Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Differential effects of ERP systems on user outcomes : a longitudinal investigation

Adopting a model of job enrichment we report on a longitudinal case investigating the perceived impact of an Enterprise Resource Planning (ERP) system on user job design characteristics. Our results indicated that in the context of an ERP geared towards centralisation and standardisation the extent to which users perceived an increase or decrease in job enrichment was associated with aspects such as formal authority and the nature of their work role. Experienced operational employees proficient in the original legacy system perceived ERP system protocols to constrain their actions, limit training and increase dependence on others in the workflow. Conversely, managerial users reported a number of benefits relating to report availability, improved organisational transparency and increased overall job enrichment. These results supported our argument concerning the relationship between ERPs with a standardisation intent and positive job enrichment outcomes for managerial users and negative job-related outcomes for operational users.

Differential expression of chemokine and matrix re-modelling genes is associated with contrasting schistosome-induced hepatopathology in murine models

The pathological outcomes of schistosomiasis are largely dependent on the molecular and cellular mechanisms of the host immune response. In this study, we investigated the contribution of variations in host gene expression to the contrasting hepatic pathology observed between two inbred mouse strains following Schistosoma japonicum infection. Whole genome microarray analysis was employed in conjunction with histological and immunohistochemical analysis to define and compare the hepatic gene expression profiles and cellular composition associated with the hepatopathology observed in S. japonicum-infected BALB/c and CBA mice. We show that the transcriptional profiles differ significantly between the two mouse strains with high statistical confidence. We identified specific genes correlating with the more severe pathology associated with CBA mice, as well as genes which may confer the milder degree of pathology associated with BALB/c mice. In BALB/c mice, neutrophil genes exhibited striking increases in expression, which coincided with the significantly greater accumulation of neutrophils at granulomatous regions seen in histological sections of hepatic tissue. In contrast, up-regulated expression of the eosinophil chemokine CCL24 in CBA mice paralleled the cellular influx of eosinophils to the hepatic granulomas. Additionally, there was greater down-regulation of genes involved in metabolic processes in CBA mice, reflecting the more pronounced hepatic damage in these mice. Profibrotic genes showed similar levels of expression in both mouse strains, as did genes associated with Th1 and Th2 responses. However, imbalances in expression of matrix metalloproteinases (e.g. MMP12, MMP13) and tissue inhibitors of metalloproteinases (TIMP1) may contribute to the contrasting pathology observed in the two strains. Overall, these results provide a more complete picture of the molecular and cellular mechanisms which govern the pathological outcome of hepatic schistosomiasis. This improved understanding of the immunopathogenesis in the murine model schistosomiasis provides the basis for a better appreciation of the complexities associated with chronic human schistosomiasis.

IS service quality as a multi-dimensional formative constuct

This study is motivated by, and proceeds from, a central interest in the importance of evaluating IS service quality and adopts the IS ZOT SERVQUAL instrument (Kettinger & Lee, 2005) as its core theory base. This study conceptualises IS service quality as a multidimensional formative construct and seeks to answer the main research questions: “Is the IS service quality construct valid as a 1st-order formative, 2nd-order formative multidimensional construct?” Additionally, with the aim of validating the IS service quality construct within its nomological net, as in prior service marketing work, Satisfaction was hypothesised as its immediate consequence. With the goal of testing the above research question, IS service quality and Satisfaction were operationalised in a quantitative survey instrument. Partial least squares (PLS), employing 219 valid responses, largely evidenced the validity of IS service quality as a multidimensional formative construct. The nomological validity of the IS service quality construct was also evidenced by demonstrating that 55% of Satisfaction was explained by the multidimensional formative IS service quality construct.

Alkyl radical geometry controls geminate cage recombination in alkylcobalamins

Abstract: The radical pair that results from photolysis of adenosylcob(II1)alamin (AdoCbl"') undergoes primary geminate recombination with a first-order rate constant of 1 x lo9 s-l. In contrast, methylcob(II1)alamin (CH3Cbl"') and aristeromicylcob(II1)alamin (AriCblII', the carbocyclic analogue of AdoCbl"' in which the ribofuranose ring oxygen has been replaced with a methylene group) does not undergo primary geminate recombination. The ribofwanose group enables a high rate of geminate recombination in the [Ado' Cbl"'] radical pair. This may be due to a stereoelectronic (p-anomeric) effect that maintains a pyramidal geometry at the 5'-carbon of the 5'-deoxyadenosyl radical, or it may be due to hindered rotation about the C4t-C5, bond such that /?-elimination to the olefin is prevented. Recombination in the geminate singlet radical pair is in competition with diffusive escape to form a solvent-separated radical pair. Hyperfine coupling from Co" promotes intersystem crossing to the triplet radical pair (Chagovetz, A. M.; Grissom, C. B. J. Am. Chem. SOC. 1993, 115, 12152). Recombination of the [CH3' Cbl"] radical pair is not prevented by a lack of intersystem crossing, as neither unlabeled or I3C-labeled CH3Cbl"' undergoes geminate recombination. There is only a small difference in the rate of diffusive recombination in the solvent cage for AdoCbl"', AriCbl"', and CH3Cbl"' following photolysis: 2.01 x 10" s-l, 2.20 x lo4 s-l, and 1.16 x lo4 s-l. The rate of diffusive recombination is limited by productive collisions and not by radical geometry or intersystem crossing. The CF3' radical that results from photolysis of (trifluoromethyl)cob(III)alamin (CF3Cbl"') maintains its pyramidal geometry and undergoes faster diffusive recombination in the solvent cage at 51 x lo4 s-l. The C-Co bond dissociation enthalpy in AriCbl"' is 37 f 1.4 kcaymol. The profound difference in geminate recombination rates for AdoCbl"' and CH3Cbl"' is consistent with their different biological roles as enzymatic cofactors: AdoCbl"' is an initiator of radical chain chemistry in the active site, whereas CH3Cbl"' is a methyl group donor in an S~2-type process.