Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

Cyclic Imide and Open-Chain Amide Carboxylic Acid Derivatives from the Facile Reaction of cis-Cyclohexane-1,2-dicarboxylic Anhydride with Three Substituted Anilines

The structures of the compounds from the reaction of cis-cyclohexane-1,2-dicarboxylic anhydride with 4-chloroaniline [rac-N-(4-chlorophenyl)-2-carboxycycloclohexane-1-carboxamide] (1), 4-bromoaniline [2-(4-bromophenyl)-perhydroisoindolyl-1,3-dione] (2) and 3-hydroxy-4-carboxyaniline (5-aminosalicylic acid) [2-(3-hydroxy-4-carboxyphenyl)-perhydroisoindolyl-1,3-dione] (3) have been determined at 200 K. Crystals of the open-chain amide carboxylic acid 1 are orthorhombic, space group Pbcn, with unit cell dimensions a = 20.1753(10), b = 8.6267(4), c = 15.9940(9) Å, and Z = 8. Compounds 2 and 3 are cyclic imides, with 1 monoclinic having space group P21 and cell dimensions a = 11.5321(3), b = 6.7095(2), c = 17.2040(5) Å, β = 102.527(3)o. Compound 3 is orthorhombic with cell dimensions a = 6.4642(3), b = 12.8196(5), c = 16.4197(7) Å. Molecules of 1 form hydrogen-bonded cyclic dimers which are extended into a two-dimensional layered structure through amide-group associations: 3 forms into one-dimensional zigzag chains through carboxylic acid…imide O-atom hydrogen bonds, while compound 2 is essentially unassociated. With both cyclic imides 2 and 3, disorder is found which involves the presence of partial enantiomeric replacement of the cis-cyclohexane-1,2-substituted ring systems.

Jackknife for bias reduction in predictive regressions

One of the fundamental econometric models in finance is predictive regression. The standard least squares method produces biased coefficient estimates when the regressor is persistent and its innovations are correlated with those of the dependent variable. This article proposes a general and convenient method based on the jackknife technique to tackle the estimation problem. The proposed method reduces the bias for both single- and multiple-regressor models and for both short- and long-horizon regressions. The effectiveness of the proposed method is demonstrated by simulations. An empirical application to equity premium prediction using the dividend yield and the short rate highlights the differences between the results by the standard approach and those by the bias-reduced estimator. The significant predictive variables under the ordinary least squares become insignificant after adjusting for the finite-sample bias. These discrepancies suggest that bias reduction in predictive regressions is important in practical applications.

Photocatalytic reduction of carbon dioxide to formic acid, formaldehyde, and methanol using dye-sensitized TiO2 film

A bifunctionalized TiO2 film containing a dye-sensitized zone and a catalysis zone is designed for visible-light photocatalytic reduction of CO2 to chemicals continuously. Charge separation can be accomplished with electron transferring to catalysis zone and positive charge transforming to anode. Highly efficient conversion of CO2 to formic acid, formaldehyde, and methanol is achieved through the transferring electrons on conduction bands (CB) of TiO2. Reduction of CO2 and O2 evolution take place in separated solutions on different catalysts. The separated solution carried out in this photo-reactor system can avoid CO2 reduction products being oxidized by anode. The yields of reduction products were enhanced remarkably by external electrical power. This study provides not only a new photocatalytic system but also a potential of renewable energy source via carbon dioxide.

A note on a reaction-diffusion model describing the bone morphogen protein gradient in Drosophila embryonic patterning

In this article, we consider the Eldar model [3] from embryology in which a bone morphogenic protein, a short gastrulation protein, and their compound react and diffuse. We carry out a perturbation analysis in the limit of small diffusivity of the bone morphogenic protein. This analysis establishes conditions under which some elementary results of [3] are valid.

Empirical analysis of the effect of dimension reduction and word order on semantic vectors

The aim of this paper is to provide a comparison of various algorithms and parameters to build reduced semantic spaces. The effect of dimension reduction, the stability of the representation and the effect of word order are examined in the context of the five algorithms bearing on semantic vectors: Random projection (RP), singular value decom- position (SVD), non-negative matrix factorization (NMF), permutations and holographic reduced representations (HRR). The quality of semantic representation was tested by means of synonym finding task using the TOEFL test on the TASA corpus. Dimension reduction was found to improve the quality of semantic representation but it is hard to find the optimal parameter settings. Even though dimension reduction by RP was found to be more generally applicable than SVD, the semantic vectors produced by RP are somewhat unstable. The effect of encoding word order into the semantic vector representation via HRR did not lead to any increase in scores over vectors constructed from word co-occurrence in context information. In this regard, very small context windows resulted in better semantic vectors for the TOEFL test.

