An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Saturated core high-temperature superconducting fault current limiters as an alternative to conventional series reactors in a distribution grid

Series reactors are used in distribution grids to reduce the short-circuit fault level. Some of the disadvantages of the application of these devices are the voltage drop produced across the reactor and the steep front rise of the transient recovery voltage (TRV), which generally exceeds the rating of the associated circuit breaker. Simulations were performed to compare the characteristics of a saturated core High-Temperature Superconducting Fault Current Limiter (HTS FCL) and a series reactor. The design of the HTS FCL was optimized using the evolutionary algorithm. The resulting Pareto frontier curve of optimum solution is presented in this paper. The results show that the steady-state impedance of an HTS FCL is significantly lower than that of a series reactor for the same level of fault current limiting. Tests performed on a prototype 11 kV HTS FCL confirm the theoretical results. The respective transient recovery voltages (TRV) of the HTS FCL and an air core reactor of comparable fault current limiting capability are also determined. The results show that the saturated core HTS FCL has a significantly lower effect on the rate of rise of the circuit breaker TRV as compared to the air core reactor. The simulations results are validated with shortcircuit test results.

Characterization of precursors to methanol synthesis catalysts Cu/ZnO system

The composition of a series of hydroxycarbonate precursors to copper/zinc oxide methanol synthesis catalysts prepared under conditions reported as optimum for catalytic activity has been studied. Techniques employed included thermogravimetry (TG), temperature-programmed decomposition (TPD), X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), and Raman and FTIR spectroscopies. Evidence was obtained for various structural phases including hydrozincite, copper hydrozincite, aurichalcite, zincian malachite and malachite (the concentrations of which depended upon the exact Cu/Zn ratio used). Significantly, previously reported phases such as gerhardite and rosasite were not identified when catalysts were synthesized at optimum solution pH and temperature values, and after appropriate aging periods. Calcination of the hydroxycarbonate precursors resulted in the formation of catalysts containing an intimate mixture of copper and zinc oxides. Temperature-programmed reduction (TPR) revealed that a number of discrete copper oxide species were present in the catalyst, the precise concentrations of which were determined to be related to the structure of the catalyst precursor. Copper hydrozincite decomposed to give zinc oxide particles decorated by highly dispersed, small copper oxide species. Aurichalcite appeared to result ultimately in the most intimately mixed catalyst structure whereas zincian malachite decomposed to produce larger copper oxide and zinc oxide grains. The reason for the stabilization of small copper oxide and zinc oxide clusters by aurichalcite was investigated by using carefully selected calcination temperatures. It was concluded that the unique formation of an 'anion-modified' oxide resulting from the initial decomposition stage of aurichalcite was responsible for the 'binding' of copper species to zinc moieties.

Raman, infrared and near-infrared spectroscopic characterization of the herderite-hydroxylherderite mineral series

Natural single-crystal specimens of the herderite-hydroxylherderite series from Brazil, with general formula CaBePO4(F,OH), were investigated by electron microprobe, Raman, infrared and near-infrared spectroscopies. The minerals occur as secondary products in granitic pegmatites. Herderite and hydroxylherderite minerals show extensive solid solution formation. The Raman spectra of hydroxylherderite are characterized by bands at around 985 and 998 cm-1, assigned to ν1 symmetric stretching mode of the HOPO33- and PO43- units. Raman bands at around 1085, 1128 and 1138 cm-1 are attributed to both the HOP and PO antisymmetric stretching vibrations. The set of Raman bands observed at 563, 568, 577, 598, 616 and 633 cm-1 are assigned to the ν4 out of plane bending modes of the PO4 and H2PO4 units. The OH Raman stretching vibrations of hydroxylherderite were observed ranging from 3626 cm-1 to 3609 cm-1. The infrared stretching vibrations of hydroxylherderites were observed between 3606 cm-1 and 3599 cm-1. By using a Libowitzky type function, hydrogen bond distances based upon the OH stretching bands were calculated. Characteristic NIR bands at around 6961 and 7054 cm-1 were assigned to the first overtone of the fundamental, whilst NIR bands at 10194 and 10329 cm-1 are assigned to the second overtone of the fundamental OH stretching vibration. Insight into the structure of the herderite-hydroxylherderite series is assessed by vibrational spectroscopy.

