Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Who needs it? An exploratory investigation into the reaction of small and medium enterprises to mobile data technologies

The technological environment in which contemporary small and medium-sized enterprises (SMEs) operate can only be described as dynamic. The seemingly exponential nature of technological change, characterised by perceived increases in the benefits associated with various technologies, shortening product life cycles and changing standards, provides for the small and medium-sized enterprise a complex and challenging operational context. The development of infrastructures capable of supporting the Wireless Application Protocol (WAP)and associated 'wireless' applications represents the latest generation of technological innovation with potential appeal to SMEs and end-users alike. The primary aim of this research was to understand the mobile data technology needs of SMEs in a regional setting. The research was especially concerned with perceived needs across three market segments; non-adopters of new technology, partial-adopters of new technology and full-adopters of new technology. Working with an industry partner, focus groups were conducted with each of these segments with the discussions focused on the use of the latest WP products and services. Some of the results are presented in this paper.

Emotional and behavioural reaction to intrusive thoughts

A self-report measure of the emotional and behavioural reactions to intrusive thoughts was developed. The paper presents data that confirm the stability, reliability and validity of the new 7-item measure. Emotional and behavioural reactions to intrusions emerged as separate factors on the Emotional and Behavioural Reactions to Intrusions Questionnaire (EBRIQ), a finding confirmed by an independent stress study. Test retest reliability over 30-70 days was good. Expected relationships with other constructs were significant. Stronger negative responses to intrusions were associated with lower mindfulness scores and higher ratings of experiential avoidance, thought suppression and intensity and frequency of craving. The EBRIQ will help explore differences in reactions to intrusive thoughts in clinical and non clinical populations, and across different emotional and behavioural states. It will also be useful in assessing the effects of therapeutic approaches such as mindfulness.

Nonlinear control of the Reaction Wheel Pendulum

In this paper we introduce the Reaction Wheel Pendulum, a novel mechanical system consisting of a physical pendulum with a rotating bob. This system has several attractive features both from a pedagogical standpoint and from a research standpoint. From a pedagogical standpoint, the dynamics are the simplest among the various pendulum experiments available so that the system can be introduced to students earlier in their education. At the same time, the system is nonlinear and underactuated so that it can be used as a benchmark experiment to study recent advanced methodologies in nonlinear control, such as feedback linearization, passivity methods, backstepping and hybrid control. In this paper we discuss two control approaches for the problems of swingup and balance, namely, feedback linearization and passivity based control. We first show that the system is locally feedback linearizable by a local diffeomorphism in state space and nonlinear feedback. We compare the feedback linearization control with a linear pole-placement control for the problem of balancing the pendulum about the inverted position. For the swingup problem we discuss an energy approach based on collocated partial feedback linearization, and passivity of the resulting zero dynamics. A hybrid/switching control strategy is used to switch between the swingup and the balance control. Experimental results are presented.

Electron diffusion and back reaction in dye-sensitized solar cells : the effect of nonlinear recombination kinetics

The electron collection efficiency in dye-sensitized solar cells (DSCs) is usually related to the electron diffusion length, L = (Dτ)^1/2, where D is the diffusion coefficient of mobile electrons and τ is their lifetime, which is determined by electron transfer to the redox electrolyte. Analysis of incident photon-to-current efficiency (IPCE) spectra for front and rear illumination consistently gives smaller values of L than those derived from small amplitude methods. We show that the IPCE analysis is incorrect if recombination is not first-order in free electron concentration, and we demonstrate that the intensity dependence of the apparent L derived by first-order analysis of IPCE measurements and the voltage dependence of L derived from perturbation experiments can be fitted using the same reaction order, γ ≈ 0.8. The new analysis presented in this letter resolves the controversy over why L values derived from small amplitude methods are larger than those obtained from IPCE data.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Nanostructured metal oxides as adsorbents and photocatalysts

