the reality of the reported maximum in total ozone over northwest Europe in July. The existence of a longitudinal excess of ozone over the British Isles is confirmed but strong horizontal gradients can be verified only over central Europe and there is no evidence for east-west gradients over the Atlantic. Ozone sounding data as well as total ozone daily variability make it most plausible that the ozone excess over northwest Europe is confined to the lower stratosphere. The isopleths in the region of strong ozone gradients are parallel to the mean flow at 100 mb as required by the calculated constraint on the magnitude of the mean flow advection. It is proposed that analyses of the ozone distribution over oceanic areas could be improved by extending ozone isopleths parallel to the mean lower stratospheric flow from land areas where the pattern is better defined.     

Universal properties of escape in dynamical systems

This paper summarizes a numerical study of the escape properties of three two-dimensional, time-independent potentials possessing different symmetries. It was found, for all three cases, that (i) there is a rather abrupt transition in the behaviour of the late-time probability of escape, when the value of a coupling parameter, , exceeds a critical value, 2. For e > e2, it was found that (ii) the escape probability manifests an initial convergence towards a nearly time-independent value, p _o(), which exhibits a simple scaling that may be universal. However, (iii) at later times the escape probability slowly decays to zero as a power-law function of time. Finally, it was found that (iv) in a statistical sense, orbits that escape from the system at late times tend to have short time Lyapounov exponents which are lower than for orbits that escape at early times.     

中国鲤科鱼类游泳能力综合分析和应用

该研究利用学术论文数据库筛选出中国鲤科鱼类游泳能力相关论文115篇,并用Origin软件进行了数据统计分析,旨在归纳和分析中国鲤科鱼类游泳能力并建立估算方法,可为正处于规划阶段和可行性研究阶段的过鱼设施流速设计提供依据.结果表明：（1）鱼类游泳速度与鱼体长度具有显著的非线性相关关系,据此建立了一系列幂函数经验公式,可为游泳能力和过鱼设施研究及设计提供依据.（2）依据所得到的经验公式和协方差分析可知,喜流水型鲤科鱼类的游泳能力>广适型>喜静水型.根据该研究得到的经验公式并结合行业规范和文献资料,对正处于规划阶段和可行性研究阶段过鱼设施流速设计的建议如下：西南地区以裂腹鱼成鱼为主要过鱼对象的过鱼设施进鱼口吸引流速范围为0.61~0.76 m/s,通道内最高流速阈值为1.28 m/s;长江中下游以四大家鱼成鱼为主要过鱼对象的进鱼口吸引流速范围为0.76~0.93 m/s,通道内最高流速阈值为1.49 m/s,以四大家鱼幼鱼为主要过鱼对象的进鱼口吸引流速范围为0.42~0.62 m/s,通道内最高流速阈值可为0.82 m/s.     

Secondary resonances and the boundary of effective stability of Trojan motions

One of the most interesting features in the libration domain of co-orbital motions is the existence of secondary resonances. For some combinations of physical parameters, these resonances occupy a large fraction of the domain of stability and rule the dynamics within the stable tadpole region. In this work, we present an application of a recently introduced ‘basic Hamiltonian model’ \(H_\mathrm{b}\) for Trojan dynamics (Páez and Efthymiopoulos in Celest Mech Dyn Astron 121(2):139, 2015; Páez et al. in Celest Mech Dyn Astron 126:519, 2016): we show that the inner border of the secondary resonance of lowermost order, as defined by \(H_\mathrm{b}\), provides a good estimation of the region in phase space for which the orbits remain regular regardless of the orbital parameters of the system. The computation of this boundary is straightforward by combining a resonant normal form calculation in conjunction with an ‘asymmetric expansion’ of the Hamiltonian around the libration points, which speeds up convergence. Applications to the determination of the effective stability domain for exoplanetary Trojans (planet-sized objects or asteroids) which may accompany giant exoplanets are discussed.     

