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.

Synthesis and modifications of metal oxide nanostructures and their applications

Transition metal oxides are functional materials that have advanced applications in many areas, because of their diverse properties (optical, electrical, magnetic, etc.), hardness, thermal stability and chemical resistance. Novel applications of the nanostructures of these oxides are attracting significant interest as new synthesis methods are developed and new structures are reported. Hydrothermal synthesis is an effective process to prepare various delicate structures of metal oxides on the scales from a few to tens of nanometres, specifically, the highly dispersed intermediate structures which are hardly obtained through pyro-synthesis. In this thesis, a range of new metal oxide (stable and metastable titanate, niobate) nanostructures, namely nanotubes and nanofibres, were synthesised via a hydrothermal process. Further structure modifications were conducted and potential applications in catalysis, photocatalysis, adsorption and construction of ceramic membrane were studied. The morphology evolution during the hydrothermal reaction between Nb2O5 particles and concentrated NaOH was monitored. The study demonstrates that by optimising the reaction parameters (temperature, amount of reactants), one can obtain a variety of nanostructured solids, from intermediate phases niobate bars and fibres to the stable phase cubes. Trititanate (Na2Ti3O7) nanofibres and nanotubes were obtained by the hydrothermal reaction between TiO2 powders or a titanium compound (e.g. TiOSO4·xH2O) and concentrated NaOH solution by controlling the reaction temperature and NaOH concentration. The trititanate possesses a layered structure, and the Na ions that exist between the negative charged titanate layers are exchangeable with other metal ions or H+ ions. The ion-exchange has crucial influence on the phase transition of the exchanged products. The exchange of the sodium ions in the titanate with H+ ions yields protonated titanate (H-titanate) and subsequent phase transformation of the H-titanate enable various TiO2 structures with retained morphology. H-titanate, either nanofibres or tubes, can be converted to pure TiO2(B), pure anatase, mixed TiO2(B) and anatase phases by controlled calcination and by a two-step process of acid-treatment and subsequent calcination. While the controlled calcination of the sodium titanate yield new titanate structures (metastable titanate with formula Na1.5H0.5Ti3O7, with retained fibril morphology) that can be used for removal of radioactive ions and heavy metal ions from water. The structures and morphologies of the metal oxides were characterised by advanced techniques. Titania nanofibres of mixed anatase and TiO2(B) phases, pure anatase and pure TiO2(B) were obtained by calcining H-titanate nanofibres at different temperatures between 300 and 700 °C. The fibril morphology was retained after calcination, which is suitable for transmission electron microscopy (TEM) analysis. It has been found by TEM analysis that in mixed-phase structure the interfaces between anatase and TiO2(B) phases are not random contacts between the engaged crystals of the two phases, but form from the well matched lattice planes of the two phases. For instance, (101) planes in anatase and (101) planes of TiO2(B) are similar in d spaces (~0.18 nm), and they join together to form a stable interface. The interfaces between the two phases act as an one-way valve that permit the transfer of photogenerated charge from anatase to TiO2(B). This reduces the recombination of photogenerated electrons and holes in anatase, enhancing the activity for photocatalytic oxidation. Therefore, the mixed-phase nanofibres exhibited higher photocatalytic activity for degradation of sulforhodamine B (SRB) dye under ultraviolet (UV) light than the nanofibres of either pure phase alone, or the mechanical mixtures (which have no interfaces) of the two pure phase nanofibres with a similar phase composition. This verifies the theory that the difference between the conduction band edges of the two phases may result in charge transfer from one phase to the other, which results in effectively the photogenerated charge separation and thus facilitates the redox reaction involving these charges. Such an interface structure facilitates charge transfer crossing the interfaces. The knowledge acquired in this study is important not only for design of efficient TiO2 photocatalysts but also for understanding the photocatalysis process. Moreover, the fibril titania photocatalysts are of great advantage when they are separated from a liquid for reuse by filtration, sedimentation, or centrifugation, compared to nanoparticles of the