Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Effect on charitable bodies of taxation alternations

It appears that the Industry Commission terms of reference will include a review of (among other things) the appropriateness of the present taxation treatment of charitable organisations. It is uncertain exactly which taxation treatments might be reviewed. However, at a federal government level, a review of the current taxation treatment of charitable organisations could refer to a review of the following taxation measures...

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

The Cyndi Lauper affect : bodies, girlhood and popular culture [Abstract]

Using a collective biography method informed by a Deleuzian theoretical approach (Davies & Gannon, 2009), this paper analyses embodied memories of girlhood becomings through affective engagements with resonating images in media and popular culture. In this approach to analysis we move beyond an impasse in some feminist cultural studies where studies of popular culture have been understood through theories of representation and reception that retain a sense of discrete subjectivity and linear effects. In these approaches, analysis focuses respectively on decoding and deciphering images in terms of their normative and ideological baggage, and, particularly with moving images, on psychological readings (Coleman, 2011; Driscoll, 2002). Understanding bodies and popular culture through Deleuzian notions of ‘becoming’ and ‘assemblage’ opens possibilities for feminist researchers to consider the ways in which bodies are not separate to images but rather, are known, felt, materialised and mobilised with/through images (Coleman, 2008, 2009, 2011). We tease out the implications of this new approach to media affects through two memories of girls’ engagements with media images, reconceived as moments of embodied being within affective flows of popular culture that might momentarily extend upon the ways of being and doing girlhood.

A multi-stage history for carbonaceous material in extraterrestrial chondritic porous aggregate W7029*A and a new cosmothermometer

A new set of primitive extraterrestrial materials collected in the Earth's stratosphere include Chondritic Porous Aggregates (CPA's) [1]. CPAs have a complex and variable mineralogy [1-3] that include 'organic compounds' [4,5] and poorly graphitised carbon (PGC)[6]. This study presents a continuation of our detailed Analytical Electron Microscope study on carbon-rich CPA W7029*A from the JSC Cosmic Dust Collection. This CPA is an uncontaminated sample that survived atmospheric entry without appreciable alteration [7] and which contains ~44% carbonaceous material. The carbonaceous composition of selected particles was confirmed by Electron Energy Loss Spectroscopy and Selected Area Electron Diffraction (SAED). Possible carbonaceous contaminants introduced by specimen preparation techniques are easily recognised from indigenous CPA carbon particles [8] and do not bias our interpretations.

Conduction-radiation effect on natural convection flow in a fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls

The effect of conduction-convection-radiation on natural convection flow of Newtonian optically thick gray fluid, confined in a non-Darcian porous media square cavity is numerically studied. For the gray fluid consideration is given to Rosseland diffusion approximation. Further assuming that (i) the temperature of the left vertical wall is varying linearly with height, (ii) cooled right vertical and top walls and (iii) the bottom wall is uniformly-heated. The governing equations are solved using the Alternate Direct Implicit method together with the Successive Over Relaxation technique. The investigation of the effect of governing parameters namely the Forschheimer resistance (Γ), the Planck constant (Rd), and the temperature difference (Δ), on flow pattern and heat transfer characteristics has been carried out. It was seen that the reduction of flow and heat transfer occurs as the Forschheimer resistance is increased. On the other hand both the strength of flow and heat transfer increases as the temperature ratio, Δ, is increased.

Metastable carbon in two chondritic porous interplanetary dust particles

An understanding of carbonaceous matter in primitive extraterrestrial materials is an essential component of studies on dust evolution in the interstellar medium and the early history of the Solar System. We have suggested previously that a record of graphitization is preserved in chondritic porous (CP) aggregates and carbonaceous chondrites1,2 and that the detailed mineralogy of CP aggregates can place boundary conditions on the nature of both physical and chemical processes which occurred at the time of their formation2,3. Here, we report further analytical electron microscope (AEM) studies on carbonaceous material in two CP aggregates which suggest that a record of hydrocarbon carbonization may also be preserved in these materials. This suggestion is, based upon the presence of well-ordered carbon-2H (lonsdaleite) in CP aggregates W7029*A and W7010*A2. This carbon is a metastable phase resulting from hydrous pyrolysis below 300-350°C and may be a precursor to poorly graphitized carbons (PGCs) in primitive extraterrestrial materials2. © 1987 Nature Publishing Group.

