Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Long-term exposure to gaseous air pollutants and cardio-respiratory mortality in Brisbane, Australia

Air pollution is ranked by the World Health Organisation as one of the top ten contributors to the global burden of disease and injury. Exposure to gaseous air pollutants, even at a low level, has been associated with cardiorespiratory diseases (Vedal, Brauer et al. 2003). Most recent epidemiological studies of air pollution have used time-series analyses to explore the relationship between daily mortality or morbidity and daily ambient air pollution concentrations based on the same day or previous days (Hajat, Armstrong et al. 2007). However, most of the previous studies have examined the association between air pollution and health outcomes using air pollution data from a single monitoring site or average values from a few monitoring sites to represent the whole population of the study area. In fact, for a metropolitan city, ambient air pollution levels may differ significantly among the different areas. There is increasing concern that the relationships between air pollution and mortality may vary with geographical area (Chen, Mengersen et al. 2007). Additionally, some studies have indicated that socio-economic status can act as a confounder when investigating the relation between geographical location and health (Scoggins, Kjellstrom et al. 2004). This study examined the spatial variation in the relationship between long-term exposure to gaseous air pollutants (including nitrogen dioxide (NO2), ozone (O3) and sulphur dioxide (SO2)), and cardiorespiratory mortality in Brisbane, Australia, during the period 1996 - 2004.

Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

A comparison of different methods to determine diffusion length in dye-sensitized solar cells

A new steady state method for determination of the electron diffusion length in dye-sensitized solar cells (DSCs) is described and illustrated with data obtained using cells containing three different types of electrolyte. The method is based on using near-IR absorbance methods to establish pairs of illumination intensity for which the total number of trapped electrons is the same at open circuit (where all electrons are lost by interfacial electron transfer) as at short circuit (where the majority of electrons are collected at the contact). Electron diffusion length values obtained by this method are compared with values derived by intensity modulated methods and by impedance measurements under illumination. The results indicate that the values of electron diffusion length derived from the steady state measurements are consistently lower than the values obtained by the non steady-state methods. For all three electrolytes used in the study, the electron diffusion length was sufficiently high to guarantee electron collection efficiencies greater than 90%. Measurement of the trap distributions by near-IR absorption confirmed earlier observations of much higher electron trap densities for electrolytes containing Li+ ions. It is suggested that the electron trap distributions may not be intrinsic properties of the TiO2 nanoparticles, but may be associated with electron-ion interactions.

Investigation of highly regulated promoters for the production of recombinant proteins in plants

