The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

Numerical solution of an optimal control model of dendritic cell treatment of a growing tumour

A new optimal control model of the interactions between a growing tumour and the host immune system along with an immunotherapy treatment strategy is presented. The model is based on an ordinary differential equation model of interactions between the growing tu- mour and the natural killer, cytotoxic T lymphocyte and dendritic cells of the host immune system, extended through the addition of a control function representing the application of a dendritic cell treat- ment to the system. The numerical solution of this model, obtained from a multi species Runge–Kutta forward-backward sweep scheme, is described. We investigate the effects of varying the maximum al- lowed amount of dendritic cell vaccine administered to the system and find that control of the tumour cell population is best effected via a high initial vaccine level, followed by reduced treatment and finally cessation of treatment. We also found that increasing the strength of the dendritic cell vaccine causes an increase in the number of natural killer cells and lymphocytes, which in turn reduces the growth of the tumour.

The catalytic role of an isolated-Ti atom in the hydrogenation of Ti-doped Al(001) surface : An ab initio density functional theory calculation

Recent work [S. Chaudhuri, J.T. Muckerman, J. Phys. Chem. B 109 (2005) 6952] reported that two Ti-substituted atoms on an Al(0 0 1) surface can form a catalytically active site for the dissociation of H2, but the diffusion barrier of atomic H away from Ti site is as high as 1.57 eV. By using ab initio density functional calculations, we found that two hydrogen molecules can dissociate on isolated-Ti atom doped Al(0 0 1) surface with small activation barriers (0.21 and 0.235 eV for first and second H2, respectively). Additionally, the diffusion barrier of atomic H away from Ti site is also moderate (0.47 eV). These results contribute further towards understanding the improved kinetics observed in recycling of hydrogen with Ti-doped NaAlH4.

Prevalence and predictors of refractive error in a genetically isolated population : the Norfolk Island Eye Study

BACKGROUND: We aimed to determine the prevalence and associations of refractive error on Norfolk Island. DESIGN: Population-based study on Norfolk Island, South Pacific. PARTICIPANTS: All permanent residents on Norfolk Island aged ≥ 15 years were invited to participate. METHODS: Patients underwent non-cycloplegic autorefraction, slit-lamp biomicroscope examination and biometry assessment. Only phakic eyes were analysed. MAIN OUTCOME MEASURES: Prevalence and multivariate associations of refractive error and myopia. RESULTS: There were 677 people (645 right phakic eyes, 648 left phakic eyes) aged ≥ 15 years were included in this study. Mean age of participants was 51.1 (standard deviation 15.7; range 15-81). Three hundred and seventy-six people (55.5%) were female. Adjusted to the 2006 Norfolk Island population, prevalence estimates of refractive error were as follows: myopia (mean spherical equivalent ≥ -1.0 D) 10.1%, hypermetropia (mean spherical equivalent ≥ 1.0 D) 36.6%, and astigmatism 17.7%. Significant independent predictors of myopia in the multivariate model were lower age (P < 0.001), longer axial length (P < 0.001), shallower anterior chamber depth (P = 0.031) and increased corneal curvature (P < 0.001). Significant independent predictors of refractive error were increasing age (P < 0.001), male gender (P = 0.009), Pitcairn ancestry (P = 0.041), cataract (P < 0.001), longer axial length (P < 0.001) and decreased corneal curvature (P < 0.001). CONCLUSIONS: The prevalence of myopia on Norfolk Island is lower than on mainland Australia, and the Norfolk Island population demonstrates ethnic differences in the prevalence estimates. Given the significant associations between refractive error and several ocular biometry characteristics, Norfolk Island may be a useful population in which to find the genetic basis of refractive error.