same scale. The surface structure of TiO2 also plays a significant role in catalysis and photocatalysis. Four types of large surface area TiO2 nanotubes with different phase compositions (labelled as NTA, NTBA, NTMA and NTM) were synthesised from calcination and acid treatment of the H-titanate nanotubes. Using the in situ FTIR emission spectrescopy (IES), desorption and re-adsorption process of surface OH-groups on oxide surface can be trailed. In this work, the surface OH-group regeneration ability of the TiO2 nanotubes was investigated. The ability of the four samples distinctively different, having the order: NTA > NTBA > NTMA > NTM. The same order was observed for the catalytic when the samples served as photocatalysts for the decomposition of synthetic dye SRB under UV light, as the supports of gold (Au) catalysts (where gold particles were loaded by a colloid-based method) for photodecomposition of formaldehyde under visible light and for catalytic oxidation of CO at low temperatures. Therefore, the ability of TiO2 nanotubes to generate surface OH-groups is an indicator of the catalytic activity. The reason behind the correlation is that the oxygen vacancies at bridging O2- sites of TiO2 surface can generate surface OH-groups and these groups facilitate adsorption and activation of O2 molecules, which is the key step of the oxidation reactions. The structure of the oxygen vacancies at bridging O2- sites is proposed. Also a new mechanism for the photocatalytic formaldehyde decomposition with the Au-TiO2 catalysts is proposed: The visible light absorbed by the gold nanoparticles, due to surface plasmon resonance effect, induces transition of the 6sp electrons of gold to high energy levels. These energetic electrons can migrate to the conduction band of TiO2 and are seized by oxygen molecules. Meanwhile, the gold nanoparticles capture electrons from the formaldehyde molecules adsorbed on them because of gold’s high electronegativity. O2 adsorbed on the TiO2 supports surface are the major electron acceptor. The more O2 adsorbed, the higher the oxidation activity of the photocatalyst will exhibit. The last part of this thesis demonstrates two innovative applications of the titanate nanostructures. Firstly, trititanate and metastable titanate (Na1.5H0.5Ti3O7) nanofibres are used as intelligent absorbents for removal of radioactive cations and heavy metal ions, utilizing the properties of the ion exchange ability, deformable layered structure, and fibril morphology. Environmental contamination with radioactive ions and heavy metal ions can cause a serious threat to the health of a large part of the population. Treatment of the wastes is needed to produce a waste product suitable for long-term storage and disposal. The ion-exchange ability of layered titanate structure permitted adsorption of bivalence toxic cations (Sr2+, Ra2+, Pb2+) from aqueous solution. More importantly, the adsorption is irreversible, due to the deformation of the structure induced by the strong interaction between the adsorbed bivalent cations and negatively charged TiO6 octahedra, and results in permanent entrapment of the toxic bivalent cations in the fibres so that the toxic ions can be safely deposited. Compared to conventional clay and zeolite sorbents, the fibril absorbents are of great advantage as they can be readily dispersed into and separated from a liquid. Secondly, new generation membranes were constructed by using large titanate and small ã-alumina nanofibres as intermediate and top layers, respectively, on a porous alumina substrate via a spin-coating process. Compared to conventional ceramic membranes constructed by spherical particles, the ceramic membrane constructed by the fibres permits high flux because of the large porosity of their separation layers. The voids in the separation layer determine the selectivity and flux of a separation membrane. When the sizes of the voids are similar (which means a similar selectivity of the separation layer), the flux passing through the membrane increases with the volume of the voids which are filtration passages. For the ideal and simplest texture, a mesh constructed with the nanofibres 10 nm thick and having a uniform pore size of 60 nm, the porosity is greater than 73.5 %. In contrast, the porosity of the separation layer that possesses the same pore size but is constructed with metal oxide spherical particles, as in conventional ceramic membranes, is 36% or less. The membrane constructed by titanate nanofibres and a layer of randomly oriented alumina nanofibres was able to filter out 96.8% of latex spheres of 60 nm size, while maintaining a high flux rate between 600 and 900 Lm–2 h–1, more than 15 times higher than the conventional membrane reported in the most recent study.

