Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

Modelling CO2 adsorption and separation on experimentally-realized B40 fullerene

Searching for efficient solid sorbents for CO2 adsorption and separation is important for developing emergent carbon reduction and natural gas purification technology. This work, for the first time, has investigated the adsorption of CO2 on newly experimentally realized cage-like B40 fullerene (Zhai et al., 2014) based on density functional theory calculations. We find that the adsorption of CO2 on B40 fullerene involves a relatively large energy barrier (1.21 eV), however this can be greatly decreased to 0.35 eV by introducing an extra electron. A practical way to realize negatively charged B40 fullerene is then proposed by encapsulating a Li atom into the B40 fullerene (Li@B40). Li@B40 is found to be highly stable and can significantly enhance both the thermodynamics and kinetics of CO2 adsorption, while the adsorptions of N2, CH4 and H2 on the Li@B40 fullerene remain weak in comparison. Since B40 fullerene has been successfully synthesized in a most recent experiment, our results highlight a new promising material for CO2 capture and separation for future experimental validation.

Geochronological (U–Pb, U–Th–total Pb, Sm–Nd) and geochemical (REE, 87Sr/86Sr, δ18O, δ13C) tracing of intraplate tectonism and associated fluid flow in the Warburton Basin, Australia

The Warburton Basin of central Australia has experienced a complex tectonic and fluid-flow history, resulting in the formation of various authigenic minerals. Geochemical and geochronological analyses were undertaken on vein carbonates from core samples of clastic sediments. Results were then integrated with zircon U–Pb dating and uraninite U–Th–total Pb dating from the underlying granite. Stable and radiogenic isotopes (δ18O, Sr and εNd), as well as trace element data of carbonate veins indicate that >200 °C basinal fluids of evolved meteoric origin circulated through the Warburton Basin. Almost coincidental ages of these carbonates (Sm–Nd; 432 ± 12 Ma) with primary zircon (421 ± 3.8 Ma) and uraninite (407 ± 16 Ma) ages from the granitic intrusion point towards a substantial period of active tectonism and an elevated thermal regime during the mid Silurian. We hypothesise that such a thermal regime may have resulted from extensional tectonism and concomitant magmatic activity following regional orogenesis. This study shows that the combined application of geochemical and geochronological analyses of both primary and secondary species may constrain the timing of tectonomagmatic events and associated fluid flow in intraplate sedimentary basins. Furthermore, this work suggests that the Sm–Nd-isotopic system is surprisingly robust and can record geologically meaningful age data from hydrothermal mineral species.

Multipurpose nanoporous alumina-carbon nanowall bi-dimensional nano-hybrid platform via catalyzed and catalyst-free plasma CVD

Simple, rapid, plasma-assisted synthesis of large-area arrays of vertically-aligned carbon nanowalls on highly-porous, transparent bare and gold-coated alumina membranes with the two pore sizes is reported. It is demonstrated that the complex patterns of vertically aligned nanowalls can nucleate and form different morphologies in the low-temperature plasmas. The process is stable, and the twofold change in the gas flow (10 and 20 sccm) does not noticeably influence the morphology of the nanowall pattern. Application of a thin (5 nm) gold layer to nanoporous membrane prior to the nanowall growth allows controlling the network morphology.

Optical and surface characterization of radio frequency plasma polymerized 1-isopropyl-4-methyl-1,4-cyclohexadiene thin films

Low pressure radio frequency plasma-assisted deposition of 1-isopropyl-4-methyl-1,4-cyclohexadiene thin films was investigated for different polymerization conditions. Transparent, environmentally stable and flexible, these organic films are promising candidates for organic photovoltaics (OPV) and flexible electronics applications, where they can be used as encapsulating coatings and insulating interlayers. The effect of deposition RF power on optical properties of the films was limited, with all films being optically transparent, with refractive indices in a range of 1.57–1.58 at 500 nm. The optical band gap (Eg) of ~3 eV fell into the insulating Eg region, decreasing for films fabricated at higher RF power. Independent of deposition conditions, the surfaces were smooth and defect-free, with uniformly distributed morphological features and average roughness between 0.30 nm (at 10 W) and 0.21 nm (at 75 W). Films fabricated at higher deposition power displayed enhanced resistance to delamination and wear, and improved hardness, from 0.40 GPa for 10 W to 0.58 GPa for 75 W at a load of 700 μN. From an application perspective, it is therefore possible to tune the mechanical and morphological properties of these films without compromising their optical transparency or insulating property.

