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.     

Seasonal abundance of non-commercial demersal fish in the eastern Mediterranean Sea in relation to hydrographic and sediment characteristics

Fish-habitat associations were investigated for twenty-five non-commercial demersal species in the Aegean Sea (eastern Mediterranean) using Generalized Additive Modeling techniques. Fishery related abundance indices, derived from experimental bottom trawl surveys, were linked to various habitat variables: substrate characteristics, area, season, depth, temperature and salinity. Depth was the most important factor for all species. Eleven species showed decreasing abundance with depth, while the remaining species were more abundant in specific depth zones either on the continental shelf or in the upper continental slope. Most species were associated with specific substratum characteristics such as the dry weight percentage of sand-gravel and the carbonate content. The dry weight percentage of sand-gravel in the sediments was selected as a predictor of the relative abundance of most (twenty three) species. Seasonal patterns in the relative abundance of species were observed, related in most cases to the seasonal differentiation of temperature. The effect of temperature was more pronounced in summer and autumn, when a marked thermocline is observed, while it was much less intense in winter. For most of the species, the preferable habitat was identified, that contributes valuable information for the successful implementation of an ecosystem approach to fisheries management.     

Spatial patterns of biodiversity in the Black Sea: An assessment using benthic polychaetes

The current study broadens the biodiversity information available for the Black Sea and neighbouring regions and improves our knowledge about the polychaete biogeographic patterns to be discerned in them. There appears to be a well-defined zoogeocline from the Marmara Sea and Bosphorus Strait to the inner parts of the region (Azov Sea), depicted both as a multivariate pattern and in terms of species (or taxa) numbers. The emergent multivariate pattern complies, to a certain extent, with Jakubova’s (1935) views: three main sectors can be defined in the basin: (a) Prebosphoric, (b) the Black Sea and, (c) the Azov Sea, whereas the Bosphorus Strait and Marmara Sea show less faunal affinities with the afore-mentioned sectors. Patterns derived both from the cosmopolitan and Atlanto-Mediterranean species closely follow the one coming from the polychaete species and genera inventories. As a general trend, species numbers decrease along with the decrease in salinity towards the inner parts of the region. The trend is homologous to that seen in the benthic invertebrate inventories of all the major European semi-enclosed regional seas. Salinity and food availability appear to be the dominant abiotic factors correlated, though weakly, with the various patterns deriving from the taxonomic/zoogeographic categories. With the exception of the Anatolia, polychaete inventories from all sectors appear to be random samples of the total inventory of the region, in terms of taxonomic distinctness values. Therefore, these sectoral inventories can be used for future biodiversity/environmental impact assessment studies. A massive invasion of Mediterranean species after the opening of the Black Sea, in the lower Quaternary period, appears to be the likely biogeographic mechanism through which the old Sarmatic fauna was almost completely replaced by species of marine origin.     

Climate change and impacts in the Eastern Mediterranean and the Middle East

The Eastern Mediterranean and the Middle East (EMME) are likely to be greatly affected by climate change, associated with increases in the frequency and intensity of droughts and hot weather conditions. Since the region is diverse and extreme climate conditions already common, the impacts will be disproportional. We have analyzed long-term meteorological datasets along with regional climate model projections for the 21st century, based on the intermediate IPCC SRES scenario A1B. This suggests a continual, gradual and relatively strong warming of about 3.5–7°C between the 1961–1990 reference period and the period 2070–2099. Daytime maximum temperatures appear to increase most rapidly in the northern part of the region, i.e. the Balkan Peninsula and Turkey. Hot summer conditions that rarely occurred in the reference period may become the norm by the middle and the end of the 21st century. Projected precipitation changes are quite variable. Annual precipitation is expected to decrease in the southern Europe – Turkey region and the Levant, whereas in the Arabian Gulf area it may increase. In the former region rainfall is actually expected to increase in winter, while decreasing in spring and summer, with a substantial increase of the number of days without rainfall. Anticipated regional impacts of climate change include heat stress, associated with poor air quality in the urban environment, and increasing scarcity of fresh water in the Levant.     

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0.61～0.76m/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0.76～0.93m/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.     

Vertical and rocking impedances for rigid rectangular foundations on soils with bounded non-homogeneity

The vertical and rocking response of rigid rectangular foundations resting on a linear-elastic, compressible, non-homogeneous half-space soil model is studied. The non-homogeneity is described by a continuous yet bounded increase of shear modulus with depth. The mixed boundary value problem is solved by means of the semi-analytical method of the subdivision of the foundation/soil contact area whereby the influence functions for the sub-regions are determined by integration of the corresponding surface-to-surface Green's functions for the particular soil model. Impedance functions are given for representative values of the non-homogeneity parameters, the Poisson's ratio and the foundation geometry over a wide range of frequencies. Significant features associated with the soil non-homogeneity are pointed out. Copyright © 1999 John Wiley & Sons Ltd.     

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.