Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Optimal management of the critically Ill: Anaesthesia, monitoring, data capture, and point-of-care technological practices in ovine models of critical care

Animal models of critical illness are vital in biomedical research. They provide possibilities for the investigation of pathophysiological processes that may not otherwise be possible in humans. In order to be clinically applicable, the model should simulate the critical care situation realistically, including anaesthesia, monitoring, sampling, utilising appropriate personnel skill mix, and therapeutic interventions. There are limited data documenting the constitution of ideal technologically advanced large animal critical care practices and all the processes of the animal model. In this paper, we describe the procedure of animal preparation, anaesthesia induction and maintenance, physiologic monitoring, data capture, point-of-care technology, and animal aftercare that has been successfully used to study several novel ovine models of critical illness. The relevant investigations are on respiratory failure due to smoke inhalation, transfusion related acute lung injury, endotoxin-induced proteogenomic alterations, haemorrhagic shock, septic shock, brain death, cerebral microcirculation, and artificial heart studies. We have demonstrated the functionality of monitoring practices during anaesthesia required to provide a platform for undertaking systematic investigations in complex ovine models of critical illness.

Functional localization of the human color center by decreased water displacement using diffusion-weighted fMRI

Introduction Decreased water displacement following increased neural activity has been observed using diffusion-weighted functional MRI (DfMRI) at high b-values. The physiological mechanisms underlying the diffusion signal change may be unique from the standard blood oxygenation level-dependent (BOLD) contrast and closer to the source of neural activity. Whether DfMRI reflects neural activity more directly than BOLD outside the primary cerebral regions remains unclear. Methods Colored and achromatic Mondrian visual stimuli were statistically contrasted to functionally localize the human color center Area V4 in neurologically intact adults. Spatial and temporal properties of DfMRI and BOLD activation were examined across regions of the visual cortex. Results At the individual level, DfMRI activation patterns showed greater spatial specificity to V4 than BOLD. The BOLD activation patterns were more prominent in the primary visual cortex than DfMRI, where activation was localized to the ventral temporal lobe. Temporally, the diffusion signal change in V4 and V1 both preceded the corresponding hemodynamic response, however the early diffusion signal change was more evident in V1. Conclusions DfMRI may be of use in imaging applications implementing cognitive subtraction paradigms, and where highly precise individual functional localization is required.

Determination of diffusion parameters and activation energy of diffusion in V3Si phase with A15 crystal structure

Diffusion such is the integrated diffusion coefficient of the phase, the tracer diffusion coefficient of species at different temperatures and the activation energy for diffusion, are determined in V3Si phase with A15 crystal structure. The tracer diffusion coefficient of Si Was found to be negligible compared to the tracer diffusion coefficient of V. The calculated diffusion parameters will help to validate the theoretical analysis of defect structure of the phase, which plays an important role in the superconductivity.

Molecular theory for the effects of specific solute-solvent interaction on the diffusion of a solute particle in a molecular liquid

An understanding of the effect of specific solute-solvent interactions on the diffusion of a solute probe is a long standing problem of physical chemistry. In this paper a microscopic treatment of this effect is presented. The theory takes into account the modification of the solvent structure around the solute due to this specific interaction between them. It is found that for strong, attractive interaction, there is an enhanced coupling between the solute and the solvent dynamic modes (in particular, the density mode), which leads to a significant increase in the friction on the solute. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of the attractive interaction. An interesting observation is that specific solute-solvent interaction can induce a crossover from a sliplike to a sticklike diffusion. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. On the other hand, for repulsive interaction, the diffusion coefficient of the solute increases. These results are in qualitative agreement with recent experimental observations.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Interdiffusion and Growth of the Superconductor Nb3Sn in Nb/Cu(Sn) Diffusion Couples

The confusion over the growth rate of the Nb3Sn superconductor compound following the bronze technique is addressed. Furthermore, a possible explanation for the corrugated structure of the product phase in the multifilamentary structure is discussed. Kirkendall marker experiments are conducted to study the relative mobilities of the species, which also explains the reason for finding pores in the product phase layer. The movement of the markers after interdiffusion reflects that Sn is the faster diffusing species. Furthermore, different concentrations of Sn in the bronze alloy are considered to study the effect of Sn content on the growth rate. Based on the parabolic growth constant at different temperatures, the activation energy for the growth is determined.

Preliminary investigations into the use of a functionalised polymer to reduce diffusion in Fricke gel dosimeters

Purpose A modification of the existing PVA-​FX hydrogel has been made to investigate the use of a functionalised polymer in a Fricke gel dosimetry system to decrease Fe3+ diffusion. Methods The chelating agent, xylenol orange, was chem. bonded to the gelling agent, polyvinyl alc. (PVA) to create xylenol orange functionalised PVA (XO-​PVA)​. A gel was created from the XO-​PVA (20​% w​/v) with ferrous sulfate (0.4 mM) and sulfuric acid (50 mM)​. Results This resulted in an optical d. dose sensitivity of 0.014 Gy-​1, an auto-​oxidn. rate of 0.0005 h-​1, and a diffusion rate of 0.129 mm2 h-​1; an 8​% redn. compared to the original PVA-​FX gel, which in practical terms adds approx. 1 h to the time span between irradn. and accurate read-​out. Conclusions Because this initial method of chem. bonding xylenol orange to polyvinyl alc. has inherently low conversion, the improvement on existing gel systems is minimal when compared to the drawbacks. More efficient methods of functionalising polyvinyl alc. with xylenol orange must be developed for this system to gain clin. relevance.

