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.

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.

An application of near-infrared and mid-infrared spectroscopy to the study of selected minerals

Near-infrared spectroscopy is a somewhat unutilised technique for the study of minerals. The technique has the ability to determine water content, hydroxyl groups and transition metals. In this paper we show the application of NIR spectroscopy to the study of selected minerals. The structure and spectral properties of two Cu-tellurite minerals graemite and teineite are compared with bismuth containing tellurite mineral smirnite by the application of NIR and IR spectroscopy. The position of Cu2+ bands and their splitting in the electronic spectra of tellurites are in conformity with octahedral geometry distortion. The spectral pattern of smirnite resembles graemite and the observed band at 10855 cm-1 with a weak shoulder at 7920 cm-1 is identified as due to Cu2+ ion. Any transition metal impurities may be identified by their bands in this spectral region. Three prominent bands observed in the region of 7200-6500 cm-1 are the overtones of water whilst the weak bands observed near 6200 cm-1in tellurites may be attributed to the hydrogen bonding between (TeO3)2- and H2O. The observation of a number of bands centred at around 7200 cm-1 confirms molecular water in tellurite minerals. A number of overlapping bands in the low wavenumbers 4500-4000 cm-1 is the result of combinational modes of (TeO3)2−ion. The appearance of the most intense peak at 5200 cm-1 with a pair of weak bands near 6000 cm-1 is a common feature in all the spectra and is related to the combinations of OH vibrations of water molecules, and bending vibrations ν2 (δ H2O). Bending vibrations δ H2O observed in the IR spectra shows a single band for smirnite at 1610 cm-1. The resolution of this band into number of components is evidenced for non-equivalent types of molecular water in graemite and teineite. (TeO3)2- stretching vibrations are characterized by three main absorptions at 1080, 780 and 695 cm-1.

A comparison of different methods to determine diffusion length in dye-sensitized solar cells

A new steady state method for determination of the electron diffusion length in dye-sensitized solar cells (DSCs) is described and illustrated with data obtained using cells containing three different types of electrolyte. The method is based on using near-IR absorbance methods to establish pairs of illumination intensity for which the total number of trapped electrons is the same at open circuit (where all electrons are lost by interfacial electron transfer) as at short circuit (where the majority of electrons are collected at the contact). Electron diffusion length values obtained by this method are compared with values derived by intensity modulated methods and by impedance measurements under illumination. The results indicate that the values of electron diffusion length derived from the steady state measurements are consistently lower than the values obtained by the non steady-state methods. For all three electrolytes used in the study, the electron diffusion length was sufficiently high to guarantee electron collection efficiencies greater than 90%. Measurement of the trap distributions by near-IR absorption confirmed earlier observations of much higher electron trap densities for electrolytes containing Li+ ions. It is suggested that the electron trap distributions may not be intrinsic properties of the TiO2 nanoparticles, but may be associated with electron-ion interactions.

Hydrogen bonding in the water stabilized structure of the modified unsymmetrically substituted viologen chromophore, N-ethyl-N'-(2-phosphonomethyl)-4,4'-bipyridylium dichloride

The crystal structure of the modified unsymmetrically N, N'-substituted viologen chromophore, N-ethyl- N'-(2-phosphonoethyl)-4, 4'-bipyridinium dichloride 0.75 hydrate. (1) has been determined. Crystals are triclinic, space group P-1 with Z = 2 in a cell with a = 7.2550(1), b = 13.2038(5), c = 18.5752(7) Å, α = 86.495(3), β = 83.527(2), γ = 88.921(2)o. The two independent but pseudo-symmetrically related cations in the asymmetric unit form one-dimensional hydrogen-bonded chains through short homomeric phosphonic acid O-H...O links [2.455(4), 2.464(4)A] while two of the chloride anions are similarly strongly linked to phosphonic acid groups [O-H…Cl, 2.889(4), 2.896(4)Å]. The other two chloride anions together with the two water molecules of solvation (one with partial occupancy) form unusual cyclic hydrogen-bonded bis(Cl...water) dianion units which lie between the layers of bipyridylium rings of the cation chain structures with which they are weakly associated.

Mobile data technologies and SME adoption and diffusion : an empirical study on barriers and facilitators

The technological environment in which Australian SMEs operate can be best described as dynamic and vital. The rate of technological change provides the SME owner/manager a complex and challenging operational context. Wireless applications are being developed that provide mobile devices with Internet content and e-business services. In Australia the adoption of e-commerce by large organisations has been relatively high, however the same cannot be said for SMEs where adoption has been slower than other developed countries. In contrast however mobile telephone adoption and diffusion is relatively high by SMEs. This exploratory study identifies attitudes, perceptions and issues for mobile data technologies by regional SME owner/managers across a range of industry sectors. The major issues include the sector the firm belongs to, the current adoption status of the firm, the level of mistrust of the IT industry, the cost of the technologies and the applications and attributes of the technologies.

