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.

X-ray computed tomography

X-ray computed tomography (CT) is a medical imaging technique that produces images of trans-axial planes through the human body. When compared with a conventional radiograph, which is an image of many planes superimposed on each other, a CT image exhibits significantly improved contrast although this is at the expense of reduced spatial resolution.----- A CT image is reconstructed mathematically from a large number of one dimensional projections of the chosen plane. These projections are acquired electronically using a linear array of solid-state detectors and an x ray source that rotates around the patient.----- X-ray computed tomography is used routinely in radiological examinations. It has also be found to be useful in special applications such as radiotherapy treatment planning and three-dimensional imaging for surgical planning.

Thermally activated seawater neutralised red mud used for the removal of arsenate, vanadate and molybdate from aqueous solutions.

The effectiveness of using thermally activated hydrotalcite materials has been investigated for the removal of arsenate, vanadate, and molybdate in individual and mixed solutions. Results show that increasing the Mg,Al ratio to 4:1 causes an increase in the percentage of anions removed from solution. The order of affinity of the three anions analysed in this investigation is arsenate, vanadate, and molybdate. By comparisons with several synthetic hydrotalcite materials, the hydrotalcite structure in the seawater neutralised red mud (SWN-RM) has been determined to consist of magnesium and aluminium with a ratio between 3.5:1 and 4:1. Thermally activated seawater neutralised red mud removes at least twice the concentration of anionic species than thermally activated red mud alone, due to the formation of 40 to 60 % Bayer hydrotalcite during the neutralisation process.

Smectite flocculation structure modified by AI13 macromolecules; as revealed by the Transmission X-ray Microscopy (TXM)

The aggregate structure which occurs in aqueous smectitic suspensions is responsible for poor water clarification, difficulties in sludge dewatering and the unusual rheological behaviour of smectite rich soils. These macroscopic properties are dictated by the 3-D structural arrangement of smectite finest fraction within flocculated aggregates. Here, we report results from a relatively new technique, Transmission X-ray Microscopy (TXM), which makes it possible to investigate the internal structure and 3-D tomographic reconstruction of the smectite clay aggregates modified by Al13 keggin macro-molecule [Al13(O)4(OH)24(H2O)12 ]7+. Three different treatment methods were shown resulted in three different micro-structural environments of the resulting flocculation.

The encapsulation of gold nanoparticles using RAFT, ATRP and miniemulsion polymerisation techniques

The investigation into the encapsulation of gold nanoparticles (AuNPs) by poly(methyl methacrylate) (PMMA) was undertaken. This was performed by three polymerisation techniques including: grafting PMMA synthesised by reversible addition-fragmentation chain transfer (RAFT) polymerisation to AuNPs, grafting PMMA synthesised by atom transfer radical polymerisation (ATRP) from the surface of functionalised AuNPs and by encapsulation of AuNPs within PMMA latexes produced through photo-initiated oil-in-water (o/w) miniemulsion polymerisation. The grafting of RAFT PMMA to AuNPs was performed by the addition of the RAFT functionalised PMMA to citrate stabilised AuNPs. This was conducted with a range of PMMA of varying molecular weight distribution (MWD) as either the dithioester or thiol end-group functionalities. The RAFT PMMA polymers were characterised by gel permeation chromatography (GPC), ultraviolet-visible (UV-vis), Fourier transform infrared-attenuated total reflectance (FTIR-ATR), Fourier transform Raman (FT-Raman) and proton nuclear magnetic resonance (1H NMR) spectroscopies. The attachment of PMMA to AuNPs showed a tendency for AuNPs to associate with the PMMA structures formed, though significant aggregation occurred. Interestingly, thiol functionalised end-group PMMA showed very little aggregation of AuNPs. The spherical polymer-AuNP structures did not vary in size with variations in PMMA MWD. The PMMA-AuNP structures were characterised using scanning electron microscopy (SEM), transition electron microscopy (TEM), energy dispersive X-ray analysis (EDAX) and UV-vis spectroscopy. The surface confined ATRP grafting of PMMA from initiator functionalised AuNPs was polymerised in both homogeneous and heterogeneous media. 11,11’- dithiobis[1-(2-bromo-2-methylpropionyloxy)undecane] (DSBr) was used as the surface-confined initiator and was synthesised in a three step procedure from mercaptoundecanol (MUD). All compounds were characterised by 1H NMR, FTIR-ATR and Raman spectroscopies. The grafting in homogeneous media resulted in amorphous PMMA with significant AuNP aggregation. Individually grafted AuNPs were difficult to separate and characterise, though SEM, TEM, EDAX and UV-vis spectroscopy was used. The heterogeneous polymerisation did not produce grafted AuNPs as characterised by SEM and EDAX. The encapsulation of AuNPs within PMMA latexes through the process of photoinitiated miniemulsion polymerisation was successfully achieved. Initially, photoinitiated miniemulsion polymerisation was conducted as a viable low temperature method of miniemulsion initiation. This proved successful producing a stable PMMA with good conversion efficiency and narrow particle size distribution (PSD). This is the first report of such a system. The photo-initiated technique was further optimised and AuNPs were included into the miniemulsion. AuNP encapsulation was very effective, producing reproducible AuNP encapsulated PMMA latexes. Again, this is the first reported case of this. The latexes were characterised by TEM, SEM, GPC, gravimetric analysis and dynamic light scattering (DLS).