Residence time investigation in a co-axial dielectric barrier discharge reactor

The residence time distribution (RTD) is a crucial parameter when treating engine exhaust emissions with a Dielectric Barrier Discharge (DBD) reactor. In this paper, the residence time of such a reactor is investigated using a finite element based software: COMSOL Multiphysics 4.3. Non-thermal plasma (NTP) discharge is being introduced as a promising method for pollutant emission reduction. DBD is one of the most advantageous of NTP technologies. In a two cylinder co-axial DBD reactor, tubes are placed between two electrodes and flow passes through the annuals between these barrier tubes. If the mean residence time increases in a DBD reactor, there will be a corresponding increase in reaction time and consequently, the pollutant removal efficiency can increase. However, pollutant formation can occur during increased mean residence time and so the proportion of fluid that may remain for periods significantly longer than the mean residence time is of great importance. In this study, first, the residence time distribution is calculated based on the standard reactor used by the authors for ultrafine particle (10-500 nm) removal. Then, different geometrics and various inlet velocities are considered. Finally, for selected cases, some roughness elements added inside the reactor and the residence time is calculated. These results will form the basis for a COMSOL plasma and CFD module investigation.

Identification of copper species present in Cu-ZSM-5 catalysts for NOx reduction

The structure of Cu-ZSM-5 catalysts that show activity for direct NO decomposition and selective catalytic reduction of NOx by hydrocarbons has been investigated by a multitude of modern surface analysis and spectroscopy techniques including X-ray photoelectron spectroscopy, thermogravimetric analysis, and in situ Fourier transform infrared spectroscopy. A series of four catalysts were prepared by exchange of Na-ZSM-5 with dilute copper acetate, and the copper loading was controlled by variation of the solution pH. Underexchanged catalysts contained isolated Cu2+OH-(H2O) species and as the copper loading was increased Cu2+ ions incorporated into the zeolite lattice appeared. The sites at which the latter two copper species were located were fundamentally different. The Cu2+OH-(H2O) moieties were bound to two lattice oxygen ions and associated with one aluminum framework species. In contrast, the Cu2+ ions were probably bound to four lattice oxygen ions and associated with two framework aluminum ions. Once the Cu-ZSM-5 samples attained high levels of exchange, the development of [Cu(μ-OH)2Cu]n2+OH-(H2O) species along with a small concentration of Cu(OH)2 was observed. On activation in helium to 500°C the Cu2+OH-(H2O) species transformed into Cu2+O- and Cu+ moieties, whereas the Cu2+ ions were apparently unaffected by this treatment (apart from the loss of ligated water molecules). Calcination of the precursors resulted in the formation of Cu2+O2- and a one-dimensional CuO species. Temperature-programmed desorption studies revealed that oxygen was removed from the latter two species at 407 and 575°C, respectively. © 1999 Academic Press.

Reaction products between Bi-Sr-Ca-Cu-oxide thick films and alumina substrates

The structure and composition of reaction products between Bi-Sr-Ca-Cu-oxide (BSCCO) thick films and alumina substrates have been characterized using a combination of electron diffraction, scanning electron microscopy and energy dispersive X-ray spectrometry (EDX). Sr and Ca are found to be the most reactive cations with alumina. Sr4Al6O12SO4 is formed between the alumina substrates and BSCCO thick films prepared from paste with composition close to Bi-2212 (and Bi-2212 + 10 wt.% Ag). For paste with composition close to Bi(Pb)-2223 + 20 wt.% Ag, a new phase with f.c.c. structure, lattice parameter about a = 24.5 A and approximate composition Al3Sr2CaBi2CuOx has been identified in the interface region. Understanding and control of these reactions is essential for growth of high quality BSCCO thick films on alumina. (C) 1997 Elsevier Science S.A.

Oxide reduction in NiO-containing solid solution systems during transmission electron microscopy

The effects of electron irradiation on NiO-containing solid solution systems are described. Partially hydrated NiO solid solutions, e. g. , NiO-MgO, undergo surface reduction to Ni metal after examination by TEM. This surface layer results in the formation of Moire interference patterns.

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge-Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E coli, and conclude with a discussion on the significance of this work. (C) 2004 Elsevier Ltd. All rights reserved.

Characterization and catalytic performance of Fe3Ni8/palygorskite for catalytic cracking of benzene

Catalytic decomposition is a very attractive way to convert tar components into H2, CO and other useful chemicals. The performance of Fe3Ni8/PG (palygorskite, PG) reduced in hydrogen at different temperatures for the catalytic decomposition of benzene has been assessed. Benzene was used as the model biomass tar. The effects of calcination atmosphere, temperatures and benzene concentration on catalytic cracking of benzene were measured. The results of XRD (X-Ray Diffraction), TEM (Transmission Electron Microscope), TPR (Temperature Program Reduction), TPSR (Temperature Program Surface Reduction), TC (Total Carbon), the reactivity component and reaction mechanism over Fe3Ni8/PG for catalytic cracking of benzene are discussed. The results showed particles of awaruite (Fe, Ni) about 2–30 nm were found on the surface of palygorskite by TEM when the calcination temperature was 600 °C. Particles with size smaller than 30 nm were obtained on all prepared Fe3Ni8/PG catalysts as shown by XRD. The nanoparticles proved to be the reactive component for catalytic cracking of benzene and the increase of active particle size caused the decrease in the reactivity of Fe3Ni8/PG. Fe3Ni8/PG annealed in hydrogen at 600 °C was proved to have the best reactivity in experiments (45% hydrogen yield). High concentration benzene (448 g/m3) accelerated the formation of carbon deposition. However, iron oxide decreases carbon deposition and increases the stability of catalyst for catalytic cracking of benzene. The application of Fe3Ni8/PG catalysts was proved a very effective catalyst for the catalytic cracking of benzene.