The electrochemical corrosion behaviour of quaternary gold alloys when exposed to 3.5% NaCl solution

Lower carat gold alloys, specifically 9 carat gold alloys, containing less than 40 % gold, and alloying additions of silver, copper and zinc, are commonly used in many jewellery applications, to offset high costs and poor mechanical properties associated with pure gold. While gold is considered to be chemically inert, the presence of active alloying additions raises concerns about certain forms of corrosion, particularly selective dissolution of these alloys. The purpose of this study was to systematically study the corrosion behaviour of a series of quaternary gold–silver–copper–zinc alloys using dc potentiodynamic scanning in saline (3.5 % NaCl) environment. Full anodic/cathodic scans were conducted to determine the overall corrosion characteristics of the alloy, followed by selective anodic scans and subsequent morphological and compositional analysis of the alloy surface and corroding media to determine the extent of selective dissolution. Varying degrees of selective dissolution and associated corrosion rates were observed after anodic polarisation in 3.5 % NaCl, depending on the alloy composition. The corrosion behaviour of the alloys was determined by the extent of anodic reactions which induce (1) formation of oxide scales on the alloy surface and or (2) dissolution of Zn and Cu species. In general, the improved corrosion characteristics of alloy #3 was attributed to the composition of Zn/Cu in the alloy and thus favourable microstructure promoting the formation of protective oxide/chloride scales and reducing the extent of Cu and Zn dissolution.

1,3,6,8-Tetrasubstituted Pyrenes: Solution-Processable Materials for Application in Organic Electronics

(Equation Presented). A series of star-shaped organic semiconductors have been synthesized from 1,3,6,8-tetrabromopyrene. The materials are soluble in common organic solvents allowing for solution processing of devices such as light-emitting diodes (OLEDs). One of the materials, 1,3,6,8-tetrakis(4- butoxyphenyl)pyrene, has been used as the active emitting layer in simple solution-processed OLEDs with deep blue emission (CIE = 0.15, 0.18) and maximum efficiencies and brightness levels of 2.56 cd/A and >5000 cd/m2, respectively.

Synthesis of novel interlocked architectures in solution and solid phase

Mechanically interlocked molecules, such as catenanes and rotaxanes, are fascinating due to their unique sensing and catalytic properties and their potential to act as molecular motors or switches. Traditionally their synthesis has been laborious and expensive, however this research project endeavoured to overcome this challenge by exploring novel ways of preparing mechanically interlocked molecules both in solution and on surfaces. A series of disulfide-linked macrocycles, [2]catenanes and [2]rotaxanes were synthesised in solution using reversible dynamic covalent chemistry. Subsequently, the interlocked architectures were adapted into solid-tethered systems via attachment to swelling polystyrene resins.

On the efficacy of Fourier series approximations for pricing European options

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the halfrange cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together,these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

Standardised antibacterial Manuka honey in the management of persistent post-operative corneal oedema: A case series

Background Corneal oedema is a common post-operative problem that delays or prevents visual recovery from ocular surgery. Honey is a supersaturated solution of sugars with an acidic pH, high osmolarity and low water content. These characteristics inhibit the growth of micro-organisms, reduce oedema and promote epithelialisation. This clinical case series describes the use of a regulatory approved Leptospermum species honey ophthalmic product, in the management of post-operative corneal oedema and bullous keratopathy. Methods A retrospective review of 18 consecutive cases (30 eyes) with corneal oedema persisting beyond one month after single or multiple ocular surgical procedures (phacoemulsification cataract surgery and additional procedures) treated with Optimel Antibacterial Manuka Eye Drops twice to three times daily as an adjunctive therapy to conventional topical management with corticosteroid, aqueous suppressants, hypertonic sodium chloride five per cent, eyelid hygiene and artificial tears. Visual acuity and central corneal thickness were measured before and at the conclusion of Optimel treatment. Results A temporary reduction in corneal epithelial oedema lasting up to several hours was observed after the initial Optimel instillation and was associated with a reduction in central corneal thickness, resolution of epithelial microcysts, collapse of epithelial bullae, improved corneal clarity, improved visualisation of the intraocular structures and improved visual acuity. Additionally, with chronic use, reduction in punctate epitheliopathy, reduction in central corneal thickness and improvement in visual acuity were achieved. Temporary stinging after Optimel instillation was experienced. No adverse infectious or inflammatory events occurred during treatment with Optimel. Conclusions Optimel was a safe and effective adjunctive therapeutic strategy in the management of persistent post-operative corneal oedema and warrants further investigation in clinical trials.

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.