This research underlines the extensive application of nanostructured metal oxides in environmental systems such as hazardous waste remediation and water purification. This study tries to forge a new understanding of the complexity of adsorption and photocatalysis in the process of water treatment. Sodium niobate doped with a different amount of tantalum, was prepared via a hydrothermal reaction and was observed to be able to adsorb highly hazardous bivalent radioactive isotopes such as Sr2+ and Ra2+ions. This study facilitates the preparation of Nb-based adsorbents for efficiently removing toxic radioactive ions from contaminated water and also identifies the importance of understanding the influence of heterovalent substitution in microporous frameworks. Clay adsorbents were prepared via a two-step method to remove anionic and non-ionic herbicides from water. Firstly, layered beidellite clay was treated with acid in a hydrothermal process; secondly, common silane coupling agents, 3-chloro-propyl trimethoxysilane or triethoxy silane, were grafted onto the acid treated samples to prepare the adsorption materials. In order to isolate the effect of the clay surface, we compared the adsorption property of clay adsorbents with ƒ×-Al2O3 nanofibres grafted with the same functional groups. Thin alumina (£^-Al2O3) nanofibres were modified by the grafting of two organosilane agents 3-chloropropyltriethoxysilane and octyl triethoxysilane onto the surface, for the adsorptive removal of alachlor and imazaquin herbicides from water. The formation of organic groups during the functionalisation process established super hydrophobic sites along the surfaces and those non-polar regions of the surfaces were able to make close contact with the organic pollutants. A new structure of anatase crystals linked to clay fragments was synthesised by the reaction of TiOSO4 with laponite clay for the degradation of pesticides. Based on the Ti/clay ratio, these new catalysts showed a high degradation rate when compared with P25. Moreover, immobilized TiO2 on laponite clay fragments could be readily separated out from a slurry system after the photocatalytic reaction. Using a series of partial phase transition methods, an effective catalyst with fibril morphology was prepared for the degradation of different types of phenols and trace amount of herbicides from water. Both H-titanate and TiO2-(B) fibres coated with anatase nanocrystal were studied. When compared with a laponite clay photocatalyst, it was found that anatase dotted TiO2-(B) fibres prepared by a 45 h hydrothermal treatment followed by calcination were not only superior in performance in photocatalysis but could also be readily separated from a slurry system after photocatalytic reactions. This study has laid the foundation for the development of the ability to fabricate highly efficient nanostructured solids for the removal of radioactive ions and organic pollutants from contaminated water. These results now seem set to contribute to the development of advanced water purification devices in the future. These modified nanostructured materials with unusual properties have broadened their application range beyond their traditional use as adsorbents, to also encompass the storage of nuclear waste after concentrating from contaminated water.

Multiple analysis of three common genetic alterations associated with thrombophilia

We have previously reported the use of a novel mini-sequencing protocol for detection of the factor V Leiden variant, the first nucleotide change (FNC) technology. This technology is based on a single nucleotide extension of a primer, which is hybridized immediately adjacent to the site of mutation. The extended nucleotide that carries a reporter molecule (fluorescein) has the power to discriminate the genotype at the site of mutation. More recently, the prothrombin 20210 and thermolabile methylene tetrahydrofolate reductase (MTHFR) 677 variants have been identified as possible risk factors associated with thrombophilia. This study describes the use of the FNC technology in a combined assay to detect factor V, prothrombin and MTHFR variants in a population of Australian blood donors, and describes the objective numerical methodology used to determine genotype cut-off values for each genetic variation. Using FNC to test 500 normal blood donors, the incidence of Factor V Leiden was 3.6% (all heterozygous), that of prothrombin 20210 was 2.8% (all heterozygous) and that of MTHFR was 10% (homozygous). The combined FNC technology offers a simple, rapid, automatable DNA-based test for the detection of these three important mutations that are associated with familial thrombophilia. (C) 2000 Lippincott Williams and Wilkins.

Use of first nucleotide change technology to determine the frequency of factor V Leiden in a population of Australian blood donors

Activated protein C resistance (APCR), the most common risk factor for venous thrombosis, is the result of a G to A base substitution at nucleotide 1691 (R506Q) in the factor V gene. Current techniques to detect the factor V Leiden mutation, such as determination of restriction length polymorphisms, do not have the capacity to screen large numbers of samples in a rapid, cost- effective test. The aim of this study was to apply the first nucleotide change (FNC) technology, to the detection of the factor V Leiden mutation. After preliminary amplification of genomic DNA by polymerase chain reaction (PCR), an allele-specific primer was hybridised to the PCR product and extended using fluorescent terminating dideoxynucleotides which were detected by colorimetric assay. Using this ELISA-based assay, the prevalence of the factor V Leiden mutation was determined in an Australian blood donor population (n = 500). A total of 18 heterozygotes were identified (3.6%) and all of these were confirmed with conventional MnlI restriction digest. No homozygotes for the variant allele were detected. We conclude from this study that the frequency of 3.6% is compatible with others published for Caucasian populations. In addition, the FNC technology shows promise as the basis for a rapid, automated DNA based test for factor V Leiden.