Dynamical behaviour of the primitive asteroid belt

In this paper we consider the dynamical evolution and orbital stability of objects in the asteroid belt. A simple physical model, including full gravitational perturbations from both giant planets, is used to compute the dynamical evolution of 1000 test particles simulating the primitive asteroids. The criterion of planet crossing (or close approach in the case of resonant objects) is used to reject particles from the simulation. 44 per cent of the particles survived for the whole time-span covered by the numerical integration (∼10⁹ yr).
The 4:1, 3:1 and to a lesser extent the 2:1 Kirkwood gaps are formed in ∼10⁷ yr of evolution, representing direct numerical evidence about their gravitational origin.
We found that the rms eccentricity and inclination of the sample experience a fast increase during the first 10⁶ yr. The final rms eccentricity is 0.11, ∼60 per cent smaller than the present rms eccentricity (0.17). Nevertheless, the gravitational action of the giant planets suffices to prevent the formation of large objects, allowing catastrophic collisions and the subsequent depletion of material from this zone of the Solar system. The excited eccentricity by Jupiter and Saturn may favour mutual encounters and the further increase of the relative velocities up to their present values.     

Filaments within the Perseid meteoroid stream and their coincidence with the location of mean-motion resonances

Positions of 17 filaments found inside the Perseid meteoroid stream by method of indices are compared with those of low-order mean-motion resonances with Jupiter and Saturn. By this comparing, the Jupiter and Saturn branches of the Perseid stream were identified. The existence of gaps in the distribution of the semi-major axes of the Perseids is confirmed using the more numerous material of a new version of the IAU Meteor Data Center Catalogue. Our integrations of the motion of particles in the Perseid stream lead to an extraordinary important fact. The found filaments are located in close proximity of strong resonances. They represent, with a high probability, increased numbers of particles gravitationally expelled from a resonant gap and (temporary) settled down in its close proximity.     

Efstadalsvatn – a multi-proxy study of a Holocene lacustrine sequence from NW Iceland

Multi-proxy data, both lithostratigraphic and biostratigraphic, are presented from Efstadalsvatn, a lake in NW Iceland. The sequence covers the period 10,000 to 3500 ¹⁴C yr B.P. The biostratgraphic data include the first Icelandic chironomid-based reconstruction of Holocene mean July air temperatures, using a Norwegian training set in the absence of modern Icelandic data. The results show that deglaciation and ecosystem development probably began before 10,000 ¹⁴C yr B.P. and that July temperatures were around 4°C at ca. 9500 ¹⁴C yr B.P. Temperatures then rose to ca. 8°C at the time of the deposition of the Saksunarvatn tephra (9100 ¹⁴C yr B.P.), reaching ca. 10°C by 8500 ¹⁴C yr B.P., high enough for the growth of tree birch, although successful birch colonisation did not take place until 6750 ¹⁴C yr B.P. There is some evidence for cooling immediately preceding 9100 ¹⁴C yr B.P. There is little firm biostratigraphic evidence for the 8200 cal. B.P. event, although this may be due to a relatively low resolution pollen sampling interval, but there are changes at this time in the total carbon (TC) and mass susceptibility (MS) data. Optimal temperatures and relative vegetation stability may have occurred between 8000–6100 ¹⁴C yr B.P. but the chironomid assemblages indicate higher temperatures after 5000 ¹⁴C yr B.P. This latter interpretation may, however, reflect delayed colonisation of thermophilous taxa and requires further investigation. There is evidence in the lithostratigraphy for greater local terrestrial instability after 6100 ¹⁴C yr B.P. but it seems unlikely that this led to the redevelopment of ice in the catchment. The biostratigraphic records appear to show a degree of resistence to climate forcing throughout the early and middle Holocene. The new chironomid-based temperature reconstruction needs to be refined by further studies in Iceland, particularly the development of an Icelandic training set, but has already demonstrated the problems of paleoclimatic interpretations based on pollen and/or macrofossil evidence alone.     

