On the period of the periodic orbits of the restricted three body problem

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, \(2 T=k\pi +\int _\Omega g\) where k is an integer, \(\Omega \) is the region enclosed by the periodic orbit and \(g:{\mathbb {R}}^2\rightarrow {\mathbb {R}}\) is a function that only depends on the constant C known as the Jacobian constant; it does not depend on \(\Omega \). This theorem has a Keplerian flavor in the sense that it relates the period with the space “swept” by the orbit. As an application we prove that there is a neighborhood around \(L_4\) such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for \(L_5\).     

Energy balance and evaporation loss of an agricultural reservoir in a semi‐arid climate (south‐eastern Spain)

A typical agricultural water reservoir (AWR) of 2400 m² area and 5 m depth, located in a semi‐arid area (southern Spain), was surveyed on a daily basis for 1 year. The annual evaporation flux was 102·7 W m^?2, equivalent to an evaporated water depth of 1310 mm year^?1. The heat storage rate G exhibited a clear annual cycle with a peak gain in April (G ～ 45 W m^?2) and a peak loss in November (G ～ 40 W m^?2), leading to a marked annual hysteretic trend when evaporation (λE) was related to net radiation (R_n). λE was strongly correlated with the available energy A, representing 91% of the annual AWR energy loss. The sensible heat flux H accounted for the remaining 9%, leading to an annual Bowen ratio in the order of 0·10. The equilibrium and advective evaporation terms of the Penman formula represented 76 and 24%, respectively, of the total evaporation, corresponding to a annual value of the Priestley–Taylor (P–T) coefficient (α) of 1·32. The P–T coefficient presented a clear seasonal pattern, with a minimum of 1·23 (July) and a maximum of 1·65 (December), indicating that, during periods of limited available energy, AWR evaporation increased above the potential evaporation as a result of the advection process. Overall, the results stressed that accurate prediction of monthly evaporation by means of the P–T formula requires accounting for both the annual cycle of storage and the advective component. Some alternative approaches to estimating R_n, G and α are proposed and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Argon diffusion domains in K-feldspar II: kinetic properties of MH-10

Viewing K-feldspars as containing a discrete distribution of diffusion domain sizes reconciles otherwise disconsonant features common in their ⁴⁰Ar/³⁹Ar age spectra and Arrhenius plots but raises a fundamental question. What are the features in K-feldspar that endow it with this behavior? We report here the results of two different kinds of experiments that help isolate the nature of the responsible diffusion properties. To assess the thermal stability of the diffusion domains during laboratory treatment, MH-10 K-feldspar was step-heated to 850°C, removed from the furnace and split. One split was reirradiated and the other returned to the furnace and completely degassed. Following re-irradiation, the original heating schedule was used to degas the second aliquot. Apart from the first 5% of gas released, the diffusion properties show little change relative to the original result but, it appears, the physical character of a portion of the smallest domain has been altered. Results of duplicate step-heating experiments of samples treated at 750°C, 950°C and 1100°C prior to irradiation are consistent with the conclusions of the double irradiation experiment. In a second series of experiments, sized aggregates of MH-10 K-feldspar were analyzed by the ⁴⁰Ar/³⁹Ar step-heating method. The resultant log(r/r _o) plots reveal that the largest domain is annihilated when the particle size is reduced to about 50 μm. From this result we infer that the largest diffusion domain size is between 60 and about 130 μm in diameter. This estimate, together with knowledge of the relative domain size distribution obtained from modeling the log(r/r _o) plot, sets the size of the smallest domain to be less than about 1 μm. Microstructural examination of MH-10 K-feldspar identifies sub-grain features that correspond in size to our independent estimates for the largest and smallest diffusion domains. These results strongly support the view that low-temperature K-feldspars contain a distribution of diffusion length scales that are well approximated as discrete domain sizes and that laboratory heating below the onset of melting does not significatly affect the ability to obtain thermal reconstructions from the ⁴⁰Ar/³⁹Ar systematics.     

Swimming behavior of Dungeness crab,Cancer magister Dana,megalopae in still and moving water

In the Grays Harbor estuary, juvenile Dungeness crab (Cancer magister Dana) are found at higher densities in epibenthic shell deposits compared to open mud flat. Differences in predation rate between habitats have been suggested to be due to habitat preference and differential survival. Megalopae preferred shell over open space in still-water conditions. However, it is not known whether megalopae are able to select shell in flowing water since larval preference is known to differ between still and flowing water. Here we report the first experimental study of swimming behavior of Dungeness crab megalopae in a range of current velocities (0–40 cm s^?1) equivalent to natural flow in Grays Harbor estuary. Experiments were conducted in daylight using a recirculating flume. Megalopae swimming speeds ranged from 8.5 cm s^?1 (8 body lengths s^?1) in still water to 44.8 cm s^?1 (44 body lengths s^?1) at flow speeds of 40 cm s^?1, Neither swimming behavior nor sheltering behavior in shells showed any flow-related pattern. Megalopae spent a large proportion of time swimming against the current and made headway upstream against all current velocities tested. The results suggest that Dungeness crab megalopae are able to maneuver and actively search for settlement sites under current velocities found in natural habitats, including intertidal shell deposits, and support the hypothesis of active selection of shell by megalopae.     