Numerical modelling of industrial microwave heating

The numerical modelling of electromagnetic waves has been the focus of many research areas in the past. Some specific applications of electromagnetic wave scattering are in the fields of Microwave Heating and Radar Communication Systems. The equations that govern the fundamental behaviour of electromagnetic wave propagation in waveguides and cavities are the Maxwell's equations. In the literature, a number of methods have been employed to solve these equations. Of these methods, the classical Finite-Difference Time-Domain scheme, which uses a staggered time and space discretisation, is the most well known and widely used. However, it is complicated to implement this method on an irregular computational domain using an unstructured mesh. In this work, a coupled method is introduced for the solution of Maxwell's equations. It is proposed that the free-space component of the solution is computed in the time domain, whilst the load is resolved using the frequency dependent electric field Helmholtz equation. This methodology results in a timefrequency domain hybrid scheme. For the Helmholtz equation, boundary conditions are generated from the time dependent free-space solutions. The boundary information is mapped into the frequency domain using the Discrete Fourier Transform. The solution for the electric field components is obtained by solving a sparse-complex system of linear equations. The hybrid method has been tested for both waveguide and cavity configurations. Numerical tests performed on waveguides and cavities for inhomogeneous lossy materials highlight the accuracy and computational efficiency of the newly proposed hybrid computational electromagnetic strategy.

Use of hydrotalcites for the removal of toxic anions from aqueous solutions

The removal of toxic anions has been achieved using hydrotalcite via two methods: (1) coprecipitation and (2) thermal activation. Hydrotalcite formed via the coprecipitation method, using solutions containing arsenate and vanadate up to pH 10, are able to remove more than 95% of the toxic anions (0.2 M) from solution. The removal of toxic anions in solutions with a pH of >10 reduces the removal uptake percentage to 75%. Raman spectroscopy observed multiple A1 stretching modes of V−O and As−O at 930 and 810 cm−1, assigned to vanadate and arsenate, respectively. Analysis of the intensity and position of the A1 stretching modes helped to identify the vanadate and arsenate specie intercalated into the hydrotalcite structure. It has been determined that 3:1 hydrotalcite structure predominantly intercalate anions into the interlayer region, while the 2:1 and 4:1 hydrotalcite structures shows a large portion of anions being removed from solution by adsorption processes. Treatment of carbonate solutions (0.2 M) containing arsenate and vanadate (0.2 M) three times with thermally activated hydrotalcite has been shown to remove 76% and 81% of the toxic anions, respectively. Thermally activated hydrotalcite with a Mg:Al ratio of 2:1, 3:1, and 4:1 have all been shown to remove 95% of arsenate and vanadate (25 ppm). At increased concentrations of arsenate and vanadate, the removal uptake percentage decreased significantly, except for the 4:1 thermally activated hydrotalcite. Thermally activated Bayer hydrotalcite has also been shown to be highly effective in the removal of arsenate and vanadate. The thermal activation of the solid residue component (red mud) removes 30% of anions from solution (100 ppm of both anions), while seawater-neutralized red mud removes 70%. The formation of hydrotalcite during the seawater neutralization process removes anions via two mechanisms, rather than one observed for thermally activated red mud.