Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Do derivatives have a role in the risk-shifting behaviour of fund managers?

In this paper we examine the extent to which derivatives are used to affect the risk-shifting behaviour of Australian equity fund managers. We find, after periods of good and poor performance, the risk-shifting behaviour of fund managers is different between derivative users and non-users. Our results support the gaming and active competition hypotheses but there is little support for the cash flow hypothesis. The study also allows for a complex reporting environment by analysing data across three alternate time periods: the calendar year, financial year and quarterly frames. Given that our results are not consistent across time periods for users and non-users of derivatives, some caution in interpretation is required.

The effect of amphiphilic siloxane oligomers on fibroblast and keratinocyte proliferation and apoptosis

The formation of hypertrophic scars is a frequent medical outcome of wound repair and often requires further therapy with treatments such as Silicone Gel Sheets (SGS) or apoptosis-inducing agents, including bleomycin. Although widely used, knowledge regarding SGS and their mode of action is limited. Preliminary research has shown that small amounts of amphiphilic silicone present in SGS have the ability to move into skin during treatment. We demonstrate herein that a commercially available analogue of these amphiphilic siloxane species, the rake copolymer GP226, decreases collagen synthesis upon exposure to cultures of fibroblasts derived from hypertrophic scars (HSF). By size exclusion chromatography, GP226 was found to be a mixture of siloxane species, containing five fractions of different molecular weight. By studies of collagen production, cell viability and proliferation, it was revealed that a low molecular weight fraction (fraction IV) was the most active, reducing the number of viable cells present following treatment and thereby reducing collagen production as a result. Upon exposure of fraction IV to human keratinocytes, viability and proliferation was also significantly affected. HSF undergoing apoptosis after application of fraction IV were also detected via real-time microscopy and by using the TUNEL assay. Taken together, these data suggests that these amphiphilic siloxanes could be potential non-invasive substitutes to apoptotic-inducing chemical agents that are currently used as scar treatments.

Pre-clinical evaluation of amphiphilic silicone oligomers for scar remediation

The formation of hypertrophic scars is a frequent outcome of wound repair and often requires further therapy with treatments such as silicone gel sheets (SGS; Perkins et al., 1983). Although widely used, knowledge regarding SGS and their mechanism of action on hypertrophic scars is limited. Furthermore, SGS require consistent application for at least twelve hours a day for up to twelve consecutive months, beginning as soon as wound reepithelialisation has occurred. Preliminary research at QUT has shown that some species of silicone present in SGS have the ability to permeate into collagen gel skin mimetics upon exposure. An analogue of these species, GP226, was found to decrease both collagen synthesis and the total amount of collagen present following exposure to cultures of cells derived from hypertrophic scars. This silicone of interest was a crude mixture of silicone species, which resolved into five fractions of different molecular weight. These five fractions were found to have differing effects on collagen synthesis and cell viability following exposure to fibroblasts derived from hypertrophic scars (HSF), keloid scars (KF) and normal skin (nHSF and nKF). The research performed herein continues to further assess the potential of GP226 and its fractions for scar remediation by determining in more detail its effects on HSF, KF, nHSF, nKF and human keratinocytes (HK) in terms of cell viability and proliferation at various time points. Through these studies it was revealed that Fraction IV was the most active fraction as it induced a reduction in cell viability and proliferation most similar to that observed with GP226. Cells undergoing apoptosis were also detected in HSF cultures exposed to GP226 and Fraction IV using the Tunel assay (Roche). These investigations were difficult to pursue further as the fractionation process used for GP226 was labour-intensive and time inefficient. Therefore a number of silicones with similar structure to Fraction IV were synthesised and screened for their effect following application to HSF and nHSF. PDMS7-g-PEG7, a silicone-PEG copolymer of low molecular weight and low hydrophilic-lipophilic balance factor, was found to be the most effective at reducing cell proliferation and inducing apoptosis in cultures of HSF, nHSF and HK. Further studies investigated gene expression through microarray and superarray techniques and demonstrated that many genes are differentially expressed in HSF following treatment with GP226, Fraction IV and PDMS7-g-PEG7. In brief, it was demonstrated that genes for TGFβ1 and TNF are not differentially regulated while genes for AIFM2, IL8, NSMAF, SMAD7, TRAF3 and IGF2R show increased expression (>1.8 fold change) following treatment with PDMS7-g-PEG7. In addition, genes for αSMA, TRAF2, COL1A1 and COL3A1 have decreased expression (>-1.8 fold change) following treatment with GP226, Fraction IV and PDMS7-g-PEG7. The data obtained suggest that many different pathways related to apoptosis and collagen synthesis are affected in HSF following exposure to PDMS7-g-PEG7. The significance is that silicone-PEG copolymers, such as GP226, Fraction IV and PDMS7-g-PEG7, could potentially be a non-invasive substitute to apoptosis-inducing chemical agents that are currently used as scar treatments. It is anticipated that these findings will ultimately contribute to the development of a novel scar therapy with faster action and improved outcomes for patients suffering from hypertrophic scars.

