Finite element formulation and algorithms for unsaturated soils. Part II: Verification and application

The finite‐element formulation and integration algorithms developed in Part I are used to analyse a number of practical problems involving unsaturated and saturated soils. The formulation and algorithms perform well for all the cases analysed, with the robustness of the latter being largely insensitive to user‐defined parameters such as the number of coarse time steps and error control tolerances. The efficiency of the algorithms, as measured by the CPU time consumed, does not depend on the number of coarse time steps, but may be influenced by the error control tolerances. Based on the analyses presented here, typical values for the error control tolerances are suggested. It is also shown that the constitutive modelling framework presented in Part I can, by adjusting one constitutive equation and one or two material parameters, be used to simulate soils that expand or collapse upon wetting. Treating the suction as a strain variable instead of a stress variable proves to be an efficient and robust way of solving suction‐dependent plastic yielding. Moreover, the concept of the constitutive stress is a particularly convenient way of handling the transition between saturation and unsaturation. Copyright © 2003 John Wiley & Sons, Ltd.     

The effects of Population III stars on the chemical and photometrical evolution of ellipticals

We have studied the effects of a hypothetical initial generation containing very massive stars [   M > 100 M_⊙  , pair-creation supernovae] on the chemical and photometric evolution of elliptical galaxies. To this purpose, we have computed the evolution of a typical elliptical galaxy with luminous mass of the order of  10¹¹ M_⊙  and adopted chemical evolution models already tested to reproduce the main features of ellipticals. We have tested several sets of yields for very massive zero-metallicity stars: these stars should produce quite different amounts of heavy elements than lower-mass stars. We found that the effects of Population III stars on the chemical enrichment is negligible if only one or two generations of such stars occurred, whereas they produce quite different results from the standard models if they continuously formed for a period not shorter than 0.1 Gyr. In this case, the results are at variance with the main observational constraints of ellipticals such as the average  [〈α/ Fe〉_*]  ratio in stars and the integrated colours. Therefore, we conclude that if Population III stars ever existed they must have been present for a very short period of time and their effects on the following evolution of the parent galaxy must have been negligible. This effect is minimum if a more realistic model with initial infall of gas rather than the classic monolithic model is adopted. Ultimately, we conclude that there is no need to invoke a generation of very massive stars in ellipticals to explain their chemical and photometric properties.     

Chemical evolution of Elliptical Galaxies and the ICM

We present a new model for the chemical evolution of elliptical galaxies taking into account SN feedback, detailed nucleosynthesis and galactic winds. We discuss the effect of galactic winds on the chemical enrichment of the ICM and compute the energy per particle injected by the galaxies into the ICM. This revised version was published online in August 2006 with corrections to the Cover Date.     

Temporal and spatial variations in the biogeochemical cycling of cobalt in two urban estuaries: Hudson River Estuary and San Francisco Bay

Despite the fact that Co is an essential trace element for the growth of marine phytoplankton, there is very limited information on the cycling of this trace metal in the marine environment. We report here the distribution of dissolved (<0.4 μm) and particulate (>0.4 μm) Co in surface waters of the Hudson River Estuary (HRE) and San Francisco Bay (SFB). Samples were collected during several cruises (from 1990 to 1995 in SFB and from 1995 to 1997 in the HRE) along the whole salinity gradient. Dissolved Co concentrations (mean±1 standard deviation) were nearly identical in magnitude in both estuaries despite differences in climate, hydrography, riverine-flow conditions and land-usage (HRE=0.91±0.61 nM; SFB=1.12±0.69 nM). Dissolved Co levels in each system showed non-conservative distributions when plotted as a function of salinity, with increasing concentrations downstream from the riverine end-members. Desorption from suspended particulates and sewage inputs, therefore, seems to be the major processes responsible for the non-conservative behavior of Co observed. Mass balance estimates also indicated that most of the estuarine Co is exported out of both estuaries, indicating that they and other estuarine systems are principal sources of this essential trace element to the open ocean.     

Optimizing interpolation of shoot density data from a Posidonia oceanica seagrass bed

A case study on the optimization of Posidonia oceanica density interpolation, using a data set from a large meadow at Porto Conte Bay (NW Sardinia, Italy), is presented. Ordinary point kriging, cokriging and a weighted average based on inverse square distance were used to interpolate density data measured in 36 sampling stations. The results obtained from different methods were then compared by means of a leave‐one‐out cross‐validation procedure. The scale at which interpolation was carried out was defined on the basis of the Hausdorff dimension of the variogram. Optimizing spatial scale and data points search strategy allowed obtaining more accurate density estimates independently of the interpolation method.     