Some elements of mathematical information theory and total inversion algorithm applied to travel time inversion

The total inversion algorithm and some elements of Mathematical Information Theory are used in the treatment of travel-time data belonging to a seismic refraction experiment from the southern segment (Sardinia Channel) of the European Geotraverse Project. The inversion algorithm allows us to improve a preliminary propagating model obtained by means of usual trial and error procedure and to quantify the resolution degree of parameters defining the crust and upper mantle of such a model. Concepts related to Mathematical Information Theory detect some seismic profiles of the refraction experiment which give the most homogeneous coverage of the model in terms of number of trajectories crossing it. Finally, the efficiency of the inversion procedure is quantified and the uncertainties regarding knowledge of different parts of the model are also evaluated.     

The control of the production process of phytoplankton by the physical structure of the aquatic environment with special reference to its optical properties

This tutorial was designed for nonbiologists requiring an introduction to the nature and general timescales of phytoplankton responses to physical forcing in aquatic environments. As such, an effort was made to highlight biological markers which might assist in identifying, measuring and/or validating physical processes controlling the variability in the distribution, abundance, composition and activity of phytoplankton communities. Given the recent advances in environmental optics and remote sensing capabilities, a special emphasis was placed on the nature and utility of phytoplankton optical properties in current bio-optical modelling efforts to predict temporal and spatial variability in phytoplankton productivity and growth.     

Ephemeris errors of GPS satellites

Ephemeris errors are supposed to be a major factor limiting the usefulness ofGPS in high precision geodesy. Considerations of orbital mechanics suggest that, regardless of their complexity, the uncertainties in the solar radiation pressure model, the gravity field model, and the estimated initial state, may have simple effects on the ephemeris. This possibility has been tested by fitting linear combinations of simple functions—chosen on theoretical grounds—to simulated errors of three-day ephemerides. With a set of five functions for the across-track component, six for the radial, and seven for the along-track, it has been possible to fit the position errors to better than 1% of theirr.m.s values, in all the caces studied. The simulations included —besides solar radiation pressure errors—gravity field model and initial state uncertainties, as well as an unknown constant force along the axis of the solar panels. The solar radiation force was calculated taking into account the shape, orientation, and physical properties (reflectivity and specularity) of the main parts of the spacecraft, under various conditions of illumination (continuous sunlight, eclipses, etc.).     

A Parametric Approach for Dealing with Compositional Rounded Zeros

In this work, a parametric approach for replacing data below the detection limit, also known as rounded zeros, in compositional data sets is proposed. Compositional rounded zeros correspond to small proportions of some whole that cannot be reliably detected by the analytical instruments under given operating conditions. This kind of zeros appear frequently in the data collection process in geosciences. They must be treated in an adequate way before some multivariate analysis can be applied. Our procedure results from a modification of the Expectation-Maximization (EM) algorithm and is based on the additive log-ratio transformation. Its coherence with the nature of compositional data and with basic operations in the simplex sample space is checked. Using real data sets, we find that this approach improves other parametric and non-parametric techniques for compositional rounded zeros.     

Dynamic of the freshwater–saltwater interface in a karstic aquifer under extraordinary recharge action: the Merida Yucatan case study

A hydraulic analysis of the interface between freshwater–saltwater behavior was done in the Merida Yucatan zone, two machines that constantly register the groundwater levels were installed, and three electric conductivity logs were taken from wells. When comparing the measured results with the ones obtained using theoretical equations developed to calculate the freshwater–saltwater interface position, it was proved that in some cases these equations can be applied, and in others not. Two effects that rule the behavior of karst aquifers in extraordinary conditions were found.     

Heavy metals pollution of aquatic ecosystems in the vicinity of a recently closed underground lead-zinc mine (Basque Country, Spain)

A presentation is made of the study of an underground polymetallic sulphide mine and the pollution caused by this in the adjoining aquatic ecosystems. Troya Mine is in the Basque Cantabrian region (northern Spain). The annual production of the ore deposit of over 3.7 million tons of Pb (0.9%), Zn (11.2%) and Cu (0.2%) was 300,000 t. It was open and producing from 1986-1993. The mineralization was made up of pyrite, marcasite, sphalerite, galena, chalcopyrite and arsenopyrite. Only the Zn and the Pb were mined. We studied the distribution and behaviour of the heavy metals Zn, Pb, Fe, Mn, Cu, Cr and Cd in the water column, dissolved and suspended fractions, and in the sediments of Estanda Stream and of Gezala Creek. Zn, Cd and Mn tend to be found in the water; Fe, Pb, Cu and Cr appear as an adsorbed fractionin the solid phases. Those of the second group are significantly linked to the fluvial sediments and present very high levels. The concentrations of the metals are conditioned by the waters from the mine galleries, by the leached waste, by the surface runoff, and by overflow from the spillway of the tailings pond. Our observations provide knowledge on the extent of the polluting power of the metals, the physico-chemical effects in play and the subsequent chances of recovering these highly affected environments.