Notes on Hori Method for Canonical Systems

In this paper a slightly different approach is proposed for the process of determining the functions S _m and H _m ^* of the algorithm of the canonical version of Hori method. This process will be referred to as integration theory of the mth order equation of the method. It will be shown that the ordinary differential equation with an auxiliary parameter t ^* as independent variable, introduced through Hori auxiliary system, can be replaced by a partial differential equation in the time t. In this way, the mth order equation of the algorithm assumes a form very similar to the one of other perturbation methods. In virtue of this new approach of the integration theory for Hori method, Lagrange's variational equations introduced by Sessin are revised. As an example, the Duffing equation is solved through this new approach.     

Geochemistry, petrology and ages of the lunar meteorites Kalahari 008 and 009: New constraints on early lunar evolution

Kalahari 008 and 009 are two lunar meteorites that were found close to each other in Botswana. Kalahari 008 is a typical lunar anorthositic breccia; Kalahari 009 a monomict breccia with basaltic composition and mineralogy. Based on minor and trace elements Kalahari 009 is classified as VLT (very-low-Ti) mare basalt with extremely low contents of incompatible elements, including the REE. The Lu-Hf data define an age of 4286 ± 95 Ma indicating that Kalahari 009 is one of the oldest known basalt samples from the Moon. It provides evidence for lunar basalt volcanism prior to 4.1 Ga (pre-Nectarian) and may represent the first sample from a cryptomare. The very radiogenic initial ¹⁷⁶Hf/¹⁷⁷Hf (εHf = +12.9 ± 4.6), the low REE, Th and Ti concentrations indicate that Kalahari 009 formed from re-melting of mantle material that had undergone strong incompatible trace element depletion early in lunar history. This unusually depleted composition points toward a hitherto unsampled basalt source region for the lunar interior that may represent a new depleted endmember source for low-Ti mare basalt volcanism. Apparently, the Moon became chemically very heterogeneous at an early stage in its history and different cumulate sources are responsible for the diverse mare basalt types.Evidence that Kalahari 008 and 009 may be paired includes the similar fayalite content of their olivine, the identical initial Hf isotope composition, the exceptionally low exposure ages of both rocks and the fact that they were found close to each other. Since cryptomaria are covered by highland ejecta, it is possible that these rocks are from the boundary area, where basalt deposits are covered by highland ejecta. The concentrations of cosmogenic radionuclides and trapped noble gases are unusually low in both rocks, although Kalahari 008 contains slightly higher concentrations. A likely reason for this difference is that Kalahari 008 is a polymict breccia containing a briefly exposed regolith, while Kalahari 009 is a monomict brecciated rock that may never have been at the surface of the Moon.Altogether, the compositions of Kalahari 008 and 009 permit new insight into early lunar evolution, as both meteorites sample lunar reservoirs hitherto unsampled by spacecraft missions. The very low Th and REE content of Kalahari 009 as well as the depletion in Sm and the lack of a KREEP-like signature in Kalahari 008 point to a possible source far from the influence of the Procellarum-KREEP Terrane, possibly the lunar farside.     

Weibull statistical analysis of granite bending strength

Summary  This paper describes and discusses the adequacy of Weibull statistical analysis to analyse the bending strength of granite. The experimental results show that strength variability is related with a specific origin of failure. This conclusion is based on analysing the influence of the surface condition (extrinsic defects) on the bending strength results treated by the Weibull statistics. The conclusions drawn from this study have been validated by analysing the results of the critical flaw dimension estimated by applying the linear elastic fracture mechanics (LEFM) formulae. Results obtained from fractographic examination also have been used to describe the location of the origin of the fracture and understand the distribution of defects; i.e., there is a unimodal distribution of defects (intrinsic defects), despite the fact that some outlier values are normally observed in the fractured surfaces. Correspndence: P. M. Amaral, Department of Materials Engineering, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal     

Impact of lightning on organic matter-rich soils: influence of soil grain size and organic matter content on underground fires

A detailed study was carried out on a piece of land that had been struck by lightning during the violent rainstorm that raged over the Island of S?o Miguel (Azores Archipelago) in late October 2006. Temperature and gas measurements (CO₂, CO, H₂S and CH₄) were performed in four study trenches, dug in an area of ∼3 m², where an underground fire had been initiated by the impact with a lightning stroke, followed by the emission of a column of gases and smoke. The soil under study was originally a well-pedogenized about 80 cm thick bed, made of volcanic clayey to silty tephra fallouts and contained 5.5–9.7% of organic matter. The underground fire was monitored for one week and revealed a peak release of 404 ppm CO and 3.4% CO₂ originating from a horizon located about 45 cm under the soil surface. Measurements of temperature, performed one week after the impact, indicated a maximum value of 326°C inside the soil, while 516.5°C were measured on the surface of a lava block interred about 20 cm under the surface. Subsequently, a stratigraphic and sedimentologic study proved the role of the grain-size of the soil and of the organic matter content of the different horizons of the impact area, in determining the ratio between anoxic/oxidised combustion conditions and in the progress of the process itself. It was also noticed that combustion was not total all over in the soil bed and that the process had slightly migrated toward SW during the observation period. The combustion process went on for about ten days, in spite of several other violent rainstorms, until it was artificially extinguished through the excavations made to obtain study trenches. This particular circumstance evidenced the potential natural hazard represented by this kind of atmospheric event, especially in a land where the volcanic nature of the soil may easily mislead inexperienced observers and, consequently, delay proper action.     