Layer silicates in a chondritic porous interplanetary dust particle

Analytical electron microscopy on individual grains from a portion of a chondritic porous interplanetary dust particle (aggregate W7029C1 from the NASA Johnson Space Center Cosmic Dust Collection) shows that layer silicates compose 50 percent of the silicate fraction examined. These layer silicates can be classified into two distinct crystallochemical groups: (1) fine-grained, polycrystalline smectite minerals; and (2) well-ordered, single crystals of kaolinite and Mg-poor talc. The layer silicates in this portion of sample W7029(asterisk)A are dissimilar to those described in other chondritic porous aggregates. The predominant layer silicate assemblage in W7029(asterisk)A indicates that heating of the aggregate during atmospheric entry was brief and probably to a temperature less than 300C. Comparison with terrestrial phyllosilicate occurrences suggests that some layer silicates in aggregate W7029(asterisk)A may have been formed by alteratiton from preexisting silicate minerals at low temperatures (less than 25C) after aggregate formation.

Diagenesis in interplanetary dust - chondritic porous aggregate w7029-star-a

In previous Analytical Electron Microscope studies of extraterrestrial Chondritic Porous Aggregate (CPA) W7029* A, we have reported on the presence of layer silicates(Rietmeijer and Mackinnon, 1984a; Mackinnon and Rietmeijer, 1983) and metal oxides (Rietmeijer and Mackinnon, 1984a; Mackinnon and Rietmeijer, 1984). We present here a continuation ofthis detailed mineralogical study and propose a scenario which may account for the variety and types of phases observed in this CPA. At least 50% ofCPA W7029*A is carbonaceous material, primarily poorly graphitised carbon (POC) with morphologies similar to POC in acid residues of carbonaceous chondrites (Smith and Busek, 1981; Lumpkin, 1983). The basal spacing of graphite in CPA W7029*A ranges from 3.47-3.52 A and compares with doo, of graphite in the Allende residues (Smith and Buseck, 1981; Lumpkin, 1983). Low-temperature phases comprise - 20% of CPA W7029*A and include layer silicates, Bi,O" a-FeOOH(Rietmeijer and Mackinnon, 1984a; Mackinnon and Rietmeijer, 1983), BaSO.,.Ti.O, plates, pentlandite-violarite and bornite. Clusters of Mg-rich olivine and pyroxene make up - 12% of the aggregate...

Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

Were intercalated komatiites and dacites at the Black Swan nickel sulphide mine, Yilgarn Craton, Western Australia, emplaced as extrusive lavas or intrusive bodies? The significance of breccia textures and contact relationships

Intercalated Archean komatiites and dacites sit above a thick footwall dacite unit in the host rock succession at the Black Swan Nickel Mine, north of Kalgoorlie in the Yilgarn Craton, Western Australia. Both lithofacies occur in units that vary in scale from laterally extensive at the scale of the mine lease to localized, thin, irregular bodies, from > 100 m thick to only centimetres thick. Some dacites are only slightly altered and deformed, and are interpreted to post-date major deformation and alteration (late porphyries). However, the majority of the dacites display evidence of deformation, especially at contacts, and metamorphism, varying from silicification and chlorite alteration at contacts to pervasive low grade regional metamorphic alteration represented by common assemblages of chlorite, sericite and albite. Texturally, the dacites vary from entirely massive and coherent to partially brecciated to totally brecciated. Strangely, some dacites are coherent at the margins and brecciated internally. Breccia textures vary from cryptically defined, to blocky, closely packed, in situ jig-saw fit textures with secondary minerals in fractures between clasts, to more apparent matrix rich textures with round clast forms, giving apparent conglomerate textures. Some clast zones have multi-coloured clasts, giving the impression of varied provenance. Strangely however, all these textural variants have gradational relationships with each other, and no bedding or depositional structures are present. This indicates that all textures have an in situ origin. The komatiites are generally altered and pervasively carbonate veined. Preservation of original textures is patchy and local, but includes coarse adcumulate, mesocumulate, orthocumulate, crescumulate-harrisite and occasionally spinifex textures. Where original contacts between komatiites and dacites are preserved intact (i.e. not sheared or overprinted by alteration), the komatiites have chilled margins, whereas the dacites do not. The margins of the dacites are commonly silicified, and inclusions of dacite occur in komatiite, even at the top contacts of komatiite units, but komatiite clasts do not occur in the dacites. The komatiites therefore were emplaced as sills into the dacites, and the intercalated relationships are interpreted as intrusive. The brecciation and alteration in the dacites are interpreted as being largely due to hydraulic fracturing and alteration induced by contact metamorphic effects and hydrothermal alteration deriving from the intrusion of komatiites into the felsic pile. The absence of autobreccia and hyaloclastite textures in the dacites suggest that they were emplaced as an earlier intrusive (sill?) complex at a high level in the crust.