Fabrication and characterization of plasma polymer thin films from monoterpene alcohols for applications in organic electronics and biotechnology

After more than twenty years of basic and applied research, the use of nanotechnology in the design and manufacture of nanoscale materials is rapidly increasing, particularly in commercial applications that span from electronics across renewable energy areas, and biomedical devices. Novel polymers are attracting significant attention for they promise to provide a low−cost high−performance alternative to existing materials. Furthermore, these polymers have the potential to overcome limitations imposed by currently available materials thus enabling the development of new technologies and applications that are currently beyond our reach. This work focuses on the development of a range of new low−cost environmentally−friendly polymer materials for applications in areas of organic (flexible) electronics, optics, and biomaterials. The choice of the monomer reflects the environmentally−conscious focus of this project. Terpinen−4−ol is a major constituent of Australian grown Melaleuca alternifolia (tea tree) oil, attributed with the oil's antimicrobial and anti−inflammatory properties. Plasma polymerisation was chosen as a deposition technique for it requires minimal use of harmful chemicals and produces no hazardous by−products. Polymer thin films were fabricated under varied process conditions to attain materials with distinct physico−chemical, optoelectrical, biological and degradation characteristics. The resultant materials, named polyterpenol, were extensively characterised using a number of well−accepted and novel techniques, and their fundamental properties were defined. Polyterpenol films were demonstrated to be hydrocarbon rich, with variable content of oxygen moieties, primarily in the form of hydroxyl and carboxyl functionalities. The level of preservation of original monomer functionality was shown to be strongly dependent on the deposition energy, with higher applied power increasing the molecular fragmentation and substrate temperature. Polyterpenol water contact angle contact angle increased from 62.7° for the 10 W samples to 76.3° for the films deposited at 100 W. Polymers were determined to resist solubilisation by water, due to the extensive intermolecular and intramolecular hydrogen bonds present, and other solvents commonly employed in electronics and biomedical processing. Independent of deposition power, the surface topography of the polymers was shown to be smooth (Rq <0.5 nm), uniform and defect free. Hardness of polyterpenol coatings increased from 0.33 GPa for 10 W to 0.51 GPa for 100 W (at 500 μN load). Coatings deposited at higher input RF powers showed less mechanical deformation during nanoscratch testing, with no considerable damage, cracking or delamination observed. Independent of the substrate, the quality of film adhesion improved with RF power, suggesting these coatings are likely to be more stable and less susceptible to wear. Independent of fabrication conditions, polyterpenol thin films were optically transparent, with refractive index approximating that of glass. Refractive index increased slightly with deposition power, from 1.54 (10 W) to 1.56 (100 W) at 500 nm. The optical band gap values declined with increasing power, from 2.95 eV to 2.64 eV, placing the material within the range for semiconductors. Introduction of iodine impurity reduced the band gap of polyterpenol, from 2.8 eV to 