Ecological and functional roles of mycorrhizas in semi-arid ecosystems of Southeast Spain

Mycorrhizas are worldwide symbiotic associations established between certain soil fungi and most vascular plants and are fundamental in optimizing plant fitness and soil quality. Mycorrhizal symbioses improve the resilience of plant communities against environment stresses, including nutrient deficiency, drought and soil disturbance. Since these stresses are paramount in the degradation of semi-arid ecosystems in the SE Spain, a series of basic, strategic and applied studies have been made to ascertain how the activity and diversity of mycorrhizal fungi affect plant community composition, structure and dynamics in this region. These investigations are reviewed here in terms of: (i) analysing the diversity of mycorrhizal fungi; (ii) assessing the ecological and functional interactions among plant communities and their associated mycorrhizal fungal populations; and (iii) using mycorrhizal inoculation technology for the restoration of degraded semi-arid areas in Southeast Spain. Disturbance of the target semi-arid ecosystems decreases the density and diversity of mycorrhizal fungust populations. Nevertheless, the mycorrhizal propagules do not disappear completely suggesting a certain degree of stress adaptation, and these remaining, resilient ecotypes are being used as plant inoculants. Numerous field experiments, using plant species from the natural succession inoculated with a community of indigenous mycorrhizal fungi, have been carried out in revegetation projects in the semi-arid Iberian Southeast. This management strategy improved both plant development and soil quality, and is a successful biotechnological tool to aid the restoration of self-sustaining ecosystems. However, despite a 20-year history of this work, we lack a comprehensive view of the mycorrhizal potential to improve the composition, diversity, structure and functionality of drought-adapted plant communities in the Region.     

The role of visualisation in the choice of stationary non-separable space–time covariance functions: an application to air pollution data

Modelling spatio-temporal dependencies resulting from dynamic processes that evolve in both space and time is essential in many scientific fields. Spatio-temporal Kriging is one of the space–time procedures, which has progressed the most over the last few years. Kriging predictions strongly depend on the covariance function associated with the stochastic process under study. Therefore, the choice of such a covariance function, which is usually based on empirical covariance, is a core aspect in the prediction procedure. As the empirical covariance is not necessarily a permissible covariance function, it is necessary to fit a valid covariance model. Due to the complexity of these valid models in the spatio-temporal case, visualising them is of great help, at least when selecting the set of candidate models to represent the spatio-temporal dependencies suggested by the empirical covariogram. We focus on the visualisation of the most interesting stationary non-separable covariance functions and how they change as their main parameters take different values. We wrote a specialised code for visualisation purposes. In order to illustrate the usefulness of visualisation when choosing the appropriate non-separable spatio-temporal covariance model, we focus on an important pollution problem, namely the levels of carbon monoxide, in the city of Madrid, Spain.     

Least-squares prediction of horizontal coordinate distortions in Canada

A least-squares prediction method is described to estimate horizontal coordinate distortions at lower order points of a network using known coordinate differences (NAD27 coordinate distortions Δϕ′s and Δλ′s) at higher order points between NAD27 coordinates and coordinates derived from a recent (MAY 76), relatively distortion free, adjustment of these points. Empirical autocovariance functions of Δϕ and Δλ and crosscovariance function between Δϕ and Δλ are derived from some 5,250 data points and modelled using series of exponential functions. Empirical mean square values of Δϕ and Δλ, which are a measure of the distortions in NAD27 ϕ and λ, are 0.051 and 0.645 arcsecs² respectively. The corresponding mean value of the product ΔϕΔλ, which is a measure of the correlation between Δϕ and Δλ, is 0.056 arcsecs². The accuracy obtainable for predicted Δϕ and Δλ at an arbitrary point (e.g., lower order station) is a function of the accuracy and configuration of known Δϕ′s and Δλ′s in the surrounding area. Accuracies obtainable for various types of data configuration are given. Under favorable conditions taking place in about 60% of cases, accuracies in terms of ms agreement with known values of 0″.02 (0.6 m) and 0″.01 (0.2 m along parallel at latitude 50°) for the predicted latitude and longitude distortions are obtainable. Finally, a comparison with a method based on the use of complex polynomials is made. Presented at International Symposium on Geodetic Networks and Computations, Munich, August–September 1981.     

A detailed study of the duality relation for the least squares adjustment in euclidean spaces

The Euclidean spaces with their inner products are used to describe methods of least squares adjustment as orthogonal projections on finite-dimensional subspaces. A unified Euclidean space approach to the least squares adjustment methods “observation equations” and “condition equations” is suggested. Hence not only the two adjustment solutions are treated from the view-point of Euclidean space theory in a unified frame but also the existing duality relation between the methods of “observation equations” and “condition equations” is discussed in full detail. Another purpose of this paper is to contribute to the development of some familiarity with Euclidean and Hilbert space concepts. We are convinced that Euclidean and Hilbert space techniques in least squares adjustment are elegant and powerful geodetic methods.