Plants have been identified as promising expression systems for the commercial production of recombinant proteins. Plant-based protein production or “biofarming” offers a number of advantages over traditional expression systems in terms of scale of production, the capacity for post-translation processing, providing a product free of contaminants and cost effectiveness. A number of pharmaceutically important and commercially valuable proteins, such as antibodies, biopharmaceuticals and industrial enzymes are currently being produced in plant expression systems. However, several challenges still remain to improve recombinant protein yield with no ill effect on the host plant. The ability for transgenic plants to produce foreign proteins at commercially viable levels can be directly related to the level and cell specificity of the selected promoter driving the transgene. The accumulation of recombinant proteins may be controlled by a tissue-specific, developmentally-regulated or chemically-inducible promoter such that expression of recombinant proteins can be spatially- or temporally- controlled. The strict control of gene expression is particularly useful for proteins that are considered toxic and whose expression is likely to have a detrimental effect on plant growth. To date, the most commonly used promoter in plant biotechnology is the cauliflower mosaic virus (CaMV) 35S promoter which is used to drive strong, constitutive transgene expression in most organs of transgenic plants. Of particular interest to researchers in the Centre for Tropical Crops and Biocommodities at QUT are tissue-specific promoters for the accumulation of foreign proteins in the roots, seeds and fruit of various plant species, including tobacco, banana and sugarcane. Therefore this Masters project aimed to isolate and characterise root- and seed-specific promoters for the control of genes encoding recombinant proteins in plant-based expression systems. Additionally, the effects of matching cognate terminators with their respective gene promoters were assessed. The Arabidopsis root promoters ARSK1 and EIR1 were selected from the literature based on their reported limited root expression profiles. Both promoters were analysed using the PlantCARE database to identify putative motifs or cis-acting elements that may be associated with this activity. A number of motifs were identified in the ARSK1 promoter region including, WUN (wound-inducible), MBS (MYB binding site), Skn-1, and a RY core element (seed-specific) and in the EIR1 promoter region including, Skn-1 (seed-specific), Box-W1 (fungal elicitor), Aux-RR core (auxin response) and ABRE (ABA response). However, no previously reported root-specific cis-acting elements were observed in either promoter region. To confirm root specificity, both promoters, and truncated versions, were fused to the GUS reporter gene and the expression cassette introduced into Arabidopsis via Agrobacterium-mediated transformation. Despite the reported tissue-specific nature of these promoters, both upstream regulatory regions directed constitutive GUS expression in all transgenic plants. Further, similar levels of GUS expression from the ARSK1 promoter were directed by the control CaMV 35S promoter. The truncated version of the EIR1 promoter (1.2 Kb) showed some differences in the level of GUS expression compared to the 2.2 Kb promoter. Therefore, this suggests an enhancer element is contained in the 2.2 Kb upstream region that increases transgene expression. The Arabidopsis seed-specific genes ATS1 and ATS3 were selected from the literature based on their seed-specific expression profiles and gene expression confirmed in this study as seed-specific by RT-PCR analysis. The selected promoter regions were analysed using the PlantCARE database in order to identify any putative cis elements. The seed-specific motifs GCN4 and Skn-1 were identified in both promoter regions that are associated with elevated expression levels in the endosperm. Additionaly, the seed-specific RY element and the ABRE were located in the ATS1 promoter. Both promoters were fused to the GUS reporter gene and used to transform Arabidopsis plants. GUS expression from the putative promoters was consitutive in all transgenic Arabidopsis tissue tested. Importantly, the positive control FAE1 seed-specific promoter also directed constitutive GUS expression throughout transgenic Arabidopsis plants. The constitutive nature seen in all of the promoters used in this study was not anticipated. While variations in promoter activity can be caused by a number of influencing factors, the variation in promoter activity observed here would imply a major contributing factor common to all plant expression cassettes tested. All promoter constructs generated in this study were based on the binary vector pCAMBIA2300. This vector contains the plant selection gene (NPTII) under the transcriptional control of the duplicated CaMV 35S promoter. This CaMV 35S promoter contains two enhancer domains that confer strong, constitutive expression of the selection gene and is located immediately upstream of the promoter-GUS fusion. During the course of this project, Yoo et al. (2005) reported that transgene expression is significantly affected when the expression cassette is located on the same T-DNA as the 35S enhancer. It was concluded, the trans-acting effects of the enhancer activate and control transgene expression causing irregular expression patterns. This phenomenon seems the most plausible reason for the constitutive expression profiles observed with the root- and seed-specific promoters assessed in this study. The expression from some promoters can be influenced by their cognate terminator sequences. Therefore, the Arabidopsis ARSK1, EIR1, ATS1 and ATS3 terminator sequences were isolated and incorporated into expression cassettes containing the GUS reporter gene under the control of their cognate promoters. Again, unrestricted GUS activity was displayed throughout transgenic plants transformed with these reporter gene fusions. As previously discussed constitutive GUS expression was most likely due to the trans-acting effect of the upstream CaMV 35S promoter in the selection cassette located on the same T-DNA. The results obtained in this study make it impossible to assess the influence matching terminators with their cognate promoters have on transgene expression profiles. The obvious future direction of research continuing from this study would be to transform pBIN-based promoter-GUS fusions (ie. constructs containing no CaMV 35S promoter driving the plant selection gene) into Arabidopsis in order to determine the true tissue specificity of these promoters and evaluate the effects of their cognate 3’ terminator sequences. Further, promoter truncations based around the cis-elements identified here may assist in determining whether these motifs are in fact involved in the overall activity of the promoter.

Mobile data technologies and SME adoption and diffusion : an empirical study on barriers and facilitators

The technological environment in which Australian SMEs operate can be best described as dynamic and vital. The rate of technological change provides the SME owner/manager a complex and challenging operational context. Wireless applications are being developed that provide mobile devices with Internet content and e-business services. In Australia the adoption of e-commerce by large organisations has been relatively high, however the same cannot be said for SMEs where adoption has been slower than other developed countries. In contrast however mobile telephone adoption and diffusion is relatively high by SMEs. This exploratory study identifies attitudes, perceptions and issues for mobile data technologies by regional SME owner/managers across a range of industry sectors. The major issues include the sector the firm belongs to, the current adoption status of the firm, the level of mistrust of the IT industry, the cost of the technologies and the applications and attributes of the technologies.

Confusion with diffusion? Unravelling is diffusion and innovation literature with a focus on SMEs

The aim of this paper is to contribute to the understanding of various models used in research for the adoption and diffusion of information technology in small and medium-sized enterprises (SMEs). Starting with Rogers' diffusion theory and behavioural models, technology adoption models used in IS research are discussed. Empirical research has shown that the reasons why firms choose to adopt or not adopt technology is dependent on a number of factors. These factors can be categorised as owner/manager characteristics, firm characteristics and other characteristics. The existing models explaining IS diffusion and adoption by SMEs overlap and complement each other. This paper reviews the existing literature and proposes a comprehensive model which includes the whole array of variables from earlier models.