1.64 eV, by extending the density of states more into the visible region of the electromagnetic spectrum. Doping decreased the transparency and increased the refractive index from 1.54 to 1.70 (at 500 nm). At optical frequencies, the real part of permittivity (k) was determined to be between 2.34 and 2.65, indicating a potential low-k material. These permittivity values were confirmed at microwave frequencies, where permittivity increased with input RF energy – from 2.32 to 2.53 (at 10 GHz ) and from 2.65 to 2.83 (at 20 GHz). At low frequencies, the dielectric constant was determined from current−voltage characteristics of Al−polyterpenol−Al devices. At frequencies below 100 kHz, the dielectric constant varied with RF power, from 3.86 to 4.42 at 1 kHz. For all samples, the resistivity was in order of 10⁸−10⁹ _m (at 6 V), confirming the insulating nature of polyterpenol material. In situ iodine doping was demonstrated to increase the conductivity of polyterpenol, from 5.05 × 10⁻⁸ S/cm to 1.20 × 10⁻⁶ S/cm (at 20 V). Exposed to ambient conditions over extended period of time, polyterpenol thin films were demonstrated to be optically, physically and chemically stable. The bulk of ageing occurred within first 150 h after deposition and was attributed to oxidation and volumetric relaxation. Thermal ageing studies indicated thermal stability increased for the films manufactured at higher RF powers, with degradation onset temperature associated with weight loss shifting from 150 ºC to 205 ºC for 10 W and 100 W polyterpenol, respectively. Annealing the films to 405 °C resulted in full dissociation of the polymer, with minimal residue. Given the outcomes of the fundamental characterisation, a number of potential applications for polyterpenol have been identified. Flexibility, tunable permittivity and loss tangent properties of polyterpenol suggest the material can be used as an insulating layer in plastic electronics. Implementation of polyterpenol as a surface modification of the gate insulator in pentacene-based Field Effect Transistor resulted in significant improvements, shifting the threshold voltage from + 20 V to –3 V, enhancing the effective mobility from 0.012 to 0.021 cm²/Vs, and improving the switching property of the device from 10⁷ to 10⁴. Polyterpenol was demonstrated to have a hole transport electron blocking property, with potential applications in many organic devices, such as organic light emitting diodes. Encapsulation of biomedical devices is also proposed, given that under favourable conditions, the original chemical and biological functionality of terpinen−4−ol molecule can be preserved. Films deposited at low RF power were shown to successfully prevent adhesion and retention of several important human pathogens, including P. aeruginosa, S. aureus, and S. epidermidis, whereas films deposited at higher RF power promoted bacterial cell adhesion and biofilm formation. Preliminary investigations into in vitro biocompatibility of polyterpenol demonstrated the coating to be non−toxic for several types of eukaryotic cells, including Balb/c mice macrophage and human monocyte type (HTP−1 non-adherent) cells. Applied to magnesium substrates, polyterpenol encapsulating layer significantly slowed down in vitro biodegradation of the metal, thus increasing the viability and growth of HTP−1 cells. Recently, applied to varied nanostructured titanium surfaces, polyterpenol thin films successfully reduced attachment, growth, and viability of P. aeruginosa and S. aureus.

