Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

A transdisciplinary analysis of water problems in the mountainous karst areas of Morocco

Water management and engineering in the karstic High Atlas of Morocco are difficult tasks under the prevailing geological, hydrogeological, geomorphological, vegetational and climatic conditions. It is important to be able to understand and predict the characteristics and availability of water for future water planning in the region under changing climatic and agricultural conditions. An interdisciplinary analysis of problems and adequate hydrological modelling tools developed by geologists, hydrologists and biologists are necessary. The karst areas of the High Atlas Mountains are characterised by impermeable triassic basalt underlying substantial subsurface reservoirs with high potential discharge rates. The karst groundwater aquifers are extensive but largely unknown in dimension, probably with a hierarchical network of groundwater flow paths. It is estimated that approximately 70% of the surface water is directly lost to groundwater. Steep landslide- and debris flow prone slopes exist next to coarse-grained, highly porous river beds. Infrequent, high intensity rainfall or snowmelt causes a particularly high flood risk to these karst areas. In addition, agriculture and land use changes have degraded the karst areas. The most important driving forces for degradation include permanent overgrazing even during droughts and the use of firewood by a continually growing population. Large scale degradation of vegetation has occurred in the oro-mediterranean (mountainous Mediterranean) zone, between 2600 and 3400 m which coincides with the most important zone for karstic groundwater creation. The combination of high amounts of groundwater flow and rapid surface flow due to sparse vegetation has increased the problems of flood flow.     

Neuralizing target superresolution algorithms

Tatem et al. (2001) have designed a Hopfield network-based algorithm for superresolving discrete targets that are larger than the sample spacing of an image. The algorithm iteratively minimizes a criterion function that contains a sigmoidal activation term. We have altered their algorithm to bring it in line with Hopfield's original network by reducing the pseudotemperature of the sigmoid. We found that smaller values of the pseudotemperature lead to faster convergence to a solution and resulting solutions that are more accurate.     

Inverse groundwater modelling in the Willunga Basin,South Australia

A new inverse technique for modelling groundwater flow, based on a functional minimization technique, has been used to calibrate a groundwater flow model of a subregion of the Port Willunga aquifer within the Willunga Basin in South Australia. The Willunga Basin is the location of extensive viticulture, irrigated primarily by groundwater, the levels and quality of which have declined significantly over the last 40 years. The new method is able to generate estimates of transmissivity, storativity and groundwater recharge over the whole subregion as a time-varying continuous surface; previous methods estimate local discrete parameter values at specific times. The new method has also been shown to produce accurate head values for the subregion and very good estimates of groundwater recharge. Its ultimate goal will be to provide a new and invaluable tool for significantly improved groundwater resource management. Supported in part by US National Science Foundation grants, DMS-0107492 and DMS-0079478.     

Galaxy activity in merging binary galaxy clusters

We present the results of a study of galaxy activity in two merging binary clusters (A168 and A1750) using the Sloan Digital Sky Survey (SDSS) data supplemented with the data in the literature. We have investigated the merger histories of A168 and A1750 by combining the results from a two-body dynamical model and X-ray data. In A168, two subclusters appear to have passed each other and to be coming together from the recent maximum separation. In A1750, two major subclusters appear to have started interaction and to be coming together for the first time. We find an enhanced concentration of the galaxies showing star formation (SF) or active galactic nuclei (AGN) activity in the region between two subclusters in A168, which were possibly triggered by the cluster merger. In A1750, we do not find any galaxies with SF/AGN activity in the region between two subclusters, indicating that two major subclusters are in the early stage of merging.     

Comparison of Five Numerical Codes for Automated Tracing of Coronal Loops

The three-dimensional (3D) modeling of coronal loops and filaments requires algorithms that automatically trace curvilinear features in solar EUV or soft X-ray images. We compare five existing algorithms that have been developed and customized to trace curvilinear features in solar images: i) the oriented-connectivity method (OCM), which is an extension of the Strous pixel-labeling algorithm (developed by Lee, Newman, and Gary); ii) the dynamic aperture-based loop-segmentation method (developed by Lee, Newman, and Gary); iii) unbiased detection of curvilinear structures (developed by Steger, Raghupathy, and Smith); iv) the oriented-direction method (developed by Aschwanden); and v) ridge detection by automated scaling (developed by Inhester). We test the five existing numerical codes with a TRACE image that shows a bipolar active region and contains over 100 discernable loops. We evaluate the performance of the five codes by comparing the cumulative distribution of loop lengths, the median and maximum loop length, the completeness or detection efficiency, the accuracy, and flux sensitivity. These algorithms are useful for the reconstruction of the 3D geometry of coronal loops from stereoscopic observations with the STEREO spacecraft, or for quantitative comparisons of observed EUV loop geometries with (nonlinear force-free) magnetic field extrapolation models.     

Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace’s theorem revisited

Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg₂SiO₄). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate representation of thermodynamic properties and sound wave velocities of Mg₂SiO₄ in its complete pressure–temperature stability range. We also show that the accuracy of our results is not significantly affected by the use of a different equation of state.