Confusion with diffusion? Unravelling is diffusion and innovation literature with a focus on SMEs

The aim of this paper is to contribute to the understanding of various models used in research for the adoption and diffusion of information technology in small and medium-sized enterprises (SMEs). Starting with Rogers' diffusion theory and behavioural models, technology adoption models used in IS research are discussed. Empirical research has shown that the reasons why firms choose to adopt or not adopt technology is dependent on a number of factors. These factors can be categorised as owner/manager characteristics, firm characteristics and other characteristics. The existing models explaining IS diffusion and adoption by SMEs overlap and complement each other. This paper reviews the existing literature and proposes a comprehensive model which includes the whole array of variables from earlier models.

Mobile data technologies and small business adoption and diffusion : an empirical study of barriers and facilitators

The technological environment in which contemporary small- and medium-sized enterprises (SMEs) operate can only be described as dynamic. The exponential rate of technological change, characterised by perceived increases in the benefits associated with various technologies, shortening product life cycles and changing standards, provides for the SME a complex and challenging operational context. The primary aim of this research was to identify the needs of SMEs in regional areas for mobile data technologies (MDT). In this study a distinction was drawn between those respondents who were full-adopters of technology, those who were partial-adopters, and those who were non-adopters and these three segments articulated different needs and requirements for MDT. Overall, the needs of regional SMEs for MDT can be conceptualised into three areas where the technology will assist business practices; communication, e-commerce and security

Structure of selected basic copper (II) sulphate minerals based upon spectroscopy : implications for hydrogen bonding

The application of near-infrared and infrared spectroscopy has been used for identification and distinction of basic Cu-sulphates that include devilline, chalcoalumite and caledonite. Near-infrared spectra of copper sulphate minerals confirm copper in divalent state. Jahn-Teller effect is more significant in chalcoalumite where 2B1g ® 2B2g transition band shows a larger splitting (490 cm-1) confirming more distorted octahedral coordination of Cu2+ ion. One symmetrical band at 5145 cm-1 with shoulder band 5715 cm-1 result from the absorbed molecular water in the copper complexes are the combinations of OH vibrations of H2O. One sharp band at around 3400 cm-1 in IR common to the three complexes is evidenced by Cu-OH vibrations. The strong absorptions observed at 1685 and 1620 cm-1 for water bending modes in two species confirm strong hydrogen bonding in devilline and chalcoalumite. The multiple bands in v3 and v4(SO4)2- stretching regions are attributed to the reduction of symmetry to the sulphate ion from Td to C2V. Chalcoalumite, the excellent IR absorber over the range 3800-500 cm-1 is treated as most efficient heat insulator among the Cu-sulphate complexes.

Raman and infrared study of phyllosilicates containing heavy metals (Sb, Bi) : bismutoferrite and chapmanite.

The kaolinite-like phyllosilicate minerals bismutoferrite BiFe3+2Si2O8(OH) and chapmanite SbFe3+2Si2O8(OH) have been studied by Raman spectroscopy and complemented with infrared spectra. Tentatively interpreted spectra were related to their molecular structure. The antisymmetric and symmetric stretching vibrations of the Si-O-Si bridges,  SiOSi and  OSiO bending vibrations,  (Si-Oterminal)- stretching vibrations,  OH stretching vibrations of hydroxyl ions, and  OH bending vibrations were attributed to observed bands. Infrared bands 3289-3470 cm-1 and Raman bands 1590-1667 cm-1 were assigned to adsorbed water. O-H...O hydrogen bond lengths were calculated from the Raman and infrared spectra.

Spectroscopy of selected copper group minerals : chalcophyllite and chenevixite-implications for hydrogen bonding

NIR and IR spectroscopy has been applied for detection of chemical species and the nature of hydrogen bonding in arsenate complexes. The structure and spectral properties of copper(II) arsenate minerals chalcophyllite and chenevixite are compared with copper(II) sulphate minerals devilline, chalcoalumite and caledonite. Split NIR bands in the electronic spectrum of two ranges 11700-8500 cm-1 and 8500-7200 cm-1 confirm distortion of octahedral symmetry for Cu(II) in the arsenate complexes. The observed bands with maxima at 9860 and 7750 cm-1 are assigned to Cu(II) transitions 2B1g ® 2B2g and 2B1g ® 2A1g. Overlapping bands in the NIR region 4500-4000 cm-1 is the effect of multi anions OH-, (AsO4)3- and (SO4)2-. The observation of broad and diffuse bands in the range 3700-2900 cm-1 confirms strong hydrogen bonding in chalcophyllite relative to chenevixite. The position of the water bending vibrations indicates the water is strongly hydrogen bonded in the mineral structure. The strong absorption feature centred at 1644 cm-1 in chalcophyllite indicates water is strongly hydrogen bonded in the mineral structure. The H2O-bending vibrations shift to low wavenumbers in chenevixite and an additional band observed at 1390 cm-1 is related to carbonate impurity. The characterisation of IR spectra by ν3 antisymmetric stretching vibrations of (SO4)2- and (AsO4)3 ions near 1100 and 800 cm-1 respectively is the result of isomorphic substitution for arsenate by sulphate in both the minerals of chalcophyllite and chenevixite.