An investigation into the effect of amphiphilic siloxane oligomers on dermal fibroblasts

This study investigates the effect of well-defined poly(dimethylsiloxane)-poly(ethylene glycol) (PDMS-PEG) ABA linear block co-oligomers on the proliferation of human dermal fibroblasts. The co-oligomers assessed ranged in molecular weight (MW) from 1335 to 5208 Da and hydrophilic-lipophilic balance (HLB) from 5.9 to 16.6 by varying the number of both PDMS and PEG units. In general, it was found that co-oligomers of low MW or intermediate hydrophilicity significantly reduced fibroblast proliferation. A linear relationship between down-regulation of fibroblast proliferation, and the ratio HLB/MW was observed at concentrations of 0.1 and 1.0 wt % of the oligomers. This enabled the structures with highest efficiency to be determined. These results suggest the possible use of the PEG-PDMS-PEG block co-oligomers as an alternative to silicone gels for hypertrophic scar remediation.

Amphiphilic silicone archtectures via anaerobic thiol - ene chemistry

Despite broad application, few silicone-based surfactants of known structure or, therefore, surfactancy have been prepared because of an absence of selective routes and instability of silicones to acid and base. Herein the synthesis of a library of explicit silicone-poly(ethylene glycol) (PEG) materials is reported. Pure silicone fragments were generated by the B(C(6)F(5))(3)-catalyzed condensation of alkoxysilanes and vinyl-functionalized hydrosilanes. The resulting pure products were coupled to thiol-terminated PEG materials using photogenerated radicals under anaerobic conditions.

Hydrogen-bonding in cyclic imides and amide carboxylic acid derivatives from the facile reaction of cis-cyclohexane-1,2-carboxylic anhydride with o- and p-anisidine and m- and p-aminobenzoic acids

The structures of the open chain amide carboxylic acid rac-cis-[2-(2-methoxyphenyl)carbamoyl]cyclohexane-1-carboxylic acid, C15H19NO4, (I) and the cyclic imides rac-cis-2-(4-methoxyphenyl)-3a,4,5,6,7,7-hexahydroisoindole-1,3-dione,C15H17NO3, (II), chiral cis-2-(3-carboxyphenyl)-3a,4,5,6,7,7a-hexahydroisoindole-1,3-dione, C15H15NO4,(III) and rac-cis-2-(4-carboxyphenyl)- 3a,4,5,6,7,7a-hexahydroisoindole-1,3-dione monohydrate, C15H15NO4. H2O) (IV), are reported. In the amide acid (I), the phenylcarbamoyl group is essentially planar [maximum deviation from the least-squares plane = 0.060(1)Ang. for the amide O atom], the molecules form discrete centrosymmetric dimers through intermolecular cyclic carboxy-carboxy O-H...O hydrogen-bonding interactions [graph set notation R2/2(8)]. The cyclic imides (II)--(IV) are conformationally similar, with comparable phenyl ring rotations about the imide N-C(aromatic) bond [dihedral angles between the benzene and isoindole rings = 51.55(7)deg. in (II), 59.22(12)deg. in (III) and 51.99(14)deg. in (IV). Unlike (II) in which only weak intermolecular C-H...O(imide) hydrogen bonding is present, the crystal packing of imides (III) and (IV) shows strong intermolecular carboxylic acid O-H...O hydrogen-bonding associations. With (III), these involve imide O-atom acceptors, giving one-dimensional zigzag chains [graph set C(9)], while with the monohydrate (IV), the hydrogen bond involves the partially disordered water molecule which also bridges molecules through both imide and carboxyl O-atom acceptors in a cyclic R4/4(12) association, giving a two-dimensional sheet structure. The structures reported here expand the structural data base for compounds of this series formed from the facile reaction of cis-cyclohexane-1,2-dicarboxylic anhydride with substituted anilines, in which there is a much larger incidence of cyclic imides compared to amide carboxylic acids.