Mechanisms of change in negative thinking and urinary monoamines in depressed patients during acute treatment with group cognitive behavior therapy and antidepressant medication

This naturalistic study investigated the mechanisms of change in measures of negative thinking and in 24-h urinary metabolites of noradrenaline (norepinephrine), dopamine and serotonin in a sample of 43 depressed hospital patients attending an eight-session group cognitive behavior therapy program. Most participants (91%) were taking antidepressant medication throughout the therapy period according to their treating Psychiatrists' prescriptions. The sample was divided into outcome categories (19 Responders and 24 Non-responders) on the basis of a clinically reliable change index [Jacobson, N.S., & Truax, P., 1991. Clinical significance: a statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59, 12–19.] applied to the Beck Depression Inventory scores at the end of the therapy. Results of repeated measures analysis of variance [ANOVA] analyses of variance indicated that all measures of negative thinking improved significantly during therapy, and significantly more so in the Responders as expected. The treatment had a significant impact on urinary adrenaline and metadrenaline excretion however, these changes occurred in both Responders and Non-responders. Acute treatment did not significantly influence the six other monoamine metabolites. In summary, changes in urinary monoamine levels during combined treatment for depression were not associated with self-reported changes in mood symptoms.

Negative mood regulation expectancies, frontal lobe related behaviors and alcohol use

Negative mood regulation (NMR) expectancies have been linked to substance problems in previous research, but the neurobiological correlates of NMR are unknown. In the present study, NMR was examined in relation to self-report indices of frontal lobe functioning, mood and alcohol use in 166 volunteers of both genders who ranged in age from 17 to 43 years. Contrary to expectations based on previous findings in addicts and problem drinkers, scores on the NMR scale did not differ between Low Risk and High Risk drinkers as defined by the Alcohol Use Disorders Identification Test (AUDIT). However, NMR scores were significantly negatively correlated with all three indices of frontal lobe dysfunction on the Frontal Systems Behavior Scale (FrSBe) Self-Rating Form as well as with all three indices of negative mood on the Depression Anxiety Stress Scales (DASS), which in turn were all positively correlated with FrSBe. Path analyses indicated that NMR partially mediated the direct effects of frontal lobe dysfunction (as indexed by FrSBe) on DASS Stress and DASS Depression. Further, the High Risk drinkers scored significantly higher on the Disinhibition and Executive Dysfunction indices of the FrSBe than did Low Risk drinkers. Results are consistent with the notion that NMR is a frontal lobe function.

The role of social capital in reducing negative health outcomes among police officers

This paper investigates the role of social capital on the reduction of short and long run negative health effects associated with stress, as well as indicators of burnout among police officers. Despite the large volume of research on either social capital or the health effects of stress, the interaction of these factors remains an underexplored topic. In this empirical analysis we aim to reduce such a shortcoming focusing on a highly stressful and emotionally draining work environment, namely law enforcement agents who perform as an essential part of maintaining modern society. Using a multivariate regression analysis focusing on three different proxies of health and three proxies for social capital conducting also several robustness checks, we find strong evidence that increased levels of social capital is highly correlated with better health outcomes. Additionally we observe that while social capital at work is very important, social capital in the home environment and work-life balance are even more important. From a policy perspective, our findings suggest that work and stress programs should actively encourage employees to build stronger social networks as well as incorporate better working/home life arrangements.

Suitability of procuring large public works by PPP in Hong Kong

Purpose : The Hong Kong Special Administrative Region (referred to as Hong Kong from here onwards) is an international leading commercial hub particularly in Asia. In order to keep up its reputation a number of large public works projects have been considered. Public Private Partnership (PPP) has increasingly been suggested for these projects, but the suitability of using this procurement method in Hong Kong is yet to be studied empirically. The findings presented in this paper will specifically consider whether PPPs should be used to procure public works projects in Hong Kong by studying the attractive and negative factors for adopting PPP. Design/methodology/approach : As part of this study a questionnaire survey was conducted with industrial practitioners. The respondents were requested to rank the importance of fifteen attractive factors and thirteen negative factors for adopting PPP. Findings : The results found that in general the top attractive factors ranked by respondents from Hong Kong were efficiency related, these included (1) ‘Provide an integrated solution (for public infrastructure / services)’; (2) ‘Facilitate creative and innovative approaches’; and (3) ‘Solve the problem of public sector budget restraint’. It was found that Australian respondents also shared similar findings to those in Hong Kong, but the United Kingdom respondents showed a higher priority to those economic driven attractive factors. Also, the ranking of the attractive and negative factors for adopting PPP showed that on average the attractive factors were scored higher than the negative factors. Originality/value : The results of this research have enabled a comparison of the attractive and negative factors for adopting PPP between three administrative systems. These findings have confirmed that PPP is a suitable means to procure large public projects which are believed to be useful and interesting to PPP researchers and practitioners.

Sodium removal from Maramarua CSG waters using Ngakuru zeolites

Coal seam gas (CSG) waters are a by-product of natural gas extraction from un derground coal seams. The main issue with these waters is their elevated sodium content, which in conjunction with their low calcium and magnesium concentrations can generate soil infiltration problems in the long run , as well as short term toxicity effects in plants due to the sodium ion itself. Zeolites are minerals having a porous structure, crystalline characteristics, and an alumino-silicate configuration resulting in an overall negative charge which is balanced by loosely held cations. In New Zealand, Ngakuru zeolites have been mined for commercial use in wastewater treatment applications, cosmetics, and pet litter. This research focuses on assessing the capacity of Ngakuru zeolites to reduce sodium concentrations of CSG waters from Maramarua. Batch and column test (flow through) experiments revealed that Ngakuru zeolites are capable of sorbing sodium cations from concentrated solutions of sodium. In b atch tests, the sodium adsorption capacity ranged from 5.0 to 34.3meq/100g depending on the solution concentration and on the number of times the zeolite had been regenerated. Regeneration with CaCl2 was foun d to be effective. The calculated sodium adsorption capacity of Ngakuru zeolites under flow-through conditions ranged from 11 to 42meq/100g depending on the strength of the solution being treated and on w hether the zeolites had been previously regenerated. The slow kinetics and low cost of the zeolities, coupled with potentially remote sites for gas extraction, could make semi-batch operational processes without regeneration more favourable than in more industrial ion exchange situations.