Mid-Holocene emergence of southern Tunisian coasts

We present new sea-level data from the coasts of southern Tunisia, between the Gulf of Gabès and the Libyan border. The work tests, previously, published evidence on Holocene shorelines, and confirmed that a distinct emergence has occurred in this area during this time. The emergence peak lies at least 186 ± 11 cm above present and is inferred from: (1) AMS radiocarbon dates of subtidal vermetids and boring shells collected in growth position, and (2) careful assessment of tidal heights. Maximum emergence took place between about 6000 and 5000 ¹⁴C years BP; it cannot be ascribed to tectonics and is probably related to post-glacial hydro-isostatic effects. It challenges the inference of a 3-m global sea-level rise since 6000 years BP due to residual Antarctic melting.     

An observational study of coronal hole rotation over the sunspot cycle

An analysis of the rotation of coronal holes (CHs) spanning 18 years was done based on data from theCatalogue of Coronal Holes (Sanchez-Ibarra and Barraza-Paredes, 1992). A differential rotation of CHs is confirmed for the totality of CHs, but a different behavior was found when those were separated as equatorial or isolated, and polar hole extensions, such as in theCatalogue. Isolated CHs show a typical differential rotation, but polar hole extensions display two different types of behavior: a rotation rate below 40° ± 5° of heliographic latitude, increasing to the equator, and a rotation rate above the same heliographic latitude but increasing to the poles. Also discussed here is how this last result agrees with other studies that indicate the mostly rigid rotation of the corona at higher latitudes.     

On Szebehely's problem for holonomic systems involving generalized potential functions

We consider the problem of finding the generalized potential function V = U _i(q ¹, q ²,..., q ⁿ)q ⁱ + U(q ¹, q ²,...;q ⁿ) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U ₁, U ₂,...;, U _n, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M ₂ we obtain, for potential function U(q ¹, q ²), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council.     

Crystallization conditions of Los Angeles, a basaltic Martian meteorite

The texture of Los Angeles (stone 1) is dominated by relatively large (0.5−2.0 mm) anhedral to subhedral grains of pyroxene, and generally subhedral to euhedral shocked plagioclase feldspar (maskelynite). Minor phases include subhedral titanomagnetite and ilmenite, Fe-rich olivine, olivine+augite-dominated symplectites [some of which include a Si-rich phase and some which do not], pyrrhotite, phosphate(s), and an impact shock-related alkali- and silica-rich glass closely associated with anhedral to euhedral silica grains. Observations and model calculations indicate that the initial crystallization of Mg-rich pigeonitic pyroxenes at ≤1150 °C, probably concomitantly with plagioclase, was followed by pigeonitic and augitic compositions between 1100 and 1050 °C whereas between 1050 and 920 to 905 °C pyroxene of single composition crystallized. Below 920 to 905 °C, single composition Fe-rich clinopyroxene exsolved to augite and pigeonite. Initial appearance of titanomagnetite probably occurred near 990 °C and FMQ-1.5 whereas at and below 990 °C and ≥FMQ-1.5 titanomagnetite and single composition Fe-rich clinopyroxene may have started to react, producing ilmenite and olivine. However, judging from the most common titanomagnetite compositions, we infer that most of this reaction likely occurred between 950 and 900 °C at FMQ-1.0±0.2 and nearly simultaneously with pyroxene exsolution, thus producing assemblages of pigeonite, titanomagnetite, olivine, ilmenite, and augite. We deem this reaction as the most plausible explanation for the formation of the olivine+augite-dominated symplectites in Los Angeles. But we cannot preclude possible contributions to the symplectites from the shock-related alkali- and silica-rich glass or shocked plagioclase, and the breakdown of Fe-rich pigeonite compositions to olivine+augite+silica below 900 °C. Reactions between Fe-Ti oxides and silicate minerals in Los Angeles and other similar basaltic Martian meteorites can control the T-fO₂ equilibration path during cooling, which may better explain the relative differences in fO₂ among the basaltic Martian meteorites.