Linkage disequilibrium analysis in the genetically isolated Norfolk Island population

Norfolk Island is a human genetic isolate, possessing unique population characteristics that could be utilized for complex disease gene localization. Our intention was to evaluate the extent and strength of linkage disequilibrium (LD) in the Norfolk isolate by investigating markers within Xq13.3 and the NOS2A gene encoding the inducible nitric oxide synthase. A total of six microsatellite markers spanning approximately 11 Mb were assessed on chromosome Xq13.3 in a group of 56 men from Norfolk Island. Additionally, three single nucleotide polymorphisms (SNPs) localizing to the NOS2A gene were analyzed in a subset of the complex Norfolk pedigree. With the exception of two of the marker pairs, one of which is the most distantly spaced marker, all the Xq13.3 marker pairs were found to be in significant LD indicating that LD extends up to 9.5-11.5 Mb in the Norfolk Island population. Also, all SNPs studied showed significant LD in both Norfolk Islanders and Australian Caucasians, with two of the marker pairs in complete LD in the Norfolk population only. The Norfolk Island study population possesses a unique set of characteristics including founder effect, geographical isolation, exhaustive genealogical information and phenotypic data of use to cardiovascular disease risk traits. With LD extending up to 9.5-11 Mb, the Norfolk isolate should be a powerful resource for the localization of complex disease genes.

Linkage mapping of CVD risk traits in the isolated Norfolk Island population

To understand the underlying genetic architecture of cardiovascular disease (CVD) risk traits, we undertook a genome-wide linkage scan to identify CVD quantitative trait loci (QTLs) in 377 individuals from the Norfolk Island population. The central aim of this research focused on the utilization of a genetically and geographically isolated population of individuals from Norfolk Island for the purposes of variance component linkage analysis to identify QTLs involved in CVD risk traits. Substantial evidence supports the involvement of traits such as systolic and diastolic blood pressures, high-density lipoprotein-cholesterol, low-density lipoprotein-cholesterol, body mass index and triglycerides as important risk factors for CVD pathogenesis. In addition to the environmental inXuences of poor diet, reduced physical activity, increasing age, cigarette smoking and alcohol consumption, many studies have illustrated a strong involvement of genetic components in the CVD phenotype through family and twin studies. We undertook a genome scan using 400 markers spaced approximately 10 cM in 600 individuals from Norfolk Island. Genotype data was analyzed using the variance components methods of SOLAR. Our results gave a peak LOD score of 2.01 localizing to chromosome 1p36 for systolic blood pressure and replicated previously implicated loci for other CVD relevant QTLs.

Phenotypical characterisation of the isolated Norfolk Island population focusing on epidemiological indicators of cardiovascular disease

Objectives Only 193 people from Pitcairn Island, all descended from 9 ‘Bounty’ mutineers and 12 Tahitian women, moved to the uninhabited Norfolk Island in 1856. Our objective was to assess the population of Norfolk Island, several thousand km off the eastern coast of Australia, as a genetic isolate of potential use for cardiovascular disease (CVD) gene mapping. Methods A total of 602 participants, approximately two thirds of the island’s present adult population, were characterized for a panel of CVD risk factors. Statistical power and heritability were calculated. Results Norfolk Islander’s possess an increased prevalence of hypertension, obesity and multiple CVD risk factors when compared to outbred Caucasian populations. 64% of the study participants were descendents of the island’s original founder population. Triglycerides, cholesterol, and blood pressures all had heritabilities above 0.2. Conclusions The Norfolk land population is a potentially useful genetic isolate for gene mapping studies aimed at identifying CVD risk factor quantitative trait loci (QTL).

An isolated MOSFET gate driver

Traditional methods of isolated MOSFET/IGBT gate drive are presented, and their pros and cons assessed. The best options are chosen to meet our objective— a small, high speed, low cost, low power isolated gate drive module. Two small ferrite bead transformers are used for isolation, one transmits power at 2.5MHz, the other sends narrow set reset pulses. On the secondary these pulses drive a transistor totem pole to ensure high current drive, and the value is held by CMOS buffers with positive feedback. An alternative design for driving logic level devices uses only an HC buffer on the secondary. Double sided SMDconstruction (primary one side, secondary on the other) yields an upright module 40x18x5mm. Propagation delaywas 20ns, and rise/fall time 15ns with a 1nF load. The design places no limits on frequency of operation or duty cycle. Power supply requirementswere 5V@20mA for operation below 100kHz, dominated by magnetising current.

