A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a discrete-in-time setting. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a continuous in-time setting for a strictly positive constrained specific storage coefficient. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation, and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

Large-eddy simulation of plant canopy flows using plant-scale representation

Turbulent flow in a corn canopy is simulated using large-eddy simulation (LES) with a Lagrangian dynamic Smagorinsky model. A new numerical representation of plant canopies is presented that resolves approximately the local structure of plants and takes into account their spatial arrangement. As a validation, computational results are compared with experimental data from recent field particle image velocimetry (PIV) measurements and two previous experimental campaigns. Numerical simulation using the traditional modelling method to represent the canopy (field-scale approach) is also conducted as a comparison to the plant-scale approach. The combination of temporal PIV data, LES and spatial PIV data allows us to couple a wide range of relevant turbulence scales. There is good agreement between experimental data and numerical predictions using the plant-scale approach in terms of various turbulence statistics. Within the canopy, the plant-scale approach also allows the capture of more details than the field-scale approach, including instantaneous gusts that penetrate deep inside the canopy.     

On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy

Particle image velocimetry (PIV) data obtained in a wind-tunnel model of a canopy boundary layer is used to examine the characteristics of mean flow and turbulence. The vector spacing varies between 1.7 and 2.5 times the Kolmogorov scales. Conditional sampling based on quadrants, i.e. based on the signs of velocity fluctuations, reveals fundamental differences in flow structure, especially between sweep and ejection events, which dominate the flow. During sweeps, the downward flow generates a narrow, highly turbulent, shear layer containing multiple small-scale vortices just below canopy height. During ejections, the upward flow expands this shear layer and the associated small-scale flow structures to a broad region located above the canopy. Consequently, during sweeps the turbulent kinetic energy (TKE), Reynolds stresses, as well as production and dissipation rates, have distinct narrow peaks just below canopy height, whereas during ejections these variables have broad maxima well above the canopy. Three methods to estimate the dissipation rate are compared, including spectral fits, measured subgrid-scale (SGS) energy fluxes at different scales, and direct measurements of slightly underresolved instantaneous velocity gradients. The SGS energy flux is 40–60% of the gradient-based (direct) estimates for filter sizes inside the inertial range, while decreasing with scale, as expected, within the dissipation range. The spectral fits are within 5–30% of the direct estimates. The spectral fits exceed the direct estimates near canopy height, but are lower well above and below canopy height. The dissipation rate below canopy height increases with velocity magnitude, i.e. it has the highest values during sweep and quadrant 1 events, and is significantly lower during ejection and quadrant 3 events. Well above the canopy, ejections are the most dissipative. Turbulent transport during sweep events acts as a source below the narrow shear layer within the canopy and as a sink above it. Transport during ejection events is a source only well above the canopy. The residual term in the TKE transport equation, representing mostly the effect of pressure–velocity correlations, is substantial only within the canopy, and is dominated by sweeps.     

Using Strong Solar Coronal Emission Lines as Coronal Flux Proxies

We investigate the possibility that strong EUV lines observed with the Goddard Solar EUV Rocket Telescope and Spectrograph (SERTS) provide good proxies for estimating the total coronal flux over shorter wavelength ranges. We use coordinated SERTS and Yohkoh observations to obtain both polynomial and power-law fits relating the broad-band soft X-ray fluxes to the intensities of Fexvi 335 Ú and 361 Ú, Fexv 284 Ú and 417 Ú, and Mgix 368 Ú measured with SERTS. We found that the power-law fits best cover the full range of solar conditions from quiet Sun through active region, though not surprisingly the cooler Mgix 368 Ú line proves to be a poor proxy. The quadratic polynomial fits yield fair agreement over a large range for all but the Mgix line. However, the linear fits fail conspicuously when extrapolated into the quiet-Sun regime. The implications of this work for the Heii 304 Ú line formation problem are also briefly considered.     

