Fluid substitution in porous rocks with aligned cracks: Theory versus numerical modeling

The effect of penny-shaped cracks on the elastic properties of porous media is modeled using static finite element modeling (FEM) code. Anisotropic Gassmann theory is used to predict the effective properties of the saturated cracked media from their dry properties. There is an excellent agreement between numerical results and theory, with a small error associated with partially inequilibrated patches of fluid in the FEM. These patches of fluid result in a residual stiffness which can be subtracted from the FEM results to further improve agreement with Gassmann theory

Finite element modelling of the effective elastic properties of partially saturated rocks

Simulation of effective physical properties from microtomographic 3D images of porous structures allows one to relate properties of rocks directly to their microstructure. A static FEM code has been previously used to estimate effective elastic properties of fully saturated monomineralic (quartz) rock under wet and dry conditions. We use the code to calculate elastic properties under partially saturated conditions. The numerical predictions are compared to the Gassmann theory combined with Wood's formula (GW) for a mixture of pore fluids, which is exact for a monomineralic macroscopically homogeneous porous medium. Results of the numerical simulations performed for two Boolean sphere pack distributions show significant deviation from the GW limit and depend on the spatial distribution of fluids. This is shown to be a numerical artefact caused by incomplete equilibration of fluid pressure, which is primarily due to insufficient spatial resolution. To investigate the effect of pore-size and pore geometry, we perform FEM simulations for a model with regular pore geometry, where all pore channels have the same size and shape. Accuracy of these simulations increases with the total cross-section area of the channels and the size of individual channels. For the case where the total cross-section of the channels is large enough (on the same order as total porosity), there is a minimum of 4 voxels per channel diameter required for adequate fluid pressure equilibration throughout the pore space. Increasing the spatial resolution of the digital models reduces the discrepancy between the simulations and theory, but unfortunately increases the memory and CPU requirements of the simulations

Construction of the Femoral Neck During Growth Determines its Strength in Old Age

Study of the design of the FN in vivo in 697 women and in vitro in 200 cross-sections of different sizes and shapes along each of 13 FN specimens revealed that strength in old age was largely achieved during growth by differences in the distribution rather than the amount of bone material in a given FN cross-section from individual to individual. Introduction: We studied the design of the femoral neck (FN) to gain insight into the structural basis of FN strength in adulthood and FN fragility in old age. Materials and Methods: Studies in vivo were performed using densitometry in 697 women and in vitro using high-resolution μCT and direct measurements in 13 pairs of postmortem specimens. Results: The contradictory needs of strength for loading yet lightness for mobility were met by varying FN size, shape, spatial distribution, and proportions of its trabecular and cortical bone in a cross-section, not its mass. Wider and narrower FNs were constructed with similar amounts of bone material. Wider FNs were relatively lighter: a 1 SD higher FN volume had a 0.67 (95% CI, 0.61-0.72) SD lower volumetric BMD (vBMD). A 1 SD increment in height was achieved by increasing FN volume by 0.32 (95% CI, 0.25-0.39) SD with only 0.15 (95% CI, 0.08-0.22) SD more bone, so taller individuals had a relatively lighter FN (vBMD was 0.13 [95% CI, 0.05-0.20 SD] SD lower). Greater periosteal apposition constructing a wider FN was offset by even greater endocortical resorption so that the same net amount of bone was distributed as a thinner cortex further from the neutral axis, increasing resistance to bending and lowering vBMD. This was recapitulated at each point along the FN; varying absolute and relative degrees of periosteal apposition and endocortical resorption focally used the same amount of material to fashion an elliptical FN of mainly cortical bone near the femoral shaft to offset bending but a more circular FN of proportionally more trabecular and less cortical bone to accommodate compressive loads adjacent to the pelvis. This structural heterogeneity was largely achieved by adaptive modeling and remodeling during growth-most of the variance in FN volume, BMC, and vBMD was growth related. Conclusions: Altering structural design while minimizing mass achieves FN strength and lightness. Bone fragility may be the result of failure to adapt bone's architecture to loading, not just low bone mass

Lattice Model of Sweeping Interface for Drying Process in Water-Granule Mixture

Based on the invasion percolation model, a lattice model for the sweeping interface dynamics is constructed to describe the pattern forming process by a sweeping interface upon drying the water-granule mixture. The model is shown to produce labyrinthine patterns similar to those found in the experiment[Yamazaki and Mizuguchi, J. Phys. Soc. Jpn. \textbf{69} (2000) 2387]. Upon changing the initial granular density, resulting patterns undergo the percolation transition, but estimated critical exponents are different from those of the conventional percolation. Loopless structure of clusters in the patterns produced by the sweeping dynamics seems to influence the nature of the transition.Comment: 6 pages, 7 figure