On the variability of the surface environment response to synoptic forcing over complex terrain: a multivariate data analysis approach

Synoptic climatology relates the atmospheric circulation with the surface environment. The aim of this study is to examine the variability of the surface meteorological patterns, which are developing under different synoptic scale categories over a suburban area with complex topography. Multivariate Data Analysis techniques were performed to a data set with surface meteorological elements. Three principal components related to the thermodynamic status of the surface environment and the two components of the wind speed were found. The variability of the surface flows was related with atmospheric circulation categories by applying Correspondence Analysis. Similar surface thermodynamic fields develop under cyclonic categories, which are contrasted with the anti-cyclonic category. A strong, steady wind flow characterized by high shear values develops under the cyclonic Closed Low and the anticyclonic H–L categories, in contrast to the variable weak flow under the anticyclonic Open Anticyclone category.     

Assessment of interpolated ERA-40 reanalysis temperature and precipitation against observations of the Balkan Peninsula

Due to their ready availability and temporal and spatial consistency, reanalysis data are widely used within the climate community. Nevertheless, higher spatial resolutions are often required and statistical interpolation techniques are applied to increase the data resolution. This work aims to derive a set of high spatial resolution data through three-dimensional interpolation of daily temperature and precipitation. Thin plate spline interpolation has been chosen and used to interpolate ERA-40 temperature and precipitation from a coarse grid (110 km) into a finer one of 1-km spatial resolution. The study evaluates the method by comparing the simulated variables with available in situ meteorological measurements. The chosen stations are distributed over the study region and, most importantly, contain information from a range of altitudes. The results indicate that accounting for the topography in the interpolation process improves the comparisons, with the biggest improvements being evident in the most mountainous areas. The method is found to be better in estimating temperature than precipitation fields. Moreover, the method performs better for maximum temperature in high altitudes and for minimum temperature in low altitudes.     

Time-harmonic boussinesq problem for a continuously non-homogeneous soil

An analytical solution is presented for the response of a non-homogeneous, compressible, elastic half-space to a time-harmonic vertical point load on its surface. The shear modulus is assumed to increase continuously with depth. The model is chosen so as to describe uniformly deposited cohesionless soils. Expressions for displacements and stresses in the interior of the half-space medium are derived by means of Hankel transforms and contour integration. Selected numerical results are presented to demonstrate the influence of non-homogeneity. Finally, some effects are pointed out to be used in connection with vibration tests for subsoil investigation.     

Evaluation of Urban Local-Scale Aerodynamic Parameters: Implications for the Vertical Profile of Wind Speed and for Source Areas

Nine methods to determine local-scale aerodynamic roughness length \((z_{0})\) and zero-plane displacement \((z_{d})\) are compared at three sites (within 60 m of each other) in London, UK. Methods include three anemometric (single-level high frequency observations), six morphometric (surface geometry) and one reference-based approach (look-up tables). A footprint model is used with the morphometric methods in an iterative procedure. The results are insensitive to the initial \(z_{d}\) and \(z_{0}\) estimates. Across the three sites, \(z_{d}\) varies between 5 and 45 m depending upon the method used. Morphometric methods that incorporate roughness-element height variability agree better with anemometric methods, indicating \(z_{d}\) is consistently greater than the local mean building height. Depending upon method and wind direction, \(z_{0}\) varies between 0.1 and 5 m with morphometric \(z_{0}\) consistently being 2–3 m larger than the anemometric \(z_{0}\). No morphometric method consistently resembles the anemometric methods. Wind-speed profiles observed with Doppler lidar provide additional data with which to assess the methods. Locally determined roughness parameters are used to extrapolate wind-speed profiles to a height roughly 200 m above the canopy. Wind-speed profiles extrapolated based on morphometric methods that account for roughness-element height variability are most similar to observations. The extent of the modelled source area for measurements varies by up to a factor of three, depending upon the morphometric method used to determine \(z_{d}\) and \(z_{0}\).