Carbon stable isotopes in estuarine sediments and their utility as migration markers for nursery studies in the Firth of Forth and Forth Estuary, Scotland

The stable carbon isotope ratios (δ¹³C) of the organic fraction of intertidal sediments in the Forth Estuary and the Firth of Forth, Scotland, were measured to determine if terrestrially derived carbon was present in the estuarine sediments. It was hypothesised that differences in the inputs from marine vs. terrestrial sources to the organic carbon of estuarine and marine sediments, as well as differences in ambient seawater stable oxygen isotope (δ¹⁸O) ratios between the estuary and the Outer Firth, would allow the use of these two stable isotopes as habitat markers for juvenile plaice (Pleuronectes platessa), to allow determination of nursery habitats. Muddy and sandy sediments from the estuary and sandy sediments from the Outer Firth were sampled and δ¹³C measured. Juvenile plaice were caught at two estuarine sites and at two Outer Firth sites and otoliths were removed for δ¹³C and δ¹⁸O analysis. The sandy sediments in the estuary showed a strong gradient of δ¹³C enrichment with distance down the estuary, while the muddy sediments showed a much shallower gradient. δ¹³C and δ¹⁸O measured in the carbonate of juvenile plaice otoliths showed no clear difference between otoliths of fish caught at one of the estuarine sites and at the two Outer Firth sites. However, the isotope ratios of both carbon and oxygen in plaice otoliths from the other estuarine site showed the expected trend of depletion in the heavier isotopes. While the measurements recorded here did not conclusively distinguish between otoliths from juveniles caught in the estuarine site and those caught in the other three sites, they show that stable isotopes have potential to distinguish between estuarine habitats with terrestrial carbon inputs, and coastal marine habitats with predominantly marine carbon inputs.     

Vertical distribution of the macrobenthic community and its relationships to trace metals and natural sediment characteristics in the lower Douro estuary, Portugal

Vertical distribution (0–15 cm) of the macrobenthic community and its relationships to natural sediment characteristics and trace metal contents and bioavailability were studied at five locations in the lower Douro estuary, Portugal. An analysis of vertical metal distribution, for the interpretation of anthropogenic impact on the estuarine sediments, was also investigated. Sediment characterisation included organic matter, grain size, metals (Al, Fe, Cu, Pb, Cr, Ni, Cd, Zn and Mn), acid volatile sulphide (AVS) and simultaneously extracted metals (SEM). The macrobenthic community had low diversity (14 species), was dominated by small size opportunists and seemed to be controlled mainly by natural factors such as grain size distribution, Al and Fe contents and sediment depth. The vertically heterogeneous distribution of macrobenthic community appears to affect redox status of the sediments and consequently metal bioavailability. Despite anthropogenic contamination in terms of Zn, Cu, Pb, Cr and Ni having already been detected in the north bank, the analysis of vertical distribution was essential for the identification of current anthropogenic contamination in terms of Zn, Pb and Cd in the south bank.     

Using benthic macrofauna to assess environmental quality of four intertidal mudflats in Hong Kong and Shenzhen Coast

Abstract-Intertidal zone is a significant wetland between land and ocean. It plays an important rolein maintaining local ecological balance. Both Mai Po and Futian intertidal mudflats are located in Shen-zhen Bay and are important "refueling" point along the East Asian/Australian flyway of migratory birds.The environmental quality of Mai Po and Futian mudflats have aroused great concern due to rapid eco-nomic developments in Hong Kong and Shenzhen in recent decades. Microinfauna of Mai Po and Futianmudflats was investigated in December 2000 and the faunal data were used to assess their environmentalquality. Two other mudflats, namely Ma Wan Typhoon Shelter (a more disturbed area) and Luk Kengintertidal mudflat (a place with relatively less human disturbance), were also sampled for macroinfaunaand used as reference mudflats. Shannon-Weaver species diversity index (I_(sd)), biotic coefficient (C_b)and macrofaunal pollution index (I_(mp)) of the macrofauna community on four intertidal mudflats wereused to