Stressed backbone and elasticity of random central-force systems

We use a new algorithm to find the stress-carrying backbone of ``generic'' site-diluted triangular lattices of up to 10^6 sites. Generic lattices can be made by randomly displacing the sites of a regular lattice. The percolation threshold is Pc=0.6975 +/- 0.0003, the correlation length exponent \nu =1.16 +/- 0.03 and the fractal dimension of the backbone Db=1.78 +/- 0.02. The number of ``critical bonds'' (if you remove them rigidity is lost) on the backbone scales as L^{x}, with x=0.85 +/- 0.05. The Young's modulus is also calculated.Comment: 5 pages, 5 figures, uses epsfi

Quantitative properties of complex porous materials calculated from X-ray μCT images

A microcomputed tomography (μCT) facility and computational infrastructure developed at the Department of Applied Mathematics at the Australian National University is described. The current experimental facility is capable of acquiring 3D images made up of 20003 voxels on porous specimens up to 60 mm diameter with resolutions down to 2 μm. This allows the three-dimensional (3D) pore-space of porous specimens to be imaged over several orders of magnitude. The computational infrastructure includes the establishment of optimised and distributed memory parallel algorithms for image reconstruction, novel phase identification, 3D visualisation, structural characterisation and prediction of mechanical and transport properties directly from digitised tomographic images. To date over 300 porous specimens exhibiting a wide variety of microstructure have been imaged and analysed. In this paper, analysis of a small set of porous rock specimens with structure ranging from unconsolidated sands to complex carbonates are illustrated. Computations made directly on the digitised tomographic images have been compared to laboratory measurements. The results are in excellent agreement. Additionally, local flow, diffusive and mechanical properties can be numerically derived from solutions of the relevant physical equations on the complex geometries; an experimentally intractable problem. Structural analysis of data sets includes grain and pore partitioning of the images. Local granular partitioning yields over 70,000 grains from a single image. Conventional grain size, shape and connectivity parameters are derived. The 3D organisation of grains can help in correlating grain size, shape and orientation to resultant physical properties. Pore network models generated from 3D images yield over 100000 pores and 200000 throats; comparing the pore structure for the different specimens illustrates the varied topology and geometry observed in porous rocks. This development foreshadows a new numerical laboratory approach to the study of complex porous materials

Dynamics of Wetting Fronts in Porous Media

We propose a new phenomenological approach for describing the dynamics of wetting front propagation in porous media. Unlike traditional models, the proposed approach is based on dynamic nature of the relation between capillary pressure and medium saturation. We choose a modified phase-field model of solidification as a particular case of such dynamic relation. We show that in the traveling wave regime the results obtained from our approach reproduce those derived from the standard model of flow in porous media. In more general case, the proposed approach reveals the dependence of front dynamics upon the flow regime.Comment: 4 pages, 2 figures, revte

Chord distribution functions of three-dimensional random media: Approximate first-passage times of Gaussian processes

The main result of this paper is a semi-analytic approximation for the chord distribution functions of three-dimensional models of microstructure derived from Gaussian random fields. In the simplest case the chord functions are equivalent to a standard first-passage time problem, i.e., the probability density governing the time taken by a Gaussian random process to first exceed a threshold. We obtain an approximation based on the assumption that successive chords are independent. The result is a generalization of the independent interval approximation recently used to determine the exponent of persistence time decay in coarsening. The approximation is easily extended to more general models based on the intersection and union sets of models generated from the iso-surfaces of random fields. The chord distribution functions play an important role in the characterization of random composite and porous materials. Our results are compared with experimental data obtained from a three-dimensional image of a porous Fontainebleau sandstone and a two-dimensional image of a tungsten-silver composite alloy.Comment: 12 pages, 11 figures. Submitted to Phys. Rev.

Deletion of the GABAA α2-subunit does not alter self dministration of cocaine or reinstatement of cocaine seeking

Rationale GABAA receptors containing α2-subunits are highly represented in brain areas that are involved in motivation and reward, and have been associated with addiction to several drugs, including cocaine. We have shown previously that a deletion of the α2-subunit results in an absence of sensitisation to cocaine. Objective We investigated the reinforcing properties of cocaine in GABAA α2-subunit knockout (KO) mice using an intravenous self-administration procedure. Methods α2-subunit wildtype (WT), heterozygous (HT) and KO mice were trained to lever press for a 30 % condensed milk solution. After implantation with a jugular catheter, mice were trained to lever press for cocaine (0.5 mg/kg/infusion) during ten daily sessions. Responding was extinguished and the mice tested for cue- and cocaine-primed reinstatement. Separate groups of mice were trained to respond for decreasing doses of cocaine (0.25, 0.125, 0.06 and 0.03 mg/kg). Results No differences were found in acquisition of lever pressing for milk. All genotypes acquired self-administration of cocaine and did not differ in rates of self-administration, dose dependency or reinstatement. However, whilst WT and HT mice showed a dose-dependent increase in lever pressing during the cue presentation, KO mice did not. Conclusions Despite a reported absence of sensitisation, motivation to obtain cocaine remains unchanged in KO and HT mice. Reinstatement of cocaine seeking by cocaine and cocaine-paired cues is also unaffected. We postulate that whilst not directly involved in reward perception, the α2-subunit may be involved in modulating the “energising” aspect of cocaine’s effects on reward-seeking