Study of the underlying electrochemistry of polycrystalline gold electrodes in aqueous solution and electrocatalysis by large amplitude Fourier transformed alternating current voltammetry

Polycrystalline gold electrodes of the kind that are routinely used in analysis and catalysis in aqueous media are often regarded as exhibiting relatively simple double-layer charging/discharging and monolayer oxide formation/ removal in the positive potential region. Application of the large amplitude Fourier transformed alternating current (FT-ac) voltammetric technique that allows the faradaic current contribution of fast electron-transfer processes to be emphasized in the higher harmonic components has revealed the presence of well-defined faradaic (premonolayer oxidation) processes at positive potentials in the double-layer region in acidic and basic media which are enhanced by electrochemical activation. These underlying quasi-reversible interfacial electron-transfer processes may mediate the course of electrocatalytic oxidation reactions of hydrazine, ethylene glycol, and glucose on gold electrodes in aqueous media. The observed responses support key assumptions associated with the incipient hydrous oxide adatom mediator (IHOAM) model of electrocatalysis.

Auto-inhibition of hydrogen gas evolution on gold in aqueous acid solution

It was demonstrated recently that dramatic changes in the redox behaviour of gold/aqueous solution interfaces may be observed following either cathodic or thermal electrode pretreatment. Further work on the cathodic pretreatment of gold in acid solution revealed that as the activity of the gold surface was increased, its performance as a substrate for hydrogen gas evolution under constant potential conditions deteriorated. The change in activity of the gold atoms at the interface, which was attributed to a hydrogen embrittlement process (the occurrence of the latter was subsequently checked by surface microscopy), was confirmed, as in earlier work, by the appearance of a substantial anodic peak at ca. 0.5 V (RHE) in a post-activation positive sweep. Changes in the catalytic activity of a metal surface reflect the fact that the structure (or topography), thermodynamic activity and electronic properties of a surface are dependent not only on pretreatment but also, in the case of the hydrogen evolution reaction, vary with time during the course of reaction. As will be reported shortly, similar (and often more dramatic) time-dependent behaviour was observed for hydrogen gas evolution on other metal electrodes.

The role of defects, or active states, in surface electrochemistry with particular reference to gold in neutral solution

Metastable, active, or nonequilibrium states due to the presence of abnormal structures and various types of defects are well known in metallurgy. The role of such states at gold surfaces in neutral aqueous media (an important electrode system in the microsensor area) was explored using cyclic voltammetry. It was demonstrated that, as postulated in earlier work from this laboratory, there is a close relationship between premonolayer oxidation, multilayer hydrous oxide reduction and electrocatalytic behaviour in the case of this and other metal electrode systems. Some of the most active, and therefore most important, entities at surfaces (e.g., metal adatoms) are not readily imageable or detectable by high resolution surface microscopy techniques. Cyclic voltammetry, however, provides significant, though not highly specific, information about such species. The main conclusion is that further practical and theoretical work on active states of metal surfaces is highly desirable as their behaviour is not simple and is of major importance in many electrocatalytic processes.

The formation of gold nanoparticles using hydroquinone as a reducing agent through a localized pH change upon addition of NaOH to a solution of HAuCl4

We demonstrate a rapid synthesis of gold nanoparticles using hydroquinone as a reducing agent under acidic conditions without the need for precursor seed particles. The nanoparticle formation process is facilitated by the addition of NaOH to a solution containing HAuCl4 and hydroquinone to locally change the pH; this enhances the reducing capability of hydroquinone to form gold nucleation centres, after which further growth of gold can take place through an autocatalytic mechanism. The stability of the nanoparticles is highly dependent on the initial solution pH, and both the concentration of added NaOH and hydroquinone present in solution. The gold nanoparticles were characterized by UV–visible spectroscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, atomic force microscopy, dynamic light scattering, and zeta potential measurements. It was found that under optimal conditions that stable aqueous suspensions of 20 nm diameter nanoparticles can be achieved where benzoquinone, the oxidized product of hydroquinone, acts as a capping agent preventing nanoparticles aggregation.

