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.

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Predictions of road traffic noise on residential balconies using a specular and diffusion model

A combined specular reflection and diffusion model using the radiosity technique was developed to calculate road traffic noise level on residential balconies. The model is capable of numerous geometrical configurations for a single balcony situated in the centre of a street canyon. The geometry of the balcony and the street can be altered with width,length and height. The model was used to calculate for three different geometrical and acoustic absorption characteristics for a balcony. The calculated results are presented in this paper.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Digital processing of diffusion-tensor images of avascular tissues

Diffusion is the process that leads to the mixing of substances as a result of spontaneous and random thermal motion of individual atoms and molecules. It was first detected by the English botanist Robert Brown in 1827, and the phenomenon became known as ‘Brownian motion’. More specifically, the motion observed by Brown was translational diffusion – thermal motion resulting in random variations of the position of a molecule. This type of motion was given a correct theoretical interpretation in 1905 by Albert Einstein, who derived the relationship between temperature, the viscosity of the medium, the size of the diffusing molecule, and its diffusion coefficient. It is translational diffusion that is indirectly observed in MR diffusion-tensor imaging (DTI). The relationship obtained by Einstein provides the physical basis for using translational diffusion to probe the microscopic environment surrounding the molecule.

New insights into Crustal Contributions to Large-volume Rhyolite Generation in the Mid-Tertiary Sierra Madre Occidental Province, Mexico, revealed by U Pb Geochronology

Voluminous (≥3·9 × 105 km3), prolonged (∼18 Myr) explosive silicic volcanism makes the mid-Tertiary Sierra Madre Occidental province of Mexico one of the largest intact silicic volcanic provinces known. Previous models have proposed an assimilation–fractional crystallization origin for the rhyolites involving closed-system fractional crystallization from crustally contaminated andesitic parental magmas, with <20% crustal contributions. The lack of isotopic variation among the lower crustal xenoliths inferred to represent the crustal contaminants and coeval Sierra Madre Occidental rhyolite and basaltic andesite to andesite volcanic rocks has constrained interpretations for larger crustal contributions. Here, we use zircon age populations as probes to assess crustal involvement in Sierra Madre Occidental silicic magmatism. Laser ablation-inductively coupled plasma-mass spectrometry analyses of zircons from rhyolitic ignimbrites from the northeastern and southwestern sectors of the province yield U–Pb ages that show significant age discrepancies of 1–4 Myr compared with previously determined K/Ar and 40Ar/39Ar ages from the same ignimbrites; the age differences are greater than the errors attributable to analytical uncertainty. Zircon xenocrysts with new overgrowths in the Late Eocene to earliest Oligocene rhyolite ignimbrites from the northeastern sector provide direct evidence for some involvement of Proterozoic crustal materials, and, potentially more importantly, the derivation of zircon from Mesozoic and Eocene age, isotopically primitive, subduction-related igneous basement. The youngest rhyolitic ignimbrites from the southwestern sector show even stronger evidence for inheritance in the age spectra, but lack old inherited zircon (i.e. Eocene or older). Instead, these Early Miocene ignimbrites are dominated by antecrystic zircons, representing >33 to ∼100% of the dated population; most antecrysts range in age between ∼20 and 32 Ma. A sub-population of the antecrystic zircons is chemically distinct in terms of their high U (>1000 ppm to 1·3 wt %) and heavy REE contents; these are not present in the Oligocene ignimbrites in the northeastern sector of the Sierra Madre Occidental. The combination of antecryst zircon U–Pb ages and chemistry suggests that much of the zircon in the youngest rhyolites was derived by remelting of partially molten to solidified igneous rocks formed during preceding phases of Sierra Madre Occidental volcanism. Strong Zr undersaturation, and estimations for very rapid dissolution rates of entrained zircons, preclude coeval mafic magmas being parental to the rhyolite magmas by a process of lower crustal assimilation followed by closed-system crystal fractionation as interpreted in previous studies of the Sierra Madre Occidental rhyolites. Mafic magmas were more probably important in providing a long-lived heat and material flux into the crust, resulting in the remelting and recycling of older crust and newly formed igneous materials related to Sierra Madre Occidental magmatism.

Diffusion of business improvement processes in manufacturing companies in India

Manufacturing organisations spend more on Business Process Improvement initiatives to make them more competitive in growing global market. This paper presents a Rapid Improvement Workshop (RIW) framework which companies can used to identify the critical factors regulating the diffusion of business process improvement in their company. The framework can then be used address how process improvement can be efficiently implemented. We use the results from case studies at Caterpillar India. The paper identifies the critical factors that contribute to the successful implementation of process improvement programs in manufacturing organisations. We further identify certain technological and cultural barriers to the implementation of process improvement programs and how Indian manufacturing companies can overcome these barriers to attain competitive advantage in the global markets.