The visibility of models: using technology as a bridge between mathematics and engineering

Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. The validity of this metaphor is questioned and the case is made that engineers do in fact use mathematics as more than a set of passive tools— that mathematical models for phenomena depend critically on the settings in which they are used and the tools with which they are expressed. The perennial debate over whether mathematics should be taught by mathematicians or by engineers looks increasingly anachronistic in the light of technological change, and the authors suggest that it is more instructive to examine the potential of technology for changing the relationships between mathematicians and engineers, and for connecting their respective knowledge domains in new ways.     

Evolution of the interfacial phases in Al2O3–Kovar® joints brazed using a Ag–Cu–Ti-based alloy

Abstract

A systematic investigation of the brazing of Al₂O₃ to Kovar^® (Fe–29Ni–17Co wt.%) using the active braze alloy (ABA) Ag–35.25Cu–1.75Ti wt.% has been undertaken to study the chemical reactions at the interfaces of the joints. The extent to which silica-based secondary phases in the Al₂O₃ participate in the reactions at the ABA/Al₂O₃ interface has been clarified. Another aspect of this work has been to determine the influence of various brazing parameters, such as the peak temperature, T_p, and time at T_p, τ, on the resultant microstructure. As a consequence, the microstructural evolution of the joints as a function of T_p and τ is discussed in some detail. The formation of a Fe₂Ti layer on the Kovar^® and its growth, along with adjacent Ni₃Ti particles in the ABA, dominate the microstructural developments at the ABA/Kovar^® interface. The presence of Kovar^® next to the ABA does not change the intrinsic chemical reactions occurring at the ABA/Al₂O₃ interface. However, the extent of these reactions is limited if the purity of the Al₂O₃ is high, and so it is necessary to have some silica-rich secondary phase in the Al₂O₃ to facilitate the formation of a Ti₃Cu₃O layer on the Al₂O₃. Breakdown of the Ti₃Cu₃O layer, together with fracture of the Fe₂Ti layer and separation of this layer from the Kovar^®, has been avoided by brazing at temperatures close to the liquidus temperature of the ABA for short periods of time, e.g., for T_p between 820 and 830 °C and τ between 2 and 8 min.     

Flame chemistry of tetrahydropyran as a model heteroatomic biofuel

The flame chemistry of tetrahydropyran (THP), a cyclic ether, has been examined using vacuum-ultraviolet (VUV)-photoionization molecular-beam mass spectrometry (PI-MBMS) and flame modeling, motivated by the need to understand and predict the combustion of oxygen-containing, biomass-derived fuels. Species identifications and mole-fraction profiles are presented for a fuel-rich (Φ = 1.75), laminar premixed THP–oxygen–argon flame at 2.66 kPa (20.0 Torr). Flame species with up to six heavy atoms have been detected. A detailed reaction set was developed for THP combustion that captures relevant features of the THP flame quite well, allowing analysis of the dominant kinetic pathways for THP combustion. Necessary rate coefficients and transport parameters were calculated or were estimated by analogies with a recent reaction set [Li et al., Combust. Flame 158 (2011) 2077–2089], and necessary thermochemical properties were computed using the CBS-QB3 method. Our results show that under the low-pressure conditions, THP destruction is dominated by H-abstraction, and the three resulting THP-yl radicals decompose primarily by β-scissions to two- and four-heavy-atom species that are generally destroyed by β-scission, abstraction, or oxidation.     

Properties of an h-Bernstein-like basis and curves

Blossoming is a useful technique to study bases and curve representations in computer-aided geometric design. Recently Simeonov et al. (Comput Aided Geom Des 28:549–565, 2011) have used a blossom generalization, namely the h-blossom, to derive new results about the h-Bernstein basis and h-Bézier curves that have previously been studied in approximation theory and computer-aided geometric design. This paper introduces a basis related to the h-Bernstein basis. There is a close relationship between this new basis and the h-Bernstein basis, between the new basis and the h-blossom, and between the new basis and “progressive” curves. This paper explores these relationships and uses them to derive properties both of the new basis itself, and of curves represented in terms of the new basis.     

Role of Context in Risk-Based Reasoning

In this article we report the influence of contextual factors on mathematics and science teachers' reasoning in risk-based decision-making. We examine previous research that presents judgments of risk as being subjectively influenced by contextual factors and other research that explores the role of context in mathematical problem-solving. Our own approach has been to develop carefully designed software tools that support the user to empathize with a hypothetical person, Deborah, who suffers from a medical condition. The tools were used by a group of teachers who were asked to help Deborah decide whether to have an operation that could cure the condition but which carries particular risks. In order to make this decision, the teachers were required to model the risks of the operation and also the lifestyle decisions that Deborah might make. We trace the teachers' efforts to coordinate judgments of likelihood and impact. The data emphasize the sensitivity of reasoning to matters of context; we set out in detail the various ways in which the process was affected by context.     

Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes

Lasing modes in cyclic photonic molecules (CPMs) composed of several identical thin semiconductor microdisks in free space are studied in a linear approximation. Maxwell's equations with exact boundary conditions and the radiation condition at infinity are considered as a specific eigenvalue problem that enables one to find natural frequencies and threshold gains. It is demonstrated that careful tuning of the distance between the disks in CPMs is able to drastically reduce the lasing thresholds of the whispering-gallery modes having small azimuth indices.     

Investigation of the influence of hydroxy groups on the radical scavenging ability of polyphenols

Recently, O-H bond dissociation enthalpies (BDEs) have been successfully used to express the free radical scavenging ability of polyphenolic antioxidants. In this work, the BDEs of phenol, catechol, resorcinol, hydroquinone, pyrogallol, phloroglucinol, 1,2,4-benzenetriol, and 5-hydroxypyrogallol have been calculated at B3LYP/6-311G++(3df, 3pd) and used to elucidate the effect of OH groups. Increasing the number of OH groups in the adjacent (vicinal) position decreases the BDE of phenols. Increasing the number of O-H groups in the alternative position C(1,3) as in resorcinol and C(1,3,5) as in phloroglucinol does not show any notable change in the BDEs when compared to that of OH in C(1) as in phenol. 5-Hydroxypyrogallol has the smallest BDE (250.3 kJ mol(-1)) followed by pyrogallol (289.4 kJ mol(-1)), then 1,2,4-benzenetriol (294.8 kJ mol(-1)), and then catechol (312.8 kJ mol(-1)). Overall, our results indicated that the presence of ortho and para hydroxy groups reduces the BDEs. An intramolecular hydrogen bond (IHB) develops due to the ortho arrangement of OH's and plays a dominant role in decreasing the BDEs. This key study on phenols showed that the reactive order of OH position in the benzene ring is the following: 5-hydroxypyrogallol > pyrogallol > 1,2,4-benzenetriol > catechol > hydroquinone > phenol approximately resorcinol approximately phloroglucinol.     

Effect of water density on methanol oxidation kinetics in supercritical water

We oxidized methanol in supercritical water at 500 degrees C to explore the influence of the water concentration (or density) on the kinetics. The rate increased as the water concentration increased from 1.8 to 5.7 mol/L. This effect of water density on the kinetics observed experimentally was quantitatively reproduced by a previously validated mechanism-based, detailed chemical kinetics model. In this model, reactions of OH radicals with methanol were the fastest methanol removal steps. The rates of these removal steps increased with water density at 500 degrees C because the OH radical concentration increased. The OH radical concentration increased with density because the rates of the steps H + H2O = OH + H2 and CH3 + H2O = OH + CH4, which produce OH radicals, increased. Thus, the main role of water in accelerating methanol oxidation kinetics at 500 degrees C is as a hydrogen donor to a radical (R) in steps such as R + H2O = OH + RH. This system provides a striking example of SCW being involved on the molecular level in the free-radical oxidation as a reactant in elementary steps.     

Combustion chemistry of enols: possible ethenol precursors in flames

Before the recent discovery that enols are intermediates in many flames, they appeared in no combustion models. Furthermore, little is known about enols' flame chemistry. Enol formation in low-pressure flames takes place in the preheat zone, and its precursors are most likely fuel species or the early products of fuel decomposition. The OH + ethene reaction has been shown to dominate ethenol production in ethene flames although this reaction has appeared insufficient to describe ethenol formation in all hydrocarbon oxidation systems. In this work, the mole fraction profiles of ethenol in several representative low-pressure flames are correlated with those of possible precursor species as a means for judging likely formation pathways in flames. These correlations and modeling suggest that the reaction of OH with ethene is in fact the dominant source of ethenol in many hydrocarbon flames, and that addition-elimination reactions of OH with other alkenes are also likely to be responsible for enol formation in flames. On this basis, enols are predicted to be minor intermediates in most flames and should be most prevalent in olefinic flames where reactions of the fuel with OH can produce enols directly.     

Development and characterization of Au-YSZ surface plasmon resonance based sensing materials: high temperature detection of CO

Au-YSZ nanocomposite films exhibited a surface plasmon resonance absorption band around 600 nm that underwent a reversible blue shift and narrowed upon exposure to CO in air at 500 degrees C. A linear dependence of the sensing signal was observed for CO concentrations ranging between 0.1 and 1 vol % in an air carrier gas. This behavior of the SPR band, upon exposure to CO, was not observed when using nitrogen as the carrier gas, indicating an oxygen-dependent reaction mechanism. Additionally, the SPR band showed no measurable signal change upon exposure to CO at temperatures below approximately 400 degrees C. The oxygen and temperature-dependent characteristics, coupled with the oxygen ion formation and conduction properties of the YSZ matrix, are indicative of charge-transfer reactions occurring at the three-phase boundary region between oxygen, Au, and YSZ, which result in charge transfer into the Au nanoparticles. These reactions are associated with the oxidation of CO and a corresponding reduction of the YSZ matrix. The chemical-reaction-induced charge injection into the Au nanoparticles results in the observed blue shift and narrowing of the SPR band.