A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

Effect of hydrodynamics and surface roughness on the electrochemical behaviour of carbon steel in CSG produced water

The influence of fluid flow, surface roughness and immersion time on the electrochemical behaviour of carbon steel in coal seam gas produced water under static and hydrodynamic conditions has been studied. The disc electrode surface morphology before and after the corrosion test was characterized using scanning electron microscopy (SEM). The corrosion product was examined using X-ray photoelectron spectroscopy (XPS) and X-ray diffractometry (XRD).The results show that the anodic current density increased with increasing surface roughness and consequently a decrease in corrosion surface resistance. Under dynamic flow conditions, the corrosion rate increased with increasing rotating speed due to the high mass transfer coefficient and formation of non-protective akaganeite β- FeO(OH) and goethite α- FeO(OH) corrosion scale at the electrode surface.The corrosion rate was lowest at 0 rpm.The corrosion rate decreased in both static and dynamic conditions with increasing immersion time. The decrease in corrosion rate is attributed to the deposition of corrosion products on the electrode surface. SEM results revealed that the rougher surface exhibited a great tendency toward pitting corrosion.

Study of surface evolution in the wheel-rail interface

This paper aims to trace surface evolution in the wheel-rail interface using data obtained from a twin-disc testing machine and the surface replication technique. Changes in the surface profile of the rail testing disc are explicitly analysed according to the wear mechanism, which helps elaborate a better understanding of the attrition of asperities during the wearing-in process of surface modification. The surface profile amplitude was seen to decrease during the initial running-in phase of the experiment cycle, and after reaching a saturation value, the profile amplitude then increased. Ultimately the results show that grinding will roughen the rail surface and the wheel-rail contact conditions will then remove this surface damage to some saturation value of the profile height. The variation in the rail surface profile beyond this point is then only dependant on the contact conditions which exist between the wheel and rail during normal operation.

Nanofiber orientation and surface functionalization modulate human mesenchymal stem cell behavior in vitro

Electrospun nanofiber meshes have emerged as a new generation of scaffold membranes possessing a number of features suitable for tissue regeneration. One of these features is the flexibility to modify their structure and composition to orchestrate specific cellular responses. In this study, we investigated the effects of nanofiber orientation and surface functionalization on human mesenchymal stem cell (hMSC) migration and osteogenic differentiation. We used an in vitro model to examine hMSC migration into a cell-free zone on nanofiber meshes and mitomycin C treatment to assess the contribution of proliferation to the observed migration. Poly (ɛ-caprolactone) meshes with oriented topography were created by electrospinning aligned nanofibers on a rotating mandrel, while randomly oriented controls were collected on a stationary collector. Both aligned and random meshes were coated with a triple-helical, type I collagen-mimetic peptide, containing the glycine-phenylalanine-hydroxyproline-glycine-glutamate-arginine (GFOGER) motif. Our results indicate that nanofiber GFOGER peptide functionalization and orientation modulate cellular behavior, individually, and in combination. GFOGER significantly enhanced the migration, proliferation, and osteogenic differentiation of hMSCs on nanofiber meshes. Aligned nanofiber meshes displayed increased cell migration along the direction of fiber orientation compared to random meshes; however, fiber alignment did not influence osteogenic differentiation. Compared to each other, GFOGER coating resulted in a higher proliferation-driven cell migration, whereas fiber orientation appeared to generate a larger direct migratory effect. This study demonstrates that peptide surface modification and topographical cues associated with fiber alignment can be used to direct cellular behavior on nanofiber mesh scaffolds, which may be exploited for tissue regeneration.

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.

Radon-222 activity flux measurement using activated charcoal canisters: Revisiting the methodology

The measurement of radon ((222)Rn) activity flux using activated charcoal canisters was examined to investigate the distribution of the adsorbed (222)Rn in the charcoal bed and the relationship between (222)Rn activity flux and exposure time. The activity flux of (222)Rn from five sources of varying strengths was measured for exposure times of one, two, three, five, seven, 10, and 14 days. The distribution of the adsorbed (222)Rn in the charcoal bed was obtained by dividing the bed into six layers and counting each layer separately after the exposure. (222)Rn activity decreased in the layers that were away from the exposed surface. Nevertheless, the results demonstrated that only a small correction might be required in the actual application of charcoal canisters for activity flux measurement, where calibration standards were often prepared by the uniform mixing of radium ((226)Ra) in the matrix. This was because the diffusion of (222)Rn in the charcoal bed and the detection efficiency as a function of the charcoal depth tended to counterbalance each other. The influence of exposure time on the measured (222)Rn activity flux was observed in two situations of the canister exposure layout: (a) canister sealed to an open bed of the material and (b) canister sealed over a jar containing the material. The measured (222)Rn activity flux decreased as the exposure time increased. The change in the former situation was significant with an exponential decrease as the exposure time increased. In the latter case, lesser reduction was noticed in the observed activity flux with respect to exposure time. This reduction might have been related to certain factors, such as absorption site saturation or the back diffusion of (222)Rn gas occurring at the canister-soil interface.