Dual yolk-shell structure of carbon and silica-coated silicon for high-performance lithium-ion batteries

Silicon batteries have attracted much attention in recent years due to their high theoretical capacity, although a rapid capacity fade is normally observed, attributed mainly to volume expansion during lithiation. Here, we report for the first time successful synthesis of Si/void/SiO2/void/C nanostructures. The synthesis strategy only involves selective etching of SiO2 in Si/SiO2/C structures with hydrofluoric acid solution. Compared with reported results, such novel structures include a hard SiO2-coated layer, a conductive carbon-coated layer, and two internal void spaces. In the structures, the carbon can enhance conductivity, the SiO2 layer has mechanically strong qualities, and the two internal void spaces can confine and accommodate volume expansion of silicon during lithiation. Therefore, these specially designed dual yolk-shell structures exhibit a stable and high capacity of 956 mA h g−1 after 430 cycles with capacity retention of 83%, while the capacity of Si/C core-shell structures rapidly decreases in the first ten cycles under the same experimental conditions. The novel dual yolk-shell structures developed for Si can also be extended to other battery materials that undergo large volume changes.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

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.

Psychosocial outcomes of Hong Kong Chinese diagnosed with acute coronary syndromes: a prospective repeated measures study.

BACKGROUND: Western studies have suggested that emotional stress and distress impacted on the morbidity and mortality in people following acute coronary events. Symptoms of anxiety and depression have been associated with re-infarction and death, prolonged recovery and disability and depression may precipitate the client's low self-esteem. This study examined perceived anxiety, depression and self-esteem of Hong Kong Chinese clients diagnosed with acute coronary syndrome (ACS) over a 6-month period following hospital admission. OBJECTIVES: To examine: DESIGN: A prospective, repeated measures design with measures taken on two occasions over a 6-month period; (1) within the 1st week of hospital admission following the onset of ACS and (2) at 6 months follow up. SETTING AND PARTICIPANTS: Convenient sample of 182 voluntary consented clients admitted with ACS to a major public hospital in Hong Kong who could communicate in Chinese, complete questionnaires, cognitive intact, and were haemodynamically stable and free from acute chest pain at the time of interview. METHODS: Baseline data were obtained within 1 week after hospital admission. The follow-up data was collected 6 months after hospital discharge. The Chinese version of the Hospital Anxiety and Depression Scale (HADS), State Self-esteem Scale (SSES), and Rosenberg's Self-Esteem Scale (RSES) were used to assess anxiety and depression, state self-esteem, and trait self-esteem, respectively. RESULTS: Findings suggested gender differences in clients' perception in anxiety, depression and self-esteem. Improvements in clients' perception of these variables were evident over the 6-month period following their acute coronary events. CONCLUSION: The study confirmed the western notion that psychosocial problems are common among coronary clients and this also applies to Hong Kong Chinese diagnosed with ACS. Further studies to explore effective interventions to address these psychosocial issues are recommended.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

Near infrared optical materials from polymeric amorphous carbon synthesized by collisional plasma process

The synthesis of polymerlike amorphous carbon(a-C:H) thin-films by microwave excited collisional hydrocarbon plasma process is reported. Stable and highly aromatic a-C:H were obtained containing significant inclusions of poly(p-phenylene vinylene) (PPV). PPV confers universal optoelectronic properties to the synthesized material. That is a-C:H with tailor-made refractive index are capable of becoming absorption-free in visible (red)-near infrared wavelength range. Production of large aromatic hydrocarbon including phenyl clusters and/or particles is attributed to enhanced coagulation of elemental plasma species under collisional plasma conditions. Detailed structural and morphological changes that occur in a-C:H during the plasma synthesis are also described.

Crowded Diphosphinomethane Ligands in Catalysis: [(R2PCH2PR′2-κ2P)-NiR″]+ Cations for Ethylene Polymerization without Activators

The preparation of a series of nickel dichloride complexes with bulky diphosphinomethane chelate ligands R2PCH2PR′2 is reported. Reaction with the appropriate Grignard reagent leads to the corresponding dimethyl and dibenzyl complexes. Cationic monomethyl and mono-η3-benzyl complexes are generated from these dialkyl complexes by protonation with [H(OEt2)2]+[B(3,5-(CF3)2C6H3)4]−, while the complex [(dtbpm κ2P)Ni(η3-CH(CH2Ph)Ph]+[B(3,5-(CF3)2C6H3)4]−is obtained from protonation of the Ni(0) olefin complex (dtbpm-κ2P)N(η2-trans-stilbene). Crystal structures of examples of dichlorides, dimethyl, dibenzyl, cationic methyl, and cationic η3-benzyl complexes are reported. Solutions of the cations polymerize ethylene under mild conditions and without the necessity of an activating agent, to form polyethylene having high molecular weights and low degrees of chain branching. In comparison to the Ni methyl cations, the η3-benzyl cation complexes are more stable and somewhat less active but still very efficient in C2H4 polymerization. The effect on the resulting polyethylene of varying the substituents R, R′ on the phosphine ligand has been examined, and a clear trend for longer chain PE with less branching in the presence of more bulky substituents on the diphosphine has been found. Density functional calculations have been used to examine the rapid suprafacial η3 to η3 haptotropic shift processes of the[(R2PCH2PR′2)Ni] fragment and the η3−η1 change of the coordination mode of the benzyl group required for polymerization in those cations.