Voltammetric monitoring of gold nanoparticle formation facilitated by glycyl-L-tyrosine : relation to electronic spectra and transmission electron microscopy images

Voltammetric techniques have been introduced to monitor the formation of gold nanoparticles produced via the reaction of the amino acid glycyl-L-tyrosine with Au(III) (bromoaurate) in 0.05 M KOH conditions. The alkaline conditions facilitate amino acid binding to Au(III), inhibit the rate of reduction to Au(0), and provide an excellent supporting electrolyte for voltammetric studies. Data obtained revealed that a range of time-dependent gold solution species are involved in gold nanoparticle formation and that the order in which reagents are mixed is critical to the outcome. Concomitantly with voltammetric measurements, the properties of gold nanoparticles formed are probed by examination of electronic spectra in order to understand how the solution environment present during nanoparticle growth affects the final distribution of the nanoparticles. Images obtained by the ex situ transmission electron microscopy (TEM) technique enable the physical properties of the nanoparticles isolated in the solid state to be assessed. Use of this combination of in situ and ex situ techniques provides a versatile framework for elucidating the details of nanoparticle formation.

The electrochemical corrosion behaviour of quaternary gold alloys when exposed to 3.5% NaCl solution

Lower carat gold alloys, specifically 9 carat gold alloys, containing less than 40 % gold, and alloying additions of silver, copper and zinc, are commonly used in many jewellery applications, to offset high costs and poor mechanical properties associated with pure gold. While gold is considered to be chemically inert, the presence of active alloying additions raises concerns about certain forms of corrosion, particularly selective dissolution of these alloys. The purpose of this study was to systematically study the corrosion behaviour of a series of quaternary gold–silver–copper–zinc alloys using dc potentiodynamic scanning in saline (3.5 % NaCl) environment. Full anodic/cathodic scans were conducted to determine the overall corrosion characteristics of the alloy, followed by selective anodic scans and subsequent morphological and compositional analysis of the alloy surface and corroding media to determine the extent of selective dissolution. Varying degrees of selective dissolution and associated corrosion rates were observed after anodic polarisation in 3.5 % NaCl, depending on the alloy composition. The corrosion behaviour of the alloys was determined by the extent of anodic reactions which induce (1) formation of oxide scales on the alloy surface and or (2) dissolution of Zn and Cu species. In general, the improved corrosion characteristics of alloy #3 was attributed to the composition of Zn/Cu in the alloy and thus favourable microstructure promoting the formation of protective oxide/chloride scales and reducing the extent of Cu and Zn dissolution.

Fabrication of metal-nanoparticle-modified semiconducting copper--and silver--TCNQ materials as substrates for the reduction of chromium (VI) using thiosulfate ions at ambient temperature

The formation of readily recoverable and reusable organic semiconducting Cu- and AgTCNQ (TCNQ=7,7,8,8-tetracyanoquinodimethane) microstructures decorated with Pt and Pd metallic nanoparticles is described for the effective reduction of CrVI ions in aqueous solution at room temperature using both formic acid and an environmentally friendly thiosulfate reductant. The M-TCNQ (M=metal) materials were formed by electrocrystallisation onto a glassy carbon surface followed by galvanic replacement in the presence of H2PtCl6 or PdCl2 to form the composite material. It was found that loading of the surface with nanoparticles could easily be controlled by changing the metal salt concentration. Significantly, the M-TCNQ substrates facilitated the formation of well-isolated metal nanoparticles on their surfaces under appropriate galvanic replacement conditions. The semiconductor–metal nanoparticle combination was also found to be critical to the catalyst performance, wherein the best-performing material was CuTCNQ modified by well-isolated Pt nanoparticles with both formic acid and thiosulfate ions as the reductant.