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.

Predicting the speed of a Wave Glider autonomous surface vehicle from wave model data

A key component of robotic path planning is ensuring that one can reliably navigate a vehicle to a desired location. In addition, when the features of interest are dynamic and move with oceanic currents, vehicle speed plays an important role in the planning exercise to ensure that vehicles are in the right place at the right time. Aquatic robot design is moving towards utilizing the environment for propulsion rather than traditional motors and propellers. These new vehicles are able to realize significantly increased endurance, however the mission planning problem, in turn, becomes more difficult as the vehicle velocity is not directly controllable. In this paper, we examine Gaussian process models applied to existing wave model data to predict the behavior, i.e., velocity, of a Wave Glider Autonomous Surface Vehicle. Using training data from an on-board sensor and forecasting with the WAVEWATCH III model, our probabilistic regression models created an effective method for forecasting WG velocity.

Uniform surface growth of copper oxide nanowires in radiofrequency plasma discharge and limiting factors

The uniform growth of copper oxide nanowires on the top of copper plate has been investigated during the exposure to radiofrequency plasma discharge in respect to plasma properties and its localization. The copper samples of 10 mm radius and 1 mm in thickness were exposed to argon-oxygen plasma created at discharge power of 150 W. After 10 min, almost uniform growth of nanowires was achieved over large surface. There were significant distortions in nanowire length and shape near the edges. Based on the experimental results, we developed a theoretical model, which took into account a balance in heat released at the flow of the current to the nanowire and rejected from the nanowire. This model established a dependence of the maximal length of the nanowire at dependence on the plasma parameters, where the limiting factor for nanowire growth and distortions in distribution are ballistic effects of ions and their local fluxes. In contrast, the plasma heating by potential interactions of species has very little influence on the length and smaller deviations in flux are allowed for uniformity of growth

Revisiting the CO oxidation reaction on various Au/TiO2catalysts: Roles of the surface OH groups and the reaction mechanism

This work aims to understand the influence of TiO2 surface structure in Au/TiO2 catalysts on CO oxidation. Au nanoparticles (3 wt%) in the range of 4 to 8 nm were loaded onto four kinds of TiO2 surfaces, which had different surface structures and were synthesized by calcining hydrogen titanate nanotubes at various temperatures and in different atmospheres. The Au catalyst supported on anatase nanorods exhibited the highest activity in CO oxidation at 30 °C among all the five Au/TiO2 catalysts including the reference catalyst of Au/TiO2-P25. X-ray photoelectron spectroscopy (XPS) and infrared emission spectra (IES) results indicate that the anatase nanorods have the most active surface on which water molecules can be strongly adsorbed and OH groups can be formed readily. Theoretical calculation indicates that the surface OH can facilitate the O2 adsorption on the anatase surface. Such active surface features are conducive to the O2 activation and CO oxidation

Carbon nanotubes on nanoporous alumina: From surface mats to conformal pore filling

Control over nucleation and growth of multi-walled carbon nanotubes in the nanochannels of porous alumina membranes by several combinations of posttreatments, namely exposing the membrane top surface to atmospheric plasma jet and application of standard S1813 photoresist as an additional carbon precursor, is demonstrated. The nanotubes grown after plasma treatment nucleated inside the channels and did not form fibrous mats on the surface. Thus, the nanotube growth mode can be controlled by surface treatment and application of additional precursor, and complex nanotube-based structures can be produced for various applications. A plausible mechanism of nanotube nucleation and growth in the channels is proposed, based on the estimated depth of ion flux penetration into the channels.

Plasma polymerization of 1,1,1-trichloroethane yields a coating with robust antibacterial surface properties

Novel, highly chlorinated surface coatings were produced via a one-step plasma polymerization (pp) of 1,1,1-trichloroethane (TCE), exhibiting excellent antimicrobial properties against the vigorously biofilm-forming bacterium Staphylococcus epidermidis.

Non-Newtonian mixed convection flow from a horizontal circular cylinder with uniform surface heat flux

Mixed convection laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is investigated from a horizontal circular cylinder with uniform surface heat flux using a modified power-law viscosity model, that contains no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid temperature distributions, rate of heat transfer in terms of the local Nusselt number.

Surface materials and aspects of care: A study in modes of being in a visual art practice

Through creative practice and written research, this thesis explores the peculiar qualities of surface materials, revealing a broader ethos of practice which I identify as care. I propose that care arises as a mode of being between artist and work, work and beholder, and between the parts of the work. The thesis situates the art practice within an ethical framework, premised on, but extending, Heidegger's ontological equation of care with being. The original contribution is in the claim that the particular qualities of worldly matter generate the terms for care as a particular mode of engagement that is reciprocal and intransitive.

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.