On linear equations of variation in dynamical problems

The linear equations of variation, associated with a motion of a particle moving in a plane under a field of force which admits a first integral of the motion of any form, are drawn up in terms of the tangential and normal displacements. The existence of the first integral implies that the normal displacement satisfies a single second-order differential equation, the tangential displacement being given from the solution of this by a single quadrature. The special cases are examined in which the integral is one of energy, and in which it is one of angular momentum. The extension is made to the motion of two particles moving in a plane under a conservative force-field depending on their positions, which admits also an integral of angular momentum. (The study of the relative motion in the gravitational problem of three bodies in the plane may be put into this form by Jacobi's formulation). An equation is given for finding the non-zero characteristic exponents of a periodic solution of this second problem.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969.     

The geography of the elderly in a modernizing society: the Hong Kong case

The characteristics of the elderly population of Hong Kong are first described. Recent changes in the spatial distribution of the elderly are also detailed. The spatial distribution and internal migration patterns of the elderly are shown to be very similar to those of the population as a whole. The problems posed by the fact that many of the elderly are poorly educated and lowly paid are considered.     

The reserves of extracted resources: Historical data

The available data on known reserves of extracted resources have not previously been tabulated and graphed. In this article we compile the reserves data in one place for the first time. This serves to (1) show the trends in the reserves series, (2) make the series available to others, and (3) place the reserves data in the context of price data for which longer series have been available, and with which they can now be seen to be consistent in both showing increasing availability rather than increasing scarcity.     

First Data on the Isotopic Age of Zircons from Rocks of the Roseta Ultramafic Massif,Southern Margin of the São Francisco Craton (Brazil)

Doklady Earth Sciences - The results of isotope U–Pb dating of zircons from lherzolite and vein olivine orthopyroxenite composing the Roseta ultramafic massif are presented. The zircons...     

Influence of wind upon water quality in Liverpool Bay

Comprehensive distribution patterns of physical and chemical characteristics have been obtained from a series of cruises in Liverpool Bay. The marked feature of these distributions was their temporal variability, suggesting that the surface residual circulation is also temporally variable. The influence of wind stress upon the circulation pattern and hence water quality of this sea area is illustrated.     

The role of prior model calibration on predictions with ensemble Kalman filter

This paper, based on a real world case study (Limmat aquifer, Switzerland), compares inverse groundwater flow models calibrated with specified numbers of monitoring head locations. These models are updated in real time with the ensemble Kalman filter (EnKF) and the prediction improvement is assessed in relation to the amount of monitoring locations used for calibration and updating. The prediction errors of the models calibrated in transient state are smaller if the amount of monitoring locations used for the calibration is larger. For highly dynamic groundwater flow systems a transient calibration is recommended as a model calibrated in steady state can lead to worse results than a noncalibrated model with a well-chosen uniform conductivity. The model predictions can be improved further with the assimilation of new measurement data from on-line sensors with the EnKF. Within all the studied models the reduction of 1-day hydraulic head prediction error (in terms of mean absolute error [MAE]) with EnKF lies between 31% (assimilation of head data from 5 locations) and 72% (assimilation of head data from 85 locations). The largest prediction improvements are expected for models that were calibrated with only a limited amount of historical information. It is worthwhile to update the model even with few monitoring locations as it seems that the error reduction with EnKF decreases exponentially with the amount of monitoring locations used. These results prove the feasibility of data assimilation with EnKF also for a real world case and show that improved predictions of groundwater levels can be obtained.