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.

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.

De la reconstruction a l’augmentation du corps humain en medecine restaurative et en cybernetique

Aux confluences historiques et conceptuelles de la modernité, de la technologie, et de l’« humain », les textes de notre corpus négocient et interrogent de façon critique les possibilités matérielles et symboliques de la prothèse, ses aspects phénoménologiques et spéculatifs : du côté subjectiviste et conceptualiste avec une philosophie de la conscience, avec Merleau-Ponty ; et de l’autre avec les épistémologues du corps et historiens de la connaissance Canguilhem et Foucault. Le trope prometteur de la prothèse impacte sur les formations discursives et non-discursives concernant la reconstruction des corps, là où la technologie devient le corrélat de l’identité. La technologie s’humanise au contact de l’homme, et, en révélant une hybridité supérieure, elle phagocyte l’humain du même coup. Ce travail de sociologie des sciences (Latour, 1989), ou encore d’anthropologie des sciences (Hakken, 2001) ou d’anthropologie bioculturelle (Andrieu, 1993; Andrieu, 2006; Andrieu, 2007a) se propose en tant qu’exemple de la contribution potentielle que l’anthropologie biologique et culturelle peut rendre à la médecine reconstructrice et que la médecine reconstructrice peut rendre à la plastique de l’homme ; l’anthropologie biologique nous concerne dans la transformation biologique du corps humain, par l’outil de la technologie, tant dans son histoire de la reconstruction mécanique et plastique, que dans son projet d’augmentation bionique. Nous établirons une continuité archéologique, d’une terminologie foucaldienne, entre les deux pratiques. Nous questionnons les postulats au sujet des relations nature/culture, biologie/contexte social, et nous présentons une approche définitionnelle de la technologie, pierre angulaire de notre travail théorique. Le trope de la technologie, en tant qu’outil adaptatif de la culture au service de la nature, opère un glissement sémantique en se plaçant au service d’une biologie à améliorer. Une des clés de notre recherche sur l’augmentation des fonctions et de l’esthétique du corps humain réside dans la redéfinition même de ces relations ; et dans l’impact de l’interpénétration entre réalité et imaginaire dans la construction de l’objet scientifique, dans la transformation du corps humain. Afin de cerner les enjeux du discours au sujet de l’« autoévolution » des corps, les théories évolutionnistes sont abordées, bien que ne représentant pas notre spécialité. Dans le cadre de l’autoévolution, et de l’augmentation bionique de l’homme, la somation culturelle du corps s’exerce par l’usage des biotechnologies, en rupture épistémologique de la pensée darwinienne, bien que l’acte d’hybridation évolutionnaire soit toujours inscrit dans un dessein de maximisation bionique/génétique du corps humain. Nous explorons les courants de la pensée cybernétique dans leurs actions de transformation biologique du corps humain, de la performativité des mutilations. Ainsi technologie et techniques apparaissent-elles indissociables de la science, et de son constructionnisme social.

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

Diffusion tensor of water in model articular cartilage

We used Monte Carlo simulations of Brownian dynamics of water to study anisotropic water diffusion in an idealised model of articular cartilage. The main aim was to use the simulations as a tool for translation of the fractional anisotropy of the water diffusion tensor in cartilage into quantitative characteristics of its collagen fibre network. The key finding was a linear empirical relationship between the collagen volume fraction and the fractional anisotropy of the diffusion tensor. Fractional anisotropy of the diffusion tensor is potentially a robust indicator of the microstructure of the tissue because, in the first approximation, it is invariant to the inclusion of proteoglycans or chemical exchange between free and collagen-bound water in the model. We discuss potential applications of Monte Carlo diffusion-tensor simulations for quantitative biophysical interpretation of MRI diffusion-tensor images of cartilage. Extension of the model to include collagen fibre disorder is also discussed.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.