An exploratory study on the commercialisation of heat pump-fluidised bed drying technology

Fluidised bed-heat pump drying technology offers distinctive advantages over the existing drying technology employed in the Australian food industry. However, as is the case with many other examples of innovations that have had clear relative advantages, the rates of adoption and diffusion of this technology have been very slow. "Why does this happen?" is the theme of this research study that has been undertaken with an objective to analyse a range of issues related to the market acceptance of technological innovations. The research methodology included the development of an integrated conceptual model based on an extensive review of literature in the areas of innovation diffusion, technology transfer and industrial marketing. Three major determinants associated with the market acceptance of innovations were identified as the characteristics of the innovation, adopter information processing capability and the influence of the innovation supplier on the adoption process. This was followed by a study involving more than 30 small and medium enterprises identified as potential adopters of fluidised bed-heat pump drying technology in the Australian food industry. The findings revealed that judgment was the key evaluation strategy employed by potential adopters in the particular industry sector. Further, it was evidenced that the innovations were evaluated against a predetermined criteria covering a range of aspects with emphasis on a selected set of attributes of the innovation. Implication of these findings on the commercialisation of fluidised bed-heat pump drying technology was established, and a series of recommendations was made to the innovation supplier (DPI/FT) enabling it to develop an effective commercialisation strategy.

Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.

Comparison of the indirect haemagglutination and gel diffusion test for serotyping Haemophilus parasuis

The aim of this study was to compare the use of indirect haemagglutination (IHA) and gel diffusion (GD) tests for serotyping Haemophilus parasuis by the Kielstein-Rapp-Gabrielson scheme. All 15 serovar reference strains, 72 Australian field isolates, nine Chinese field isolates, and seven isolates from seven experimentally infected pigs were evaluated with both tests. With the IHA test, 14 of the 15 reference strains were correctly serotyped – with serovar 10 failing to give a titre with serovar 10 antiserum. In the GD test, 13 reference strains were correctly serotyped – with antigen from serovars 7 and 8 failing to react with any antiserum. The IHA methodology serotyped a total of 45 of 81 field isolates while the GD methodology serotyped a total of 48 isolates. For 29 isolates, the GD and IHA methods gave discordant results. It was concluded that the IHA is a good additional test for the serotyping of H. parasuis by the KRG scheme if the GD methodology fails to provide a result or shows unusual cross-reactions.

The Networks of Learning in Technological Innovation : The Emergence of Collaboration Across Fields of Expertise

This study addresses four issues concerning technological product innovations. First, the nature of the very early phases or "embryonic stages" of technological innovation is addressed. Second, this study analyzes why and by what means people initiate innovation processes outside the technological community and the field of expertise of the established industry. In other words, this study addresses the initiation of innovation that occurs without the expertise of established organizations, such as technology firms, professional societies and research institutes operating in the technological field under consideration. Third, the significance of interorganizational learning processes for technological innovation is dealt with. Fourth, this consideration is supplemented by considering how network collaboration and learning change when formalized product development work and the commercialization of innovation advance. These issues are addressed through the empirical analysis of the following three product innovations: Benecol margarine, the Nordic Mobile Telephone system (NMT) and the ProWellness Diabetes Management System (PDMS). This study utilizes the theoretical insights of cultural-historical activity theory on the development of human activities and learning. Activity-theoretical conceptualizations are used in the critical assessment and advancement of the concept of networks of learning. This concept was originally proposed by the research group of organizational scientist Walter Powell. A network of learning refers to the interorganizational collaboration that pools resources, ideas and know-how without market-based or hierarchical relations. The concept of an activity system is used in defining the nodes of the networks of learning. Network collaboration and learning are analyzed with regard to the shared object of development work. According to this study, enduring dilemmas and tensions in activity explain the participants' motives for carrying out actions that lead to novel product concepts in the early phases of technological innovation. These actions comprise the initiation of development work outside the relevant fields of expertise and collaboration and learning across fields of expertise in the absence of market-based or hierarchical relations. These networks of learning are fragile and impermanent. This study suggests that the significance of networks of learning across fields of expertise becomes more and more crucial for innovation activities.

Post-industrial Intervention : An Activity-Theoretical Expedition Tracing the Proximal Development of Forms of Conducting Interventions

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Evaluation Of Diffusion-Coefficient And Ionic Mobility In (Nh4)4fe(Cn)6.1.5 H2o

The diffusion coefficient, D, and the ionic mobility, μ, in the protonic conductor ammonium ferrocyanide hydrate have been determined by the isothermal transient ionic current method. D is also determined from the time dependence of the build up of potential across the samples and theretical expressions describing this build up in terms of double exponential dependence on time are obtained. The values obtained are D=3.875×10−11m2s−1 and μ=1.65×10−9 m2V−1s−1.