A Vulnerability Interpretation of the Geography of HIV/AIDS in Ghana, 1986–1995

Ten years after the human immuno-deficiency virus (HIV) was first reported in Ghana, it continues to spread throughout the country following patterns that are rare in other African countries. HIV is seen in twice as many females as males, more frequently in rural than urban regions, and regions with high rates of polygamy have significantly lower rates. The evidence presented in this paper shows that HIV diffusion patterns probably reflect the spatial distribution and social networks of vulnerable social groups. While information-based campaigns are still necessary in the fight against HIV/AIDS, they fail to enable or empower vulnerable people to protect themselves against infection.     

Geochemistry and petrogenesis of the Proterozoic dykes in Tamil nadu, southern India: another example of the Archaean lithospheric mantle source

Approximately 1650-Ma-old NW/SE and NE/SW-trending dolerite dykes in the Tiruvannamalai (TNM) area and approximately 1800-Ma-old NW/SE-trending dolerite dykes in the Dharmapuri (DP) area constitute major Proterozoic dyke swarms in the high-grade granulite region of Tamil nadu, southern India. The NW- and NE-trending TNM dykes are compositionally very similar and can be regarded as having been formed during a single magmatic episode. The DP dykes may relate to an earlier similar magmatic episode. The dolerites are Fe-rich tholeiites and most of the elemental variations can be explained in terms of fractional crystallisation. Clinopyroxene and olivine are the inferred ferromagnesian fractionation phases followed by plagioclase during the late fractionation stages. All the studied dykes have, similar to many continental flood basalts (CFB), large-ion lithophile element (LILE) and light rare-earth element (LREE) enrichment and Nb and Ta depletion. The incompatible element abundance patterns are comparable to the patterns of many other Proterozoic dykes in India and Antarctica, to the late Archaean (～2.72 Ga) Dominion volcanics in South Africa and to the early Proterozoic (～2.0 Ga) Scourie dykes of Scotland. The geochemical characteristics of the TNM and DP dykes cannot be explained by crustal contamination alone. Instead, they are consistent with derivation from an enriched lithospheric mantle source which appears to have been developed much earlier than the dyke intrusions during a major crustal building event in the Archaean. The dyke magmas may have been formed by dehydration melting induced by decompression and lithospheric attenuation or plume impingement at the base of the lithosphere. These magmas, compared with CFB, appear to be the minor partial melts from plume heads of smaller diameter and of shallow origin (650 km). Therefore, the Proterozoic thermal events could induce crustal attenuation and dyke intrusions in contrast to the extensive CFB volcanism and continental rifting generally associated with the Phanerozoic plumes of larger head diameter (>1000 km) and of deeper origin (at crust mantle boundary).     

Non-Linear Gravitational Clustering Using the Zel'dovich Approximation

As an alternative to computationally expensive N-body simulations for gravitional clustering, the Zel'dovich approximation (ZA) was studied in 3D, 2D and 1D. Plots of the density contrast were compared against linear theory and the exact solution. The ZA was found to perform very well in the linear regime, better than linear theory, and to give a good approximation well into the non-linear regime. This revised version was published online in July 2006 with corrections to the Cover Date.     

Additional Analytical Data for Gabbro, GOG-1

Additional data for gabbro, GOG-1, were determined by instrumental-neutron-activation analysis, atomic-absorption spectrometry, and semi-quantitative spectrographic analysis. F ratios calculated in the analysis of variance for 26 sets of data for elements determined by the three methods were not significant, and hence the elements are distributed homogeneously among the bottles. The agreement between our data and the averages previously published ranges from very good to poor. More analytical data are necessary to establish reliable estimates of the concentrations of elements in GOG-1 and in two other gabbros so that three gabbros may be available to geochemists for use as standards.     

A. Programmable device for simulation of tidal flux

An apparatus is described which permits precise, versatile control of simulated tidal flux in laboratory microcosms. A key component of the system, a programmable electronic control unit, can closely imitate any natural tidal function and is readily adaptable to other experimental applications that utilize timed switching capability. The programmable control unit is also cheaper and easier to operate than computer-based systems.