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Oblate Spheroids (oblate + spheroid)

Distribution by Scientific Domains
Engineering60%

Selected Abstracts

Cracking risk of partially saturated porous media,Part I: Microporoelasticity model

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2010
Bernhard Pichler
Abstract Drying of deformable porous media results in their shrinkage, and it may cause cracking provided that shrinkage deformations are hindered by kinematic constraints. This is the motivation to develop a thermodynamics-based microporoelasticity model for the assessment of cracking risk in partially saturated porous geomaterials. The study refers to 3D representative volume elements of porous media, including a two-scale double-porosity material with a pore network comprising (at the mesoscale) 3D mesocracks in the form of oblate spheroids, and (at the microscale) spherical micropores of different sizes. Surface tensions prevailing in all interfaces between solid, liquid, and gaseous matters are taken into account. To establish a thermodynamics-based crack propagation criterion for a two-scale double-porosity material, the potential energy of the solid is derived, accounting,in particular,for mesocrack geometry changes (main original contribution) and for effective micropore pressures, which depend (due to surface tensions) on the pore radius. Differentiating the potential energy with respect to crack density parameter yields the thermodynamical driving force for crack propagation, which is shown to be governed by an effective macrostrain. It is found that drying-related stresses in partially saturated mesocracks reduce the cracking risk. The drying-related effective underpressures in spherical micropores, in turn, result in a tensile eigenstress of the matrix in which the mesocracks are embedded. This way, micropores increase the mesocracking risk. Model application to the assessment of cracking risk during drying of argillite is the topic of the companion paper (Part II). Copyright © 2009 John Wiley & Sons, Ltd. [source]

Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberances

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004
Lisa F. Shatz
Abstract The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Thick gas discs in faint dwarf galaxies

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY: LETTERS (ELECTRONIC), Issue 1 2010
Sambit Roychowdhury
ABSTRACT We determine the intrinsic axial ratio distribution of the gas discs of extremely faint MB < ,14.5 dwarf irregular galaxies. We start with the measured (beam corrected) distribution of apparent axial ratios in the H i 21-cm images of dwarf irregular galaxies observed as part of the Faint Irregular Galaxy GMRT Survey (FIGGS). Assuming that the discs can be approximated as oblate spheroids, the intrinsic axial ratio distribution can be obtained from the observed apparent axial ratio distribution. We use a variety of methods to do this, and our final results are based on using Lucy's deconvolution algorithm. This method is constrained to produce physically plausible distributions, and also has the added advantage of allowing for observational errors to be accounted for. While one might a priori expect that gas discs would be thin (because collisions between gas clouds would cause them to quickly settle down to a thin disc), we find that the H i discs of faint dwarf irregulars are quite thick, with mean axial ratio ,q,, 0.6. While this is substantially larger than the typical value of ,0.2 for the stellar discs of large spiral galaxies, it is consistent with the much larger ratio of velocity dispersion to rotational velocity (,/vc) in dwarf galaxy H i discs as compared to that in spiral galaxies. Our findings have implications for studies of the mass distribution and the Tully,Fisher relation for faint dwarf irregular galaxies, where it is often assumed that the gas is in a thin disc. [source]

Spheroidal coordinate systems for modelling global atmospheres

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 630 2008
A. A. White
Abstract In meteorological dynamics it is common practice to represent the potential surfaces of apparent gravity (the geopotentials) as spheres, and consequently the use of spherical polar coordinates in models of the global atmosphere is widespread. Several writers have considered how oblate spheroidal coordinates might be used instead, thus enabling the Figure of the Earth to be better represented. It is observed here that oblate spheroidal coordinate systems are conventionally defined using confocal oblate spheroids, and that such spheroids are inappropriate representations of the geopotentials because they imply the wrong sign for the latitudinal variation of apparent gravity. Re-examination of a classical problem of Newtonian gravitation shows that, near the Earth, the geopotentials are to a very good approximation spheroids, but not spheroids of an analytically simple type. However, similar oblate spheroids are a qualitatively correct model of the near-Earth geopotentials, and are a quantitatively good approximation in so far as Newton's uniform-density model adequately describes the real Earth. An orthogonal curvilinear coordinate system based on similar oblate spheroids is proposed and examined